diff --git "a/number_of_possible_sets_of_closing_branches/meta.json" "b/number_of_possible_sets_of_closing_branches/meta.json"
new file mode 100644--- /dev/null
+++ "b/number_of_possible_sets_of_closing_branches/meta.json"
@@ -0,0 +1,25872 @@
+{
+    "id": 3217,
+    "name": "number_of_possible_sets_of_closing_branches",
+    "difficulty": "Hard",
+    "link": "https://leetcode.com/problems/number-of-possible-sets-of-closing-branches/",
+    "date": "2023-11-25 00:00:00",
+    "task_description": "There is a company with `n` branches across the country, some of which are connected by roads. Initially, all branches are reachable from each other by traveling some roads. The company has realized that they are spending an excessive amount of time traveling between their branches. As a result, they have decided to close down some of these branches (**possibly none**). However, they want to ensure that the remaining branches have a distance of at most `maxDistance` from each other. The **distance** between two branches is the **minimum** total traveled length needed to reach one branch from another. You are given integers `n`, `maxDistance`, and a **0-indexed** 2D array `roads`, where `roads[i] = [ui, vi, wi]` represents the **undirected** road between branches `ui` and `vi` with length `wi`. Return _the number of possible sets of closing branches, so that any branch has a distance of at most _`maxDistance`_ from any other_. **Note** that, after closing a branch, the company will no longer have access to any roads connected to it. **Note** that, multiple roads are allowed. **Example 1:** ``` **Input:** n = 3, maxDistance = 5, roads = [[0,1,2],[1,2,10],[0,2,10]] **Output:** 5 **Explanation:** The possible sets of closing branches are: - The set [2], after closing, active branches are [0,1] and they are reachable to each other within distance 2. - The set [0,1], after closing, the active branch is [2]. - The set [1,2], after closing, the active branch is [0]. - The set [0,2], after closing, the active branch is [1]. - The set [0,1,2], after closing, there are no active branches. It can be proven, that there are only 5 possible sets of closing branches. ``` **Example 2:** ``` **Input:** n = 3, maxDistance = 5, roads = [[0,1,20],[0,1,10],[1,2,2],[0,2,2]] **Output:** 7 **Explanation:** The possible sets of closing branches are: - The set [], after closing, active branches are [0,1,2] and they are reachable to each other within distance 4. - The set [0], after closing, active branches are [1,2] and they are reachable to each other within distance 2. - The set [1], after closing, active branches are [0,2] and they are reachable to each other within distance 2. - The set [0,1], after closing, the active branch is [2]. - The set [1,2], after closing, the active branch is [0]. - The set [0,2], after closing, the active branch is [1]. - The set [0,1,2], after closing, there are no active branches. It can be proven, that there are only 7 possible sets of closing branches. ``` **Example 3:** ``` **Input:** n = 1, maxDistance = 10, roads = [] **Output:** 2 **Explanation:** The possible sets of closing branches are: - The set [], after closing, the active branch is [0]. - The set [0], after closing, there are no active branches. It can be proven, that there are only 2 possible sets of closing branches. ``` **Constraints:** `1 <= n <= 10` `1 <= maxDistance <= 105` `0 <= roads.length <= 1000` `roads[i].length == 3` `0 <= ui, vi <= n - 1` `ui != vi` `1 <= wi <= 1000` All branches are reachable from each other by traveling some roads.",
+    "public_test_cases": [
+        {
+            "label": "Example 1",
+            "input": "n = 3, maxDistance = 5, roads = [[0,1,2],[1,2,10],[0,2,10]]",
+            "output": "5 "
+        },
+        {
+            "label": "Example 2",
+            "input": "n = 3, maxDistance = 5, roads = [[0,1,20],[0,1,10],[1,2,2],[0,2,2]]",
+            "output": "7 "
+        },
+        {
+            "label": "Example 3",
+            "input": "n = 1, maxDistance = 10, roads = []",
+            "output": "2 "
+        }
+    ],
+    "private_test_cases": [
+        {
+            "input": [
+                4,
+                8561,
+                [
+                    [
+                        2,
+                        0,
+                        945
+                    ],
+                    [
+                        3,
+                        2,
+                        83
+                    ],
+                    [
+                        1,
+                        2,
+                        44
+                    ],
+                    [
+                        2,
+                        1,
+                        492
+                    ],
+                    [
+                        0,
+                        3,
+                        417
+                    ],
+                    [
+                        2,
+                        3,
+                        242
+                    ],
+                    [
+                        3,
+                        2,
+                        188
+                    ],
+                    [
+                        2,
+                        0,
+                        142
+                    ],
+                    [
+                        1,
+                        2,
+                        106
+                    ],
+                    [
+                        2,
+                        3,
+                        418
+                    ],
+                    [
+                        3,
+                        0,
+                        803
+                    ],
+                    [
+                        1,
+                        0,
+                        255
+                    ],
+                    [
+                        3,
+                        0,
+                        618
+                    ],
+                    [
+                        0,
+                        1,
+                        219
+                    ],
+                    [
+                        2,
+                        1,
+                        460
+                    ],
+                    [
+                        2,
+                        3,
+                        12
+                    ],
+                    [
+                        1,
+                        2,
+                        888
+                    ],
+                    [
+                        0,
+                        3,
+                        199
+                    ],
+                    [
+                        1,
+                        3,
+                        568
+                    ],
+                    [
+                        1,
+                        3,
+                        767
+                    ],
+                    [
+                        2,
+                        3,
+                        587
+                    ],
+                    [
+                        0,
+                        1,
+                        15
+                    ],
+                    [
+                        3,
+                        2,
+                        999
+                    ],
+                    [
+                        3,
+                        1,
+                        778
+                    ],
+                    [
+                        1,
+                        2,
+                        347
+                    ],
+                    [
+                        0,
+                        1,
+                        548
+                    ],
+                    [
+                        1,
+                        2,
+                        891
+                    ],
+                    [
+                        3,
+                        2,
+                        355
+                    ],
+                    [
+                        2,
+                        1,
+                        123
+                    ],
+                    [
+                        3,
+                        0,
+                        806
+                    ],
+                    [
+                        3,
+                        0,
+                        557
+                    ],
+                    [
+                        3,
+                        2,
+                        46
+                    ],
+                    [
+                        3,
+                        0,
+                        851
+                    ],
+                    [
+                        3,
+                        2,
+                        901
+                    ],
+                    [
+                        0,
+                        1,
+                        250
+                    ],
+                    [
+                        2,
+                        3,
+                        613
+                    ],
+                    [
+                        1,
+                        2,
+                        153
+                    ],
+                    [
+                        2,
+                        0,
+                        325
+                    ],
+                    [
+                        3,
+                        0,
+                        4
+                    ],
+                    [
+                        3,
+                        0,
+                        284
+                    ],
+                    [
+                        3,
+                        2,
+                        82
+                    ],
+                    [
+                        0,
+                        3,
+                        970
+                    ],
+                    [
+                        2,
+                        0,
+                        363
+                    ],
+                    [
+                        3,
+                        0,
+                        664
+                    ],
+                    [
+                        3,
+                        0,
+                        225
+                    ],
+                    [
+                        2,
+                        0,
+                        670
+                    ],
+                    [
+                        2,
+                        3,
+                        747
+                    ],
+                    [
+                        1,
+                        3,
+                        459
+                    ],
+                    [
+                        1,
+                        3,
+                        71
+                    ],
+                    [
+                        3,
+                        2,
+                        99
+                    ],
+                    [
+                        3,
+                        0,
+                        985
+                    ],
+                    [
+                        3,
+                        2,
+                        151
+                    ],
+                    [
+                        3,
+                        1,
+                        989
+                    ],
+                    [
+                        1,
+                        2,
+                        47
+                    ],
+                    [
+                        3,
+                        2,
+                        606
+                    ],
+                    [
+                        1,
+                        2,
+                        565
+                    ],
+                    [
+                        2,
+                        3,
+                        106
+                    ],
+                    [
+                        1,
+                        2,
+                        808
+                    ],
+                    [
+                        1,
+                        2,
+                        765
+                    ],
+                    [
+                        1,
+                        0,
+                        334
+                    ],
+                    [
+                        2,
+                        0,
+                        601
+                    ],
+                    [
+                        2,
+                        1,
+                        848
+                    ],
+                    [
+                        3,
+                        1,
+                        73
+                    ],
+                    [
+                        2,
+                        3,
+                        824
+                    ],
+                    [
+                        0,
+                        2,
+                        930
+                    ],
+                    [
+                        3,
+                        1,
+                        954
+                    ],
+                    [
+                        0,
+                        2,
+                        27
+                    ],
+                    [
+                        1,
+                        3,
+                        299
+                    ],
+                    [
+                        2,
+                        3,
+                        423
+                    ],
+                    [
+                        3,
+                        1,
+                        777
+                    ],
+                    [
+                        2,
+                        0,
+                        236
+                    ],
+                    [
+                        2,
+                        1,
+                        79
+                    ],
+                    [
+                        3,
+                        1,
+                        14
+                    ],
+                    [
+                        2,
+                        3,
+                        644
+                    ],
+                    [
+                        3,
+                        2,
+                        137
+                    ],
+                    [
+                        1,
+                        3,
+                        34
+                    ],
+                    [
+                        3,
+                        1,
+                        446
+                    ],
+                    [
+                        0,
+                        2,
+                        43
+                    ],
+                    [
+                        0,
+                        3,
+                        863
+                    ],
+                    [
+                        0,
+                        1,
+                        974
+                    ],
+                    [
+                        1,
+                        3,
+                        512
+                    ],
+                    [
+                        2,
+                        3,
+                        947
+                    ],
+                    [
+                        3,
+                        1,
+                        651
+                    ],
+                    [
+                        1,
+                        0,
+                        980
+                    ],
+                    [
+                        3,
+                        1,
+                        833
+                    ],
+                    [
+                        1,
+                        0,
+                        249
+                    ],
+                    [
+                        2,
+                        1,
+                        948
+                    ],
+                    [
+                        0,
+                        1,
+                        421
+                    ],
+                    [
+                        3,
+                        1,
+                        94
+                    ],
+                    [
+                        1,
+                        3,
+                        306
+                    ],
+                    [
+                        3,
+                        1,
+                        560
+                    ],
+                    [
+                        1,
+                        0,
+                        950
+                    ],
+                    [
+                        0,
+                        2,
+                        291
+                    ],
+                    [
+                        3,
+                        2,
+                        106
+                    ],
+                    [
+                        3,
+                        0,
+                        831
+                    ],
+                    [
+                        1,
+                        2,
+                        739
+                    ],
+                    [
+                        3,
+                        0,
+                        480
+                    ],
+                    [
+                        0,
+                        2,
+                        260
+                    ],
+                    [
+                        1,
+                        3,
+                        671
+                    ],
+                    [
+                        3,
+                        2,
+                        524
+                    ],
+                    [
+                        1,
+                        2,
+                        90
+                    ],
+                    [
+                        0,
+                        2,
+                        163
+                    ],
+                    [
+                        3,
+                        1,
+                        21
+                    ],
+                    [
+                        3,
+                        0,
+                        537
+                    ],
+                    [
+                        1,
+                        2,
+                        716
+                    ],
+                    [
+                        0,
+                        1,
+                        553
+                    ],
+                    [
+                        1,
+                        2,
+                        348
+                    ],
+                    [
+                        1,
+                        3,
+                        915
+                    ],
+                    [
+                        2,
+                        1,
+                        448
+                    ],
+                    [
+                        3,
+                        0,
+                        321
+                    ]
+                ]
+            ],
+            "output": 16
+        },
+        {
+            "input": [
+                10,
+                36854,
+                [
+                    [
+                        2,
+                        1,
+                        412
+                    ],
+                    [
+                        4,
+                        0,
+                        918
+                    ],
+                    [
+                        9,
+                        2,
+                        773
+                    ],
+                    [
+                        3,
+                        6,
+                        19
+                    ],
+                    [
+                        6,
+                        1,
+                        330
+                    ],
+                    [
+                        7,
+                        4,
+                        226
+                    ],
+                    [
+                        0,
+                        5,
+                        510
+                    ],
+                    [
+                        7,
+                        6,
+                        330
+                    ],
+                    [
+                        7,
+                        1,
+                        296
+                    ],
+                    [
+                        5,
+                        8,
+                        835
+                    ],
+                    [
+                        8,
+                        0,
+                        863
+                    ],
+                    [
+                        4,
+                        9,
+                        592
+                    ],
+                    [
+                        3,
+                        4,
+                        478
+                    ],
+                    [
+                        1,
+                        8,
+                        603
+                    ],
+                    [
+                        6,
+                        9,
+                        859
+                    ],
+                    [
+                        6,
+                        2,
+                        509
+                    ],
+                    [
+                        0,
+                        9,
+                        691
+                    ],
+                    [
+                        7,
+                        6,
+                        506
+                    ],
+                    [
+                        1,
+                        2,
+                        944
+                    ],
+                    [
+                        5,
+                        1,
+                        148
+                    ],
+                    [
+                        1,
+                        3,
+                        131
+                    ],
+                    [
+                        6,
+                        5,
+                        440
+                    ],
+                    [
+                        7,
+                        0,
+                        128
+                    ],
+                    [
+                        5,
+                        4,
+                        269
+                    ],
+                    [
+                        3,
+                        5,
+                        849
+                    ],
+                    [
+                        3,
+                        6,
+                        365
+                    ],
+                    [
+                        0,
+                        6,
+                        834
+                    ],
+                    [
+                        6,
+                        8,
+                        31
+                    ],
+                    [
+                        4,
+                        2,
+                        894
+                    ],
+                    [
+                        4,
+                        0,
+                        898
+                    ],
+                    [
+                        8,
+                        2,
+                        20
+                    ],
+                    [
+                        6,
+                        5,
+                        537
+                    ],
+                    [
+                        1,
+                        6,
+                        199
+                    ],
+                    [
+                        2,
+                        7,
+                        199
+                    ],
+                    [
+                        4,
+                        9,
+                        460
+                    ],
+                    [
+                        8,
+                        3,
+                        389
+                    ],
+                    [
+                        0,
+                        3,
+                        323
+                    ],
+                    [
+                        7,
+                        8,
+                        939
+                    ],
+                    [
+                        6,
+                        5,
+                        794
+                    ],
+                    [
+                        7,
+                        3,
+                        981
+                    ],
+                    [
+                        2,
+                        8,
+                        355
+                    ],
+                    [
+                        4,
+                        1,
+                        515
+                    ],
+                    [
+                        5,
+                        7,
+                        866
+                    ],
+                    [
+                        0,
+                        8,
+                        143
+                    ],
+                    [
+                        0,
+                        6,
+                        258
+                    ],
+                    [
+                        9,
+                        1,
+                        962
+                    ],
+                    [
+                        4,
+                        8,
+                        456
+                    ],
+                    [
+                        4,
+                        2,
+                        464
+                    ],
+                    [
+                        3,
+                        5,
+                        757
+                    ],
+                    [
+                        8,
+                        4,
+                        671
+                    ],
+                    [
+                        4,
+                        2,
+                        579
+                    ],
+                    [
+                        2,
+                        5,
+                        729
+                    ],
+                    [
+                        2,
+                        0,
+                        329
+                    ],
+                    [
+                        1,
+                        5,
+                        558
+                    ],
+                    [
+                        2,
+                        1,
+                        823
+                    ],
+                    [
+                        2,
+                        3,
+                        526
+                    ],
+                    [
+                        3,
+                        2,
+                        205
+                    ],
+                    [
+                        8,
+                        0,
+                        466
+                    ],
+                    [
+                        1,
+                        6,
+                        982
+                    ],
+                    [
+                        5,
+                        4,
+                        763
+                    ],
+                    [
+                        3,
+                        9,
+                        285
+                    ],
+                    [
+                        2,
+                        4,
+                        450
+                    ],
+                    [
+                        8,
+                        5,
+                        790
+                    ],
+                    [
+                        6,
+                        2,
+                        777
+                    ],
+                    [
+                        2,
+                        8,
+                        845
+                    ],
+                    [
+                        2,
+                        5,
+                        369
+                    ],
+                    [
+                        4,
+                        0,
+                        713
+                    ],
+                    [
+                        3,
+                        6,
+                        220
+                    ],
+                    [
+                        6,
+                        0,
+                        570
+                    ],
+                    [
+                        9,
+                        0,
+                        691
+                    ],
+                    [
+                        7,
+                        8,
+                        743
+                    ],
+                    [
+                        7,
+                        2,
+                        184
+                    ],
+                    [
+                        0,
+                        6,
+                        165
+                    ],
+                    [
+                        2,
+                        7,
+                        581
+                    ],
+                    [
+                        9,
+                        2,
+                        585
+                    ],
+                    [
+                        2,
+                        9,
+                        799
+                    ],
+                    [
+                        8,
+                        7,
+                        794
+                    ],
+                    [
+                        5,
+                        3,
+                        484
+                    ],
+                    [
+                        0,
+                        1,
+                        461
+                    ],
+                    [
+                        1,
+                        2,
+                        99
+                    ],
+                    [
+                        9,
+                        6,
+                        640
+                    ],
+                    [
+                        9,
+                        7,
+                        739
+                    ],
+                    [
+                        2,
+                        0,
+                        333
+                    ],
+                    [
+                        1,
+                        0,
+                        454
+                    ],
+                    [
+                        1,
+                        3,
+                        874
+                    ],
+                    [
+                        1,
+                        0,
+                        458
+                    ],
+                    [
+                        3,
+                        2,
+                        994
+                    ],
+                    [
+                        6,
+                        3,
+                        463
+                    ],
+                    [
+                        5,
+                        3,
+                        241
+                    ],
+                    [
+                        4,
+                        2,
+                        301
+                    ],
+                    [
+                        2,
+                        3,
+                        477
+                    ],
+                    [
+                        2,
+                        8,
+                        533
+                    ],
+                    [
+                        9,
+                        3,
+                        537
+                    ],
+                    [
+                        3,
+                        2,
+                        412
+                    ],
+                    [
+                        0,
+                        7,
+                        952
+                    ],
+                    [
+                        2,
+                        4,
+                        624
+                    ],
+                    [
+                        2,
+                        4,
+                        890
+                    ],
+                    [
+                        5,
+                        7,
+                        499
+                    ],
+                    [
+                        1,
+                        9,
+                        862
+                    ],
+                    [
+                        0,
+                        6,
+                        633
+                    ],
+                    [
+                        3,
+                        1,
+                        716
+                    ],
+                    [
+                        3,
+                        7,
+                        429
+                    ],
+                    [
+                        8,
+                        3,
+                        503
+                    ],
+                    [
+                        1,
+                        7,
+                        265
+                    ],
+                    [
+                        6,
+                        9,
+                        581
+                    ],
+                    [
+                        6,
+                        2,
+                        622
+                    ],
+                    [
+                        4,
+                        5,
+                        84
+                    ],
+                    [
+                        2,
+                        6,
+                        618
+                    ],
+                    [
+                        1,
+                        2,
+                        380
+                    ],
+                    [
+                        9,
+                        5,
+                        339
+                    ],
+                    [
+                        1,
+                        6,
+                        134
+                    ],
+                    [
+                        4,
+                        6,
+                        26
+                    ],
+                    [
+                        1,
+                        7,
+                        938
+                    ],
+                    [
+                        6,
+                        3,
+                        687
+                    ],
+                    [
+                        9,
+                        4,
+                        300
+                    ],
+                    [
+                        0,
+                        1,
+                        842
+                    ],
+                    [
+                        5,
+                        6,
+                        997
+                    ],
+                    [
+                        1,
+                        9,
+                        391
+                    ],
+                    [
+                        3,
+                        6,
+                        261
+                    ],
+                    [
+                        5,
+                        7,
+                        165
+                    ],
+                    [
+                        3,
+                        7,
+                        653
+                    ],
+                    [
+                        7,
+                        3,
+                        715
+                    ],
+                    [
+                        5,
+                        1,
+                        913
+                    ],
+                    [
+                        5,
+                        4,
+                        714
+                    ],
+                    [
+                        7,
+                        9,
+                        545
+                    ],
+                    [
+                        8,
+                        9,
+                        735
+                    ],
+                    [
+                        7,
+                        2,
+                        824
+                    ],
+                    [
+                        5,
+                        0,
+                        931
+                    ],
+                    [
+                        1,
+                        7,
+                        344
+                    ],
+                    [
+                        3,
+                        2,
+                        821
+                    ],
+                    [
+                        1,
+                        2,
+                        232
+                    ],
+                    [
+                        2,
+                        8,
+                        489
+                    ],
+                    [
+                        5,
+                        3,
+                        58
+                    ],
+                    [
+                        6,
+                        9,
+                        814
+                    ],
+                    [
+                        5,
+                        9,
+                        413
+                    ],
+                    [
+                        8,
+                        2,
+                        18
+                    ],
+                    [
+                        9,
+                        5,
+                        520
+                    ],
+                    [
+                        9,
+                        5,
+                        901
+                    ],
+                    [
+                        6,
+                        9,
+                        386
+                    ],
+                    [
+                        8,
+                        6,
+                        890
+                    ],
+                    [
+                        7,
+                        9,
+                        968
+                    ],
+                    [
+                        9,
+                        8,
+                        107
+                    ],
+                    [
+                        7,
+                        1,
+                        368
+                    ],
+                    [
+                        6,
+                        2,
+                        503
+                    ],
+                    [
+                        3,
+                        9,
+                        123
+                    ],
+                    [
+                        0,
+                        3,
+                        357
+                    ],
+                    [
+                        3,
+                        8,
+                        870
+                    ],
+                    [
+                        2,
+                        7,
+                        345
+                    ],
+                    [
+                        5,
+                        4,
+                        727
+                    ],
+                    [
+                        4,
+                        9,
+                        535
+                    ],
+                    [
+                        0,
+                        3,
+                        870
+                    ],
+                    [
+                        7,
+                        0,
+                        978
+                    ],
+                    [
+                        7,
+                        4,
+                        241
+                    ],
+                    [
+                        8,
+                        7,
+                        118
+                    ],
+                    [
+                        9,
+                        2,
+                        466
+                    ],
+                    [
+                        1,
+                        7,
+                        27
+                    ],
+                    [
+                        4,
+                        6,
+                        167
+                    ],
+                    [
+                        2,
+                        7,
+                        661
+                    ],
+                    [
+                        4,
+                        1,
+                        396
+                    ],
+                    [
+                        2,
+                        9,
+                        627
+                    ],
+                    [
+                        8,
+                        9,
+                        733
+                    ],
+                    [
+                        3,
+                        7,
+                        653
+                    ],
+                    [
+                        2,
+                        9,
+                        957
+                    ],
+                    [
+                        0,
+                        3,
+                        171
+                    ],
+                    [
+                        8,
+                        2,
+                        313
+                    ],
+                    [
+                        9,
+                        1,
+                        808
+                    ],
+                    [
+                        3,
+                        0,
+                        878
+                    ],
+                    [
+                        9,
+                        1,
+                        566
+                    ],
+                    [
+                        5,
+                        8,
+                        119
+                    ],
+                    [
+                        1,
+                        9,
+                        428
+                    ],
+                    [
+                        2,
+                        7,
+                        975
+                    ],
+                    [
+                        2,
+                        1,
+                        874
+                    ],
+                    [
+                        4,
+                        0,
+                        555
+                    ],
+                    [
+                        0,
+                        5,
+                        667
+                    ],
+                    [
+                        3,
+                        7,
+                        319
+                    ],
+                    [
+                        7,
+                        9,
+                        729
+                    ],
+                    [
+                        3,
+                        7,
+                        278
+                    ],
+                    [
+                        3,
+                        6,
+                        34
+                    ],
+                    [
+                        7,
+                        4,
+                        573
+                    ],
+                    [
+                        8,
+                        3,
+                        899
+                    ],
+                    [
+                        7,
+                        3,
+                        686
+                    ],
+                    [
+                        9,
+                        0,
+                        16
+                    ],
+                    [
+                        1,
+                        7,
+                        845
+                    ],
+                    [
+                        2,
+                        8,
+                        127
+                    ],
+                    [
+                        1,
+                        2,
+                        905
+                    ],
+                    [
+                        0,
+                        1,
+                        685
+                    ],
+                    [
+                        5,
+                        9,
+                        68
+                    ],
+                    [
+                        4,
+                        3,
+                        9
+                    ],
+                    [
+                        7,
+                        2,
+                        129
+                    ],
+                    [
+                        8,
+                        1,
+                        6
+                    ],
+                    [
+                        6,
+                        3,
+                        45
+                    ],
+                    [
+                        5,
+                        7,
+                        617
+                    ],
+                    [
+                        7,
+                        1,
+                        5
+                    ],
+                    [
+                        0,
+                        4,
+                        457
+                    ],
+                    [
+                        5,
+                        0,
+                        476
+                    ],
+                    [
+                        7,
+                        4,
+                        356
+                    ],
+                    [
+                        9,
+                        5,
+                        705
+                    ],
+                    [
+                        1,
+                        8,
+                        326
+                    ],
+                    [
+                        2,
+                        4,
+                        51
+                    ],
+                    [
+                        5,
+                        6,
+                        965
+                    ],
+                    [
+                        1,
+                        0,
+                        200
+                    ],
+                    [
+                        6,
+                        8,
+                        24
+                    ],
+                    [
+                        9,
+                        3,
+                        622
+                    ],
+                    [
+                        5,
+                        4,
+                        804
+                    ],
+                    [
+                        9,
+                        8,
+                        824
+                    ],
+                    [
+                        7,
+                        2,
+                        333
+                    ],
+                    [
+                        3,
+                        1,
+                        882
+                    ],
+                    [
+                        2,
+                        4,
+                        931
+                    ],
+                    [
+                        3,
+                        6,
+                        183
+                    ],
+                    [
+                        2,
+                        4,
+                        613
+                    ],
+                    [
+                        2,
+                        1,
+                        868
+                    ],
+                    [
+                        5,
+                        0,
+                        962
+                    ],
+                    [
+                        5,
+                        9,
+                        8
+                    ],
+                    [
+                        8,
+                        4,
+                        57
+                    ],
+                    [
+                        5,
+                        4,
+                        206
+                    ],
+                    [
+                        4,
+                        9,
+                        683
+                    ],
+                    [
+                        8,
+                        7,
+                        894
+                    ],
+                    [
+                        7,
+                        8,
+                        547
+                    ],
+                    [
+                        8,
+                        4,
+                        463
+                    ],
+                    [
+                        6,
+                        7,
+                        625
+                    ],
+                    [
+                        2,
+                        3,
+                        8
+                    ],
+                    [
+                        4,
+                        0,
+                        441
+                    ],
+                    [
+                        1,
+                        0,
+                        116
+                    ],
+                    [
+                        5,
+                        2,
+                        503
+                    ],
+                    [
+                        6,
+                        5,
+                        292
+                    ],
+                    [
+                        5,
+                        4,
+                        151
+                    ],
+                    [
+                        7,
+                        8,
+                        510
+                    ],
+                    [
+                        9,
+                        2,
+                        602
+                    ],
+                    [
+                        3,
+                        4,
+                        218
+                    ],
+                    [
+                        1,
+                        4,
+                        868
+                    ],
+                    [
+                        8,
+                        9,
+                        632
+                    ],
+                    [
+                        6,
+                        0,
+                        276
+                    ],
+                    [
+                        7,
+                        4,
+                        771
+                    ],
+                    [
+                        7,
+                        6,
+                        916
+                    ],
+                    [
+                        5,
+                        9,
+                        789
+                    ],
+                    [
+                        2,
+                        7,
+                        134
+                    ],
+                    [
+                        6,
+                        2,
+                        611
+                    ],
+                    [
+                        7,
+                        1,
+                        567
+                    ],
+                    [
+                        6,
+                        8,
+                        122
+                    ],
+                    [
+                        7,
+                        5,
+                        336
+                    ],
+                    [
+                        3,
+                        6,
+                        288
+                    ],
+                    [
+                        4,
+                        8,
+                        573
+                    ],
+                    [
+                        1,
+                        0,
+                        747
+                    ],
+                    [
+                        8,
+                        9,
+                        657
+                    ],
+                    [
+                        2,
+                        6,
+                        989
+                    ],
+                    [
+                        4,
+                        2,
+                        625
+                    ],
+                    [
+                        9,
+                        8,
+                        766
+                    ],
+                    [
+                        0,
+                        2,
+                        530
+                    ],
+                    [
+                        6,
+                        5,
+                        418
+                    ],
+                    [
+                        5,
+                        8,
+                        740
+                    ],
+                    [
+                        8,
+                        0,
+                        967
+                    ],
+                    [
+                        4,
+                        0,
+                        20
+                    ],
+                    [
+                        6,
+                        8,
+                        855
+                    ],
+                    [
+                        8,
+                        4,
+                        398
+                    ],
+                    [
+                        5,
+                        9,
+                        831
+                    ],
+                    [
+                        7,
+                        1,
+                        918
+                    ],
+                    [
+                        4,
+                        6,
+                        316
+                    ],
+                    [
+                        0,
+                        6,
+                        632
+                    ],
+                    [
+                        1,
+                        2,
+                        423
+                    ],
+                    [
+                        7,
+                        9,
+                        73
+                    ],
+                    [
+                        1,
+                        4,
+                        131
+                    ],
+                    [
+                        7,
+                        8,
+                        252
+                    ],
+                    [
+                        7,
+                        8,
+                        12
+                    ],
+                    [
+                        3,
+                        1,
+                        41
+                    ],
+                    [
+                        8,
+                        6,
+                        635
+                    ],
+                    [
+                        7,
+                        2,
+                        244
+                    ],
+                    [
+                        5,
+                        8,
+                        537
+                    ],
+                    [
+                        6,
+                        5,
+                        999
+                    ],
+                    [
+                        7,
+                        9,
+                        868
+                    ],
+                    [
+                        8,
+                        5,
+                        715
+                    ],
+                    [
+                        8,
+                        1,
+                        580
+                    ],
+                    [
+                        7,
+                        6,
+                        198
+                    ],
+                    [
+                        1,
+                        2,
+                        977
+                    ],
+                    [
+                        1,
+                        4,
+                        267
+                    ],
+                    [
+                        1,
+                        3,
+                        411
+                    ],
+                    [
+                        4,
+                        8,
+                        777
+                    ],
+                    [
+                        5,
+                        0,
+                        202
+                    ],
+                    [
+                        1,
+                        7,
+                        219
+                    ],
+                    [
+                        0,
+                        6,
+                        697
+                    ],
+                    [
+                        1,
+                        6,
+                        612
+                    ],
+                    [
+                        3,
+                        0,
+                        601
+                    ],
+                    [
+                        7,
+                        3,
+                        805
+                    ],
+                    [
+                        1,
+                        9,
+                        610
+                    ],
+                    [
+                        3,
+                        2,
+                        486
+                    ],
+                    [
+                        5,
+                        0,
+                        51
+                    ],
+                    [
+                        9,
+                        6,
+                        433
+                    ],
+                    [
+                        9,
+                        0,
+                        740
+                    ],
+                    [
+                        4,
+                        8,
+                        406
+                    ],
+                    [
+                        3,
+                        6,
+                        221
+                    ],
+                    [
+                        3,
+                        1,
+                        881
+                    ],
+                    [
+                        1,
+                        9,
+                        129
+                    ],
+                    [
+                        4,
+                        8,
+                        11
+                    ],
+                    [
+                        1,
+                        4,
+                        751
+                    ],
+                    [
+                        0,
+                        5,
+                        831
+                    ],
+                    [
+                        3,
+                        8,
+                        934
+                    ],
+                    [
+                        2,
+                        3,
+                        940
+                    ],
+                    [
+                        4,
+                        1,
+                        317
+                    ],
+                    [
+                        4,
+                        3,
+                        485
+                    ],
+                    [
+                        8,
+                        1,
+                        523
+                    ],
+                    [
+                        5,
+                        6,
+                        707
+                    ],
+                    [
+                        5,
+                        0,
+                        300
+                    ],
+                    [
+                        3,
+                        7,
+                        974
+                    ],
+                    [
+                        0,
+                        7,
+                        559
+                    ],
+                    [
+                        4,
+                        2,
+                        507
+                    ],
+                    [
+                        0,
+                        5,
+                        474
+                    ],
+                    [
+                        5,
+                        1,
+                        220
+                    ],
+                    [
+                        7,
+                        8,
+                        413
+                    ],
+                    [
+                        0,
+                        4,
+                        485
+                    ],
+                    [
+                        2,
+                        6,
+                        357
+                    ],
+                    [
+                        7,
+                        6,
+                        192
+                    ],
+                    [
+                        6,
+                        0,
+                        821
+                    ],
+                    [
+                        5,
+                        2,
+                        985
+                    ],
+                    [
+                        4,
+                        5,
+                        279
+                    ],
+                    [
+                        4,
+                        1,
+                        381
+                    ],
+                    [
+                        0,
+                        1,
+                        927
+                    ],
+                    [
+                        3,
+                        2,
+                        259
+                    ],
+                    [
+                        0,
+                        1,
+                        872
+                    ],
+                    [
+                        7,
+                        9,
+                        120
+                    ],
+                    [
+                        9,
+                        6,
+                        880
+                    ],
+                    [
+                        8,
+                        9,
+                        426
+                    ],
+                    [
+                        6,
+                        2,
+                        368
+                    ],
+                    [
+                        8,
+                        1,
+                        3
+                    ],
+                    [
+                        6,
+                        2,
+                        476
+                    ],
+                    [
+                        1,
+                        0,
+                        830
+                    ],
+                    [
+                        5,
+                        9,
+                        534
+                    ],
+                    [
+                        7,
+                        4,
+                        448
+                    ],
+                    [
+                        1,
+                        7,
+                        489
+                    ],
+                    [
+                        3,
+                        1,
+                        272
+                    ],
+                    [
+                        7,
+                        5,
+                        1000
+                    ],
+                    [
+                        8,
+                        4,
+                        220
+                    ],
+                    [
+                        7,
+                        3,
+                        286
+                    ],
+                    [
+                        4,
+                        7,
+                        873
+                    ],
+                    [
+                        8,
+                        4,
+                        334
+                    ],
+                    [
+                        5,
+                        8,
+                        698
+                    ],
+                    [
+                        7,
+                        5,
+                        518
+                    ],
+                    [
+                        0,
+                        2,
+                        749
+                    ],
+                    [
+                        8,
+                        0,
+                        112
+                    ],
+                    [
+                        7,
+                        9,
+                        208
+                    ],
+                    [
+                        3,
+                        8,
+                        997
+                    ],
+                    [
+                        6,
+                        0,
+                        169
+                    ],
+                    [
+                        9,
+                        5,
+                        688
+                    ],
+                    [
+                        4,
+                        2,
+                        680
+                    ],
+                    [
+                        8,
+                        2,
+                        448
+                    ],
+                    [
+                        3,
+                        8,
+                        986
+                    ],
+                    [
+                        0,
+                        4,
+                        169
+                    ],
+                    [
+                        4,
+                        1,
+                        155
+                    ],
+                    [
+                        4,
+                        8,
+                        901
+                    ],
+                    [
+                        0,
+                        6,
+                        764
+                    ],
+                    [
+                        6,
+                        3,
+                        209
+                    ],
+                    [
+                        2,
+                        3,
+                        982
+                    ],
+                    [
+                        9,
+                        7,
+                        830
+                    ],
+                    [
+                        9,
+                        6,
+                        832
+                    ],
+                    [
+                        1,
+                        6,
+                        382
+                    ],
+                    [
+                        9,
+                        6,
+                        905
+                    ],
+                    [
+                        1,
+                        6,
+                        524
+                    ],
+                    [
+                        0,
+                        2,
+                        915
+                    ],
+                    [
+                        3,
+                        0,
+                        613
+                    ],
+                    [
+                        6,
+                        0,
+                        460
+                    ],
+                    [
+                        4,
+                        5,
+                        936
+                    ],
+                    [
+                        5,
+                        4,
+                        611
+                    ],
+                    [
+                        8,
+                        3,
+                        714
+                    ],
+                    [
+                        7,
+                        4,
+                        879
+                    ],
+                    [
+                        5,
+                        8,
+                        686
+                    ],
+                    [
+                        4,
+                        2,
+                        724
+                    ],
+                    [
+                        8,
+                        6,
+                        544
+                    ],
+                    [
+                        4,
+                        8,
+                        386
+                    ],
+                    [
+                        8,
+                        1,
+                        19
+                    ],
+                    [
+                        0,
+                        4,
+                        265
+                    ],
+                    [
+                        9,
+                        5,
+                        403
+                    ],
+                    [
+                        9,
+                        0,
+                        641
+                    ],
+                    [
+                        9,
+                        8,
+                        864
+                    ],
+                    [
+                        8,
+                        7,
+                        111
+                    ],
+                    [
+                        0,
+                        4,
+                        591
+                    ],
+                    [
+                        9,
+                        8,
+                        816
+                    ],
+                    [
+                        8,
+                        4,
+                        631
+                    ],
+                    [
+                        9,
+                        8,
+                        677
+                    ],
+                    [
+                        3,
+                        9,
+                        129
+                    ],
+                    [
+                        5,
+                        4,
+                        566
+                    ],
+                    [
+                        3,
+                        1,
+                        70
+                    ],
+                    [
+                        1,
+                        2,
+                        335
+                    ],
+                    [
+                        2,
+                        1,
+                        282
+                    ],
+                    [
+                        9,
+                        0,
+                        609
+                    ],
+                    [
+                        1,
+                        5,
+                        658
+                    ],
+                    [
+                        6,
+                        0,
+                        113
+                    ],
+                    [
+                        4,
+                        5,
+                        270
+                    ],
+                    [
+                        1,
+                        8,
+                        295
+                    ],
+                    [
+                        8,
+                        4,
+                        976
+                    ],
+                    [
+                        7,
+                        4,
+                        186
+                    ],
+                    [
+                        2,
+                        5,
+                        913
+                    ],
+                    [
+                        7,
+                        9,
+                        743
+                    ],
+                    [
+                        1,
+                        5,
+                        579
+                    ],
+                    [
+                        2,
+                        7,
+                        255
+                    ],
+                    [
+                        3,
+                        5,
+                        392
+                    ],
+                    [
+                        6,
+                        3,
+                        857
+                    ],
+                    [
+                        4,
+                        5,
+                        351
+                    ],
+                    [
+                        4,
+                        2,
+                        460
+                    ],
+                    [
+                        9,
+                        3,
+                        954
+                    ],
+                    [
+                        6,
+                        8,
+                        838
+                    ],
+                    [
+                        3,
+                        1,
+                        562
+                    ],
+                    [
+                        1,
+                        3,
+                        518
+                    ],
+                    [
+                        7,
+                        4,
+                        960
+                    ],
+                    [
+                        0,
+                        4,
+                        617
+                    ],
+                    [
+                        9,
+                        6,
+                        248
+                    ],
+                    [
+                        4,
+                        3,
+                        925
+                    ],
+                    [
+                        4,
+                        7,
+                        750
+                    ],
+                    [
+                        4,
+                        7,
+                        190
+                    ],
+                    [
+                        7,
+                        2,
+                        323
+                    ],
+                    [
+                        9,
+                        0,
+                        792
+                    ],
+                    [
+                        1,
+                        2,
+                        219
+                    ],
+                    [
+                        6,
+                        3,
+                        460
+                    ],
+                    [
+                        2,
+                        0,
+                        194
+                    ],
+                    [
+                        6,
+                        3,
+                        912
+                    ],
+                    [
+                        8,
+                        2,
+                        658
+                    ],
+                    [
+                        8,
+                        7,
+                        30
+                    ],
+                    [
+                        4,
+                        0,
+                        912
+                    ],
+                    [
+                        4,
+                        9,
+                        412
+                    ],
+                    [
+                        5,
+                        8,
+                        551
+                    ],
+                    [
+                        8,
+                        0,
+                        614
+                    ],
+                    [
+                        0,
+                        3,
+                        948
+                    ],
+                    [
+                        3,
+                        1,
+                        45
+                    ],
+                    [
+                        1,
+                        8,
+                        725
+                    ],
+                    [
+                        1,
+                        7,
+                        338
+                    ],
+                    [
+                        3,
+                        5,
+                        600
+                    ],
+                    [
+                        3,
+                        5,
+                        242
+                    ],
+                    [
+                        1,
+                        9,
+                        307
+                    ],
+                    [
+                        6,
+                        7,
+                        87
+                    ],
+                    [
+                        5,
+                        0,
+                        777
+                    ],
+                    [
+                        8,
+                        6,
+                        785
+                    ],
+                    [
+                        9,
+                        6,
+                        40
+                    ],
+                    [
+                        9,
+                        5,
+                        135
+                    ],
+                    [
+                        7,
+                        3,
+                        793
+                    ],
+                    [
+                        0,
+                        7,
+                        15
+                    ],
+                    [
+                        1,
+                        3,
+                        972
+                    ],
+                    [
+                        5,
+                        9,
+                        304
+                    ],
+                    [
+                        6,
+                        7,
+                        234
+                    ],
+                    [
+                        7,
+                        3,
+                        562
+                    ],
+                    [
+                        1,
+                        5,
+                        10
+                    ],
+                    [
+                        2,
+                        1,
+                        594
+                    ],
+                    [
+                        2,
+                        4,
+                        54
+                    ],
+                    [
+                        5,
+                        2,
+                        885
+                    ],
+                    [
+                        9,
+                        6,
+                        76
+                    ],
+                    [
+                        5,
+                        7,
+                        585
+                    ],
+                    [
+                        9,
+                        1,
+                        381
+                    ],
+                    [
+                        7,
+                        9,
+                        344
+                    ],
+                    [
+                        3,
+                        5,
+                        114
+                    ],
+                    [
+                        4,
+                        8,
+                        746
+                    ],
+                    [
+                        0,
+                        4,
+                        2
+                    ],
+                    [
+                        5,
+                        9,
+                        432
+                    ],
+                    [
+                        4,
+                        1,
+                        815
+                    ],
+                    [
+                        1,
+                        2,
+                        902
+                    ],
+                    [
+                        5,
+                        3,
+                        209
+                    ],
+                    [
+                        1,
+                        3,
+                        748
+                    ],
+                    [
+                        1,
+                        4,
+                        663
+                    ],
+                    [
+                        1,
+                        0,
+                        912
+                    ],
+                    [
+                        3,
+                        5,
+                        501
+                    ],
+                    [
+                        2,
+                        7,
+                        433
+                    ],
+                    [
+                        6,
+                        0,
+                        820
+                    ],
+                    [
+                        1,
+                        9,
+                        671
+                    ],
+                    [
+                        8,
+                        0,
+                        144
+                    ],
+                    [
+                        3,
+                        4,
+                        786
+                    ],
+                    [
+                        5,
+                        6,
+                        71
+                    ],
+                    [
+                        6,
+                        4,
+                        607
+                    ],
+                    [
+                        5,
+                        0,
+                        565
+                    ],
+                    [
+                        5,
+                        2,
+                        292
+                    ],
+                    [
+                        4,
+                        1,
+                        628
+                    ],
+                    [
+                        6,
+                        8,
+                        837
+                    ],
+                    [
+                        6,
+                        2,
+                        560
+                    ],
+                    [
+                        9,
+                        7,
+                        56
+                    ],
+                    [
+                        3,
+                        9,
+                        759
+                    ],
+                    [
+                        9,
+                        0,
+                        169
+                    ],
+                    [
+                        0,
+                        8,
+                        572
+                    ],
+                    [
+                        9,
+                        5,
+                        646
+                    ],
+                    [
+                        1,
+                        3,
+                        524
+                    ],
+                    [
+                        5,
+                        1,
+                        790
+                    ],
+                    [
+                        3,
+                        0,
+                        448
+                    ],
+                    [
+                        7,
+                        4,
+                        207
+                    ],
+                    [
+                        1,
+                        7,
+                        173
+                    ],
+                    [
+                        7,
+                        5,
+                        366
+                    ],
+                    [
+                        6,
+                        4,
+                        488
+                    ],
+                    [
+                        4,
+                        3,
+                        104
+                    ],
+                    [
+                        8,
+                        5,
+                        218
+                    ],
+                    [
+                        3,
+                        8,
+                        173
+                    ],
+                    [
+                        7,
+                        4,
+                        517
+                    ],
+                    [
+                        6,
+                        9,
+                        990
+                    ],
+                    [
+                        7,
+                        9,
+                        381
+                    ],
+                    [
+                        2,
+                        9,
+                        220
+                    ],
+                    [
+                        7,
+                        0,
+                        170
+                    ],
+                    [
+                        2,
+                        9,
+                        657
+                    ],
+                    [
+                        0,
+                        3,
+                        560
+                    ],
+                    [
+                        1,
+                        4,
+                        831
+                    ],
+                    [
+                        3,
+                        4,
+                        558
+                    ],
+                    [
+                        8,
+                        0,
+                        555
+                    ],
+                    [
+                        2,
+                        6,
+                        954
+                    ],
+                    [
+                        4,
+                        6,
+                        544
+                    ],
+                    [
+                        8,
+                        2,
+                        304
+                    ],
+                    [
+                        2,
+                        8,
+                        561
+                    ],
+                    [
+                        9,
+                        6,
+                        408
+                    ],
+                    [
+                        6,
+                        5,
+                        753
+                    ],
+                    [
+                        6,
+                        5,
+                        442
+                    ],
+                    [
+                        3,
+                        7,
+                        203
+                    ],
+                    [
+                        4,
+                        1,
+                        480
+                    ],
+                    [
+                        4,
+                        3,
+                        108
+                    ],
+                    [
+                        4,
+                        3,
+                        799
+                    ],
+                    [
+                        5,
+                        4,
+                        47
+                    ],
+                    [
+                        2,
+                        7,
+                        545
+                    ],
+                    [
+                        9,
+                        4,
+                        730
+                    ],
+                    [
+                        4,
+                        6,
+                        623
+                    ],
+                    [
+                        1,
+                        7,
+                        957
+                    ],
+                    [
+                        7,
+                        4,
+                        570
+                    ],
+                    [
+                        1,
+                        9,
+                        506
+                    ],
+                    [
+                        4,
+                        7,
+                        865
+                    ],
+                    [
+                        9,
+                        8,
+                        942
+                    ],
+                    [
+                        2,
+                        1,
+                        29
+                    ],
+                    [
+                        5,
+                        3,
+                        708
+                    ],
+                    [
+                        7,
+                        2,
+                        801
+                    ],
+                    [
+                        9,
+                        7,
+                        215
+                    ],
+                    [
+                        9,
+                        2,
+                        613
+                    ],
+                    [
+                        3,
+                        4,
+                        714
+                    ],
+                    [
+                        6,
+                        0,
+                        328
+                    ],
+                    [
+                        6,
+                        1,
+                        51
+                    ],
+                    [
+                        0,
+                        8,
+                        602
+                    ],
+                    [
+                        6,
+                        1,
+                        68
+                    ],
+                    [
+                        1,
+                        4,
+                        819
+                    ],
+                    [
+                        4,
+                        1,
+                        576
+                    ],
+                    [
+                        0,
+                        7,
+                        856
+                    ],
+                    [
+                        4,
+                        3,
+                        791
+                    ],
+                    [
+                        9,
+                        6,
+                        302
+                    ],
+                    [
+                        5,
+                        0,
+                        525
+                    ],
+                    [
+                        8,
+                        9,
+                        157
+                    ],
+                    [
+                        9,
+                        3,
+                        987
+                    ],
+                    [
+                        5,
+                        2,
+                        977
+                    ],
+                    [
+                        5,
+                        4,
+                        356
+                    ],
+                    [
+                        8,
+                        0,
+                        731
+                    ],
+                    [
+                        4,
+                        9,
+                        996
+                    ],
+                    [
+                        4,
+                        0,
+                        366
+                    ],
+                    [
+                        3,
+                        7,
+                        29
+                    ],
+                    [
+                        7,
+                        8,
+                        254
+                    ],
+                    [
+                        1,
+                        0,
+                        597
+                    ],
+                    [
+                        0,
+                        2,
+                        3
+                    ],
+                    [
+                        4,
+                        0,
+                        754
+                    ],
+                    [
+                        8,
+                        4,
+                        184
+                    ],
+                    [
+                        1,
+                        9,
+                        564
+                    ],
+                    [
+                        3,
+                        7,
+                        653
+                    ],
+                    [
+                        7,
+                        0,
+                        290
+                    ],
+                    [
+                        6,
+                        0,
+                        745
+                    ],
+                    [
+                        4,
+                        3,
+                        661
+                    ],
+                    [
+                        8,
+                        5,
+                        383
+                    ],
+                    [
+                        1,
+                        3,
+                        368
+                    ],
+                    [
+                        6,
+                        2,
+                        325
+                    ],
+                    [
+                        5,
+                        0,
+                        753
+                    ],
+                    [
+                        1,
+                        7,
+                        201
+                    ],
+                    [
+                        0,
+                        9,
+                        390
+                    ],
+                    [
+                        5,
+                        6,
+                        446
+                    ],
+                    [
+                        0,
+                        9,
+                        849
+                    ],
+                    [
+                        1,
+                        6,
+                        427
+                    ],
+                    [
+                        7,
+                        8,
+                        104
+                    ],
+                    [
+                        3,
+                        6,
+                        592
+                    ],
+                    [
+                        1,
+                        4,
+                        943
+                    ],
+                    [
+                        7,
+                        8,
+                        280
+                    ],
+                    [
+                        1,
+                        4,
+                        407
+                    ],
+                    [
+                        6,
+                        1,
+                        926
+                    ],
+                    [
+                        2,
+                        4,
+                        904
+                    ],
+                    [
+                        8,
+                        5,
+                        327
+                    ],
+                    [
+                        0,
+                        2,
+                        746
+                    ],
+                    [
+                        9,
+                        6,
+                        346
+                    ],
+                    [
+                        5,
+                        6,
+                        576
+                    ],
+                    [
+                        3,
+                        7,
+                        112
+                    ],
+                    [
+                        4,
+                        1,
+                        574
+                    ],
+                    [
+                        6,
+                        1,
+                        616
+                    ],
+                    [
+                        1,
+                        4,
+                        458
+                    ],
+                    [
+                        2,
+                        9,
+                        815
+                    ],
+                    [
+                        4,
+                        1,
+                        484
+                    ],
+                    [
+                        3,
+                        9,
+                        125
+                    ],
+                    [
+                        2,
+                        9,
+                        248
+                    ],
+                    [
+                        6,
+                        0,
+                        794
+                    ],
+                    [
+                        9,
+                        5,
+                        366
+                    ],
+                    [
+                        4,
+                        3,
+                        790
+                    ],
+                    [
+                        2,
+                        8,
+                        490
+                    ],
+                    [
+                        3,
+                        0,
+                        663
+                    ],
+                    [
+                        6,
+                        9,
+                        860
+                    ],
+                    [
+                        7,
+                        6,
+                        775
+                    ],
+                    [
+                        8,
+                        5,
+                        166
+                    ],
+                    [
+                        0,
+                        7,
+                        767
+                    ],
+                    [
+                        5,
+                        6,
+                        643
+                    ],
+                    [
+                        2,
+                        5,
+                        313
+                    ],
+                    [
+                        7,
+                        1,
+                        702
+                    ],
+                    [
+                        0,
+                        6,
+                        365
+                    ],
+                    [
+                        2,
+                        8,
+                        739
+                    ],
+                    [
+                        0,
+                        8,
+                        288
+                    ],
+                    [
+                        6,
+                        8,
+                        65
+                    ],
+                    [
+                        3,
+                        8,
+                        523
+                    ],
+                    [
+                        3,
+                        9,
+                        462
+                    ],
+                    [
+                        1,
+                        9,
+                        971
+                    ],
+                    [
+                        3,
+                        0,
+                        907
+                    ],
+                    [
+                        6,
+                        3,
+                        684
+                    ],
+                    [
+                        9,
+                        5,
+                        804
+                    ],
+                    [
+                        7,
+                        4,
+                        243
+                    ],
+                    [
+                        5,
+                        4,
+                        158
+                    ],
+                    [
+                        5,
+                        3,
+                        260
+                    ],
+                    [
+                        4,
+                        1,
+                        707
+                    ],
+                    [
+                        0,
+                        7,
+                        41
+                    ],
+                    [
+                        9,
+                        4,
+                        83
+                    ],
+                    [
+                        6,
+                        8,
+                        598
+                    ],
+                    [
+                        3,
+                        6,
+                        864
+                    ],
+                    [
+                        3,
+                        4,
+                        99
+                    ],
+                    [
+                        2,
+                        6,
+                        472
+                    ],
+                    [
+                        2,
+                        7,
+                        500
+                    ],
+                    [
+                        8,
+                        0,
+                        830
+                    ],
+                    [
+                        7,
+                        0,
+                        301
+                    ],
+                    [
+                        4,
+                        5,
+                        922
+                    ],
+                    [
+                        5,
+                        6,
+                        325
+                    ],
+                    [
+                        8,
+                        2,
+                        285
+                    ],
+                    [
+                        2,
+                        6,
+                        572
+                    ],
+                    [
+                        2,
+                        6,
+                        690
+                    ],
+                    [
+                        1,
+                        3,
+                        589
+                    ],
+                    [
+                        8,
+                        4,
+                        756
+                    ],
+                    [
+                        7,
+                        1,
+                        503
+                    ],
+                    [
+                        0,
+                        7,
+                        558
+                    ],
+                    [
+                        5,
+                        8,
+                        630
+                    ],
+                    [
+                        5,
+                        9,
+                        885
+                    ],
+                    [
+                        5,
+                        1,
+                        658
+                    ],
+                    [
+                        1,
+                        3,
+                        429
+                    ],
+                    [
+                        9,
+                        2,
+                        283
+                    ],
+                    [
+                        3,
+                        5,
+                        584
+                    ],
+                    [
+                        5,
+                        9,
+                        485
+                    ],
+                    [
+                        8,
+                        9,
+                        229
+                    ],
+                    [
+                        8,
+                        5,
+                        437
+                    ],
+                    [
+                        8,
+                        9,
+                        388
+                    ],
+                    [
+                        1,
+                        8,
+                        155
+                    ],
+                    [
+                        1,
+                        8,
+                        983
+                    ],
+                    [
+                        4,
+                        0,
+                        735
+                    ],
+                    [
+                        7,
+                        3,
+                        81
+                    ],
+                    [
+                        3,
+                        7,
+                        559
+                    ],
+                    [
+                        7,
+                        9,
+                        369
+                    ],
+                    [
+                        2,
+                        5,
+                        138
+                    ],
+                    [
+                        9,
+                        6,
+                        205
+                    ],
+                    [
+                        2,
+                        7,
+                        454
+                    ],
+                    [
+                        3,
+                        1,
+                        554
+                    ],
+                    [
+                        4,
+                        9,
+                        14
+                    ],
+                    [
+                        6,
+                        8,
+                        700
+                    ],
+                    [
+                        6,
+                        2,
+                        598
+                    ]
+                ]
+            ],
+            "output": 1024
+        },
+        {
+            "input": [
+                5,
+                77476,
+                [
+                    [
+                        0,
+                        3,
+                        743
+                    ],
+                    [
+                        1,
+                        2,
+                        693
+                    ],
+                    [
+                        3,
+                        1,
+                        491
+                    ],
+                    [
+                        4,
+                        3,
+                        724
+                    ],
+                    [
+                        2,
+                        1,
+                        391
+                    ],
+                    [
+                        4,
+                        0,
+                        93
+                    ],
+                    [
+                        2,
+                        4,
+                        836
+                    ],
+                    [
+                        3,
+                        4,
+                        177
+                    ],
+                    [
+                        3,
+                        1,
+                        408
+                    ],
+                    [
+                        0,
+                        1,
+                        230
+                    ],
+                    [
+                        2,
+                        3,
+                        406
+                    ],
+                    [
+                        1,
+                        3,
+                        229
+                    ],
+                    [
+                        0,
+                        2,
+                        400
+                    ],
+                    [
+                        0,
+                        1,
+                        372
+                    ],
+                    [
+                        4,
+                        2,
+                        593
+                    ],
+                    [
+                        3,
+                        0,
+                        266
+                    ],
+                    [
+                        1,
+                        4,
+                        219
+                    ],
+                    [
+                        0,
+                        2,
+                        299
+                    ],
+                    [
+                        3,
+                        2,
+                        329
+                    ],
+                    [
+                        2,
+                        0,
+                        148
+                    ],
+                    [
+                        0,
+                        1,
+                        670
+                    ],
+                    [
+                        0,
+                        3,
+                        502
+                    ],
+                    [
+                        2,
+                        3,
+                        976
+                    ],
+                    [
+                        0,
+                        1,
+                        910
+                    ],
+                    [
+                        1,
+                        3,
+                        417
+                    ],
+                    [
+                        1,
+                        3,
+                        614
+                    ],
+                    [
+                        1,
+                        0,
+                        950
+                    ],
+                    [
+                        2,
+                        4,
+                        877
+                    ],
+                    [
+                        3,
+                        0,
+                        18
+                    ],
+                    [
+                        4,
+                        0,
+                        297
+                    ],
+                    [
+                        4,
+                        2,
+                        492
+                    ],
+                    [
+                        3,
+                        1,
+                        707
+                    ],
+                    [
+                        1,
+                        2,
+                        877
+                    ],
+                    [
+                        2,
+                        3,
+                        516
+                    ],
+                    [
+                        3,
+                        1,
+                        753
+                    ],
+                    [
+                        2,
+                        1,
+                        875
+                    ],
+                    [
+                        4,
+                        0,
+                        757
+                    ],
+                    [
+                        3,
+                        0,
+                        545
+                    ],
+                    [
+                        4,
+                        3,
+                        228
+                    ],
+                    [
+                        4,
+                        0,
+                        413
+                    ],
+                    [
+                        1,
+                        4,
+                        989
+                    ],
+                    [
+                        4,
+                        1,
+                        564
+                    ],
+                    [
+                        3,
+                        4,
+                        249
+                    ],
+                    [
+                        3,
+                        4,
+                        889
+                    ],
+                    [
+                        0,
+                        3,
+                        352
+                    ],
+                    [
+                        3,
+                        2,
+                        566
+                    ],
+                    [
+                        1,
+                        2,
+                        647
+                    ],
+                    [
+                        3,
+                        1,
+                        763
+                    ],
+                    [
+                        0,
+                        2,
+                        195
+                    ],
+                    [
+                        4,
+                        0,
+                        579
+                    ],
+                    [
+                        4,
+                        0,
+                        924
+                    ],
+                    [
+                        1,
+                        4,
+                        920
+                    ],
+                    [
+                        3,
+                        1,
+                        721
+                    ],
+                    [
+                        4,
+                        3,
+                        386
+                    ],
+                    [
+                        1,
+                        2,
+                        332
+                    ],
+                    [
+                        2,
+                        3,
+                        909
+                    ],
+                    [
+                        3,
+                        0,
+                        801
+                    ],
+                    [
+                        1,
+                        2,
+                        806
+                    ],
+                    [
+                        2,
+                        4,
+                        504
+                    ],
+                    [
+                        3,
+                        1,
+                        804
+                    ],
+                    [
+                        1,
+                        4,
+                        327
+                    ],
+                    [
+                        2,
+                        3,
+                        155
+                    ],
+                    [
+                        0,
+                        1,
+                        605
+                    ],
+                    [
+                        3,
+                        4,
+                        20
+                    ],
+                    [
+                        0,
+                        2,
+                        708
+                    ],
+                    [
+                        4,
+                        3,
+                        946
+                    ],
+                    [
+                        1,
+                        4,
+                        41
+                    ],
+                    [
+                        0,
+                        4,
+                        652
+                    ],
+                    [
+                        0,
+                        2,
+                        886
+                    ],
+                    [
+                        3,
+                        1,
+                        347
+                    ],
+                    [
+                        0,
+                        4,
+                        573
+                    ],
+                    [
+                        2,
+                        3,
+                        20
+                    ],
+                    [
+                        3,
+                        2,
+                        761
+                    ],
+                    [
+                        0,
+                        1,
+                        911
+                    ],
+                    [
+                        1,
+                        3,
+                        822
+                    ],
+                    [
+                        3,
+                        1,
+                        725
+                    ],
+                    [
+                        1,
+                        4,
+                        497
+                    ],
+                    [
+                        1,
+                        4,
+                        948
+                    ],
+                    [
+                        4,
+                        1,
+                        642
+                    ],
+                    [
+                        3,
+                        4,
+                        402
+                    ],
+                    [
+                        1,
+                        4,
+                        994
+                    ],
+                    [
+                        4,
+                        0,
+                        29
+                    ],
+                    [
+                        4,
+                        2,
+                        252
+                    ],
+                    [
+                        1,
+                        3,
+                        193
+                    ],
+                    [
+                        0,
+                        4,
+                        150
+                    ],
+                    [
+                        4,
+                        3,
+                        28
+                    ],
+                    [
+                        0,
+                        3,
+                        501
+                    ],
+                    [
+                        3,
+                        4,
+                        41
+                    ],
+                    [
+                        3,
+                        2,
+                        817
+                    ],
+                    [
+                        3,
+                        2,
+                        292
+                    ],
+                    [
+                        4,
+                        2,
+                        238
+                    ],
+                    [
+                        1,
+                        4,
+                        596
+                    ],
+                    [
+                        3,
+                        4,
+                        435
+                    ],
+                    [
+                        4,
+                        1,
+                        896
+                    ],
+                    [
+                        2,
+                        0,
+                        732
+                    ],
+                    [
+                        2,
+                        0,
+                        697
+                    ],
+                    [
+                        0,
+                        4,
+                        575
+                    ],
+                    [
+                        4,
+                        1,
+                        596
+                    ],
+                    [
+                        2,
+                        4,
+                        41
+                    ],
+                    [
+                        2,
+                        1,
+                        268
+                    ],
+                    [
+                        3,
+                        4,
+                        38
+                    ],
+                    [
+                        1,
+                        4,
+                        134
+                    ],
+                    [
+                        0,
+                        2,
+                        822
+                    ],
+                    [
+                        3,
+                        1,
+                        925
+                    ],
+                    [
+                        2,
+                        1,
+                        84
+                    ],
+                    [
+                        2,
+                        3,
+                        708
+                    ],
+                    [
+                        1,
+                        0,
+                        715
+                    ],
+                    [
+                        1,
+                        2,
+                        531
+                    ],
+                    [
+                        3,
+                        0,
+                        117
+                    ],
+                    [
+                        0,
+                        3,
+                        259
+                    ],
+                    [
+                        4,
+                        0,
+                        695
+                    ],
+                    [
+                        2,
+                        0,
+                        657
+                    ],
+                    [
+                        0,
+                        4,
+                        776
+                    ],
+                    [
+                        1,
+                        3,
+                        63
+                    ],
+                    [
+                        2,
+                        1,
+                        238
+                    ],
+                    [
+                        0,
+                        4,
+                        147
+                    ],
+                    [
+                        4,
+                        2,
+                        58
+                    ],
+                    [
+                        3,
+                        2,
+                        825
+                    ],
+                    [
+                        4,
+                        2,
+                        265
+                    ],
+                    [
+                        1,
+                        4,
+                        249
+                    ],
+                    [
+                        1,
+                        2,
+                        392
+                    ],
+                    [
+                        2,
+                        3,
+                        741
+                    ],
+                    [
+                        1,
+                        2,
+                        168
+                    ],
+                    [
+                        1,
+                        4,
+                        161
+                    ],
+                    [
+                        0,
+                        3,
+                        278
+                    ],
+                    [
+                        3,
+                        1,
+                        601
+                    ],
+                    [
+                        1,
+                        2,
+                        134
+                    ],
+                    [
+                        4,
+                        1,
+                        963
+                    ],
+                    [
+                        4,
+                        3,
+                        776
+                    ],
+                    [
+                        0,
+                        4,
+                        430
+                    ],
+                    [
+                        3,
+                        0,
+                        359
+                    ],
+                    [
+                        3,
+                        2,
+                        154
+                    ],
+                    [
+                        4,
+                        1,
+                        811
+                    ],
+                    [
+                        4,
+                        2,
+                        249
+                    ],
+                    [
+                        4,
+                        3,
+                        42
+                    ],
+                    [
+                        4,
+                        3,
+                        209
+                    ],
+                    [
+                        4,
+                        3,
+                        917
+                    ],
+                    [
+                        4,
+                        0,
+                        443
+                    ],
+                    [
+                        0,
+                        2,
+                        318
+                    ],
+                    [
+                        3,
+                        4,
+                        116
+                    ],
+                    [
+                        3,
+                        0,
+                        369
+                    ],
+                    [
+                        0,
+                        2,
+                        168
+                    ],
+                    [
+                        1,
+                        4,
+                        918
+                    ],
+                    [
+                        0,
+                        4,
+                        47
+                    ],
+                    [
+                        4,
+                        3,
+                        949
+                    ],
+                    [
+                        0,
+                        3,
+                        959
+                    ],
+                    [
+                        2,
+                        4,
+                        635
+                    ],
+                    [
+                        0,
+                        3,
+                        284
+                    ],
+                    [
+                        3,
+                        0,
+                        395
+                    ],
+                    [
+                        1,
+                        2,
+                        39
+                    ],
+                    [
+                        2,
+                        3,
+                        426
+                    ],
+                    [
+                        1,
+                        3,
+                        695
+                    ],
+                    [
+                        2,
+                        0,
+                        381
+                    ],
+                    [
+                        0,
+                        1,
+                        943
+                    ],
+                    [
+                        4,
+                        0,
+                        978
+                    ],
+                    [
+                        2,
+                        3,
+                        400
+                    ],
+                    [
+                        3,
+                        2,
+                        44
+                    ],
+                    [
+                        0,
+                        4,
+                        341
+                    ],
+                    [
+                        1,
+                        2,
+                        86
+                    ],
+                    [
+                        3,
+                        1,
+                        604
+                    ],
+                    [
+                        0,
+                        4,
+                        549
+                    ],
+                    [
+                        4,
+                        0,
+                        272
+                    ],
+                    [
+                        3,
+                        0,
+                        140
+                    ],
+                    [
+                        1,
+                        0,
+                        594
+                    ],
+                    [
+                        2,
+                        3,
+                        103
+                    ],
+                    [
+                        1,
+                        0,
+                        300
+                    ],
+                    [
+                        1,
+                        4,
+                        546
+                    ],
+                    [
+                        2,
+                        4,
+                        259
+                    ],
+                    [
+                        1,
+                        3,
+                        829
+                    ],
+                    [
+                        1,
+                        0,
+                        516
+                    ],
+                    [
+                        4,
+                        0,
+                        192
+                    ],
+                    [
+                        1,
+                        2,
+                        724
+                    ],
+                    [
+                        1,
+                        4,
+                        913
+                    ],
+                    [
+                        1,
+                        2,
+                        271
+                    ],
+                    [
+                        1,
+                        2,
+                        191
+                    ],
+                    [
+                        1,
+                        4,
+                        278
+                    ],
+                    [
+                        1,
+                        3,
+                        282
+                    ],
+                    [
+                        2,
+                        3,
+                        51
+                    ],
+                    [
+                        1,
+                        0,
+                        885
+                    ],
+                    [
+                        4,
+                        1,
+                        604
+                    ],
+                    [
+                        1,
+                        4,
+                        434
+                    ],
+                    [
+                        1,
+                        2,
+                        385
+                    ],
+                    [
+                        3,
+                        1,
+                        675
+                    ],
+                    [
+                        1,
+                        0,
+                        227
+                    ],
+                    [
+                        4,
+                        0,
+                        628
+                    ],
+                    [
+                        4,
+                        1,
+                        848
+                    ],
+                    [
+                        1,
+                        0,
+                        861
+                    ],
+                    [
+                        3,
+                        1,
+                        350
+                    ],
+                    [
+                        0,
+                        2,
+                        451
+                    ],
+                    [
+                        2,
+                        3,
+                        943
+                    ],
+                    [
+                        2,
+                        1,
+                        76
+                    ],
+                    [
+                        1,
+                        2,
+                        679
+                    ],
+                    [
+                        1,
+                        3,
+                        5
+                    ],
+                    [
+                        1,
+                        2,
+                        705
+                    ],
+                    [
+                        3,
+                        4,
+                        148
+                    ],
+                    [
+                        4,
+                        0,
+                        291
+                    ],
+                    [
+                        4,
+                        3,
+                        276
+                    ],
+                    [
+                        1,
+                        4,
+                        953
+                    ],
+                    [
+                        0,
+                        2,
+                        734
+                    ],
+                    [
+                        4,
+                        3,
+                        569
+                    ],
+                    [
+                        0,
+                        2,
+                        377
+                    ],
+                    [
+                        2,
+                        1,
+                        978
+                    ],
+                    [
+                        3,
+                        2,
+                        162
+                    ],
+                    [
+                        4,
+                        1,
+                        674
+                    ],
+                    [
+                        4,
+                        3,
+                        18
+                    ],
+                    [
+                        2,
+                        0,
+                        650
+                    ],
+                    [
+                        1,
+                        3,
+                        179
+                    ],
+                    [
+                        0,
+                        3,
+                        869
+                    ],
+                    [
+                        0,
+                        4,
+                        74
+                    ],
+                    [
+                        4,
+                        2,
+                        745
+                    ],
+                    [
+                        4,
+                        0,
+                        500
+                    ],
+                    [
+                        2,
+                        4,
+                        779
+                    ],
+                    [
+                        3,
+                        1,
+                        673
+                    ],
+                    [
+                        3,
+                        0,
+                        515
+                    ],
+                    [
+                        4,
+                        0,
+                        184
+                    ],
+                    [
+                        3,
+                        0,
+                        729
+                    ],
+                    [
+                        3,
+                        2,
+                        456
+                    ],
+                    [
+                        1,
+                        2,
+                        218
+                    ],
+                    [
+                        4,
+                        1,
+                        793
+                    ],
+                    [
+                        4,
+                        3,
+                        108
+                    ],
+                    [
+                        4,
+                        3,
+                        344
+                    ],
+                    [
+                        3,
+                        0,
+                        110
+                    ],
+                    [
+                        1,
+                        4,
+                        266
+                    ],
+                    [
+                        3,
+                        2,
+                        35
+                    ],
+                    [
+                        3,
+                        0,
+                        732
+                    ],
+                    [
+                        0,
+                        2,
+                        110
+                    ],
+                    [
+                        3,
+                        4,
+                        606
+                    ],
+                    [
+                        3,
+                        2,
+                        465
+                    ],
+                    [
+                        0,
+                        4,
+                        658
+                    ],
+                    [
+                        2,
+                        4,
+                        740
+                    ],
+                    [
+                        3,
+                        2,
+                        632
+                    ],
+                    [
+                        4,
+                        0,
+                        544
+                    ],
+                    [
+                        1,
+                        3,
+                        367
+                    ],
+                    [
+                        4,
+                        1,
+                        380
+                    ],
+                    [
+                        3,
+                        1,
+                        50
+                    ],
+                    [
+                        1,
+                        0,
+                        425
+                    ],
+                    [
+                        1,
+                        2,
+                        480
+                    ],
+                    [
+                        2,
+                        3,
+                        602
+                    ],
+                    [
+                        0,
+                        4,
+                        921
+                    ],
+                    [
+                        3,
+                        1,
+                        529
+                    ],
+                    [
+                        3,
+                        2,
+                        102
+                    ],
+                    [
+                        4,
+                        0,
+                        436
+                    ],
+                    [
+                        4,
+                        1,
+                        572
+                    ],
+                    [
+                        1,
+                        2,
+                        686
+                    ],
+                    [
+                        0,
+                        4,
+                        21
+                    ],
+                    [
+                        4,
+                        0,
+                        288
+                    ],
+                    [
+                        0,
+                        4,
+                        186
+                    ],
+                    [
+                        0,
+                        3,
+                        705
+                    ],
+                    [
+                        2,
+                        4,
+                        983
+                    ],
+                    [
+                        2,
+                        1,
+                        424
+                    ],
+                    [
+                        0,
+                        3,
+                        885
+                    ],
+                    [
+                        4,
+                        0,
+                        263
+                    ],
+                    [
+                        3,
+                        4,
+                        345
+                    ],
+                    [
+                        0,
+                        4,
+                        855
+                    ],
+                    [
+                        0,
+                        4,
+                        664
+                    ],
+                    [
+                        4,
+                        3,
+                        936
+                    ],
+                    [
+                        1,
+                        3,
+                        286
+                    ],
+                    [
+                        2,
+                        4,
+                        563
+                    ],
+                    [
+                        4,
+                        3,
+                        491
+                    ],
+                    [
+                        4,
+                        0,
+                        325
+                    ],
+                    [
+                        0,
+                        2,
+                        25
+                    ],
+                    [
+                        4,
+                        1,
+                        223
+                    ],
+                    [
+                        3,
+                        4,
+                        159
+                    ],
+                    [
+                        0,
+                        3,
+                        983
+                    ],
+                    [
+                        3,
+                        4,
+                        964
+                    ],
+                    [
+                        2,
+                        3,
+                        673
+                    ],
+                    [
+                        2,
+                        0,
+                        93
+                    ],
+                    [
+                        2,
+                        3,
+                        371
+                    ],
+                    [
+                        2,
+                        3,
+                        637
+                    ],
+                    [
+                        0,
+                        3,
+                        221
+                    ],
+                    [
+                        0,
+                        2,
+                        680
+                    ],
+                    [
+                        3,
+                        0,
+                        823
+                    ],
+                    [
+                        1,
+                        4,
+                        299
+                    ],
+                    [
+                        3,
+                        1,
+                        53
+                    ],
+                    [
+                        2,
+                        1,
+                        344
+                    ],
+                    [
+                        2,
+                        0,
+                        595
+                    ],
+                    [
+                        0,
+                        4,
+                        204
+                    ],
+                    [
+                        4,
+                        0,
+                        231
+                    ],
+                    [
+                        2,
+                        1,
+                        818
+                    ],
+                    [
+                        1,
+                        3,
+                        322
+                    ],
+                    [
+                        1,
+                        3,
+                        706
+                    ],
+                    [
+                        0,
+                        4,
+                        99
+                    ],
+                    [
+                        4,
+                        3,
+                        524
+                    ],
+                    [
+                        2,
+                        0,
+                        699
+                    ],
+                    [
+                        0,
+                        1,
+                        18
+                    ],
+                    [
+                        2,
+                        4,
+                        310
+                    ],
+                    [
+                        2,
+                        3,
+                        987
+                    ],
+                    [
+                        4,
+                        1,
+                        640
+                    ],
+                    [
+                        2,
+                        1,
+                        955
+                    ],
+                    [
+                        1,
+                        2,
+                        495
+                    ],
+                    [
+                        3,
+                        4,
+                        17
+                    ],
+                    [
+                        1,
+                        3,
+                        208
+                    ],
+                    [
+                        0,
+                        1,
+                        601
+                    ],
+                    [
+                        0,
+                        1,
+                        931
+                    ],
+                    [
+                        3,
+                        0,
+                        338
+                    ],
+                    [
+                        0,
+                        3,
+                        521
+                    ],
+                    [
+                        1,
+                        4,
+                        376
+                    ],
+                    [
+                        4,
+                        2,
+                        680
+                    ],
+                    [
+                        2,
+                        1,
+                        522
+                    ],
+                    [
+                        3,
+                        0,
+                        496
+                    ],
+                    [
+                        1,
+                        4,
+                        684
+                    ],
+                    [
+                        4,
+                        1,
+                        436
+                    ],
+                    [
+                        3,
+                        4,
+                        890
+                    ],
+                    [
+                        3,
+                        4,
+                        43
+                    ],
+                    [
+                        3,
+                        4,
+                        233
+                    ],
+                    [
+                        3,
+                        0,
+                        236
+                    ],
+                    [
+                        0,
+                        4,
+                        154
+                    ],
+                    [
+                        0,
+                        2,
+                        73
+                    ],
+                    [
+                        1,
+                        3,
+                        560
+                    ],
+                    [
+                        1,
+                        3,
+                        119
+                    ],
+                    [
+                        2,
+                        3,
+                        61
+                    ],
+                    [
+                        4,
+                        2,
+                        491
+                    ],
+                    [
+                        2,
+                        4,
+                        282
+                    ],
+                    [
+                        4,
+                        1,
+                        20
+                    ],
+                    [
+                        1,
+                        2,
+                        289
+                    ],
+                    [
+                        4,
+                        3,
+                        592
+                    ],
+                    [
+                        3,
+                        1,
+                        866
+                    ],
+                    [
+                        1,
+                        3,
+                        85
+                    ],
+                    [
+                        2,
+                        4,
+                        280
+                    ],
+                    [
+                        3,
+                        1,
+                        493
+                    ],
+                    [
+                        1,
+                        3,
+                        766
+                    ],
+                    [
+                        1,
+                        2,
+                        418
+                    ],
+                    [
+                        1,
+                        4,
+                        68
+                    ],
+                    [
+                        0,
+                        3,
+                        534
+                    ],
+                    [
+                        0,
+                        2,
+                        358
+                    ],
+                    [
+                        3,
+                        2,
+                        707
+                    ],
+                    [
+                        0,
+                        3,
+                        807
+                    ],
+                    [
+                        2,
+                        3,
+                        486
+                    ],
+                    [
+                        2,
+                        4,
+                        274
+                    ],
+                    [
+                        1,
+                        4,
+                        515
+                    ],
+                    [
+                        1,
+                        3,
+                        730
+                    ],
+                    [
+                        4,
+                        1,
+                        833
+                    ],
+                    [
+                        1,
+                        2,
+                        805
+                    ],
+                    [
+                        1,
+                        4,
+                        184
+                    ],
+                    [
+                        0,
+                        1,
+                        984
+                    ],
+                    [
+                        0,
+                        4,
+                        653
+                    ],
+                    [
+                        4,
+                        1,
+                        186
+                    ],
+                    [
+                        0,
+                        2,
+                        526
+                    ],
+                    [
+                        1,
+                        3,
+                        588
+                    ],
+                    [
+                        4,
+                        3,
+                        356
+                    ],
+                    [
+                        4,
+                        0,
+                        705
+                    ],
+                    [
+                        2,
+                        1,
+                        639
+                    ],
+                    [
+                        4,
+                        2,
+                        931
+                    ],
+                    [
+                        2,
+                        3,
+                        254
+                    ],
+                    [
+                        3,
+                        1,
+                        101
+                    ],
+                    [
+                        3,
+                        4,
+                        477
+                    ],
+                    [
+                        1,
+                        0,
+                        453
+                    ],
+                    [
+                        1,
+                        4,
+                        380
+                    ]
+                ]
+            ],
+            "output": 32
+        },
+        {
+            "input": [
+                4,
+                86908,
+                [
+                    [
+                        1,
+                        2,
+                        261
+                    ],
+                    [
+                        3,
+                        0,
+                        805
+                    ],
+                    [
+                        3,
+                        0,
+                        125
+                    ],
+                    [
+                        3,
+                        1,
+                        634
+                    ],
+                    [
+                        1,
+                        2,
+                        251
+                    ],
+                    [
+                        1,
+                        2,
+                        638
+                    ],
+                    [
+                        1,
+                        0,
+                        353
+                    ],
+                    [
+                        2,
+                        0,
+                        289
+                    ],
+                    [
+                        2,
+                        3,
+                        16
+                    ],
+                    [
+                        3,
+                        2,
+                        702
+                    ],
+                    [
+                        0,
+                        2,
+                        279
+                    ],
+                    [
+                        2,
+                        3,
+                        366
+                    ],
+                    [
+                        3,
+                        0,
+                        435
+                    ],
+                    [
+                        3,
+                        0,
+                        335
+                    ],
+                    [
+                        2,
+                        0,
+                        545
+                    ],
+                    [
+                        2,
+                        1,
+                        657
+                    ],
+                    [
+                        2,
+                        0,
+                        964
+                    ],
+                    [
+                        2,
+                        3,
+                        668
+                    ],
+                    [
+                        1,
+                        3,
+                        773
+                    ],
+                    [
+                        1,
+                        3,
+                        85
+                    ],
+                    [
+                        3,
+                        2,
+                        203
+                    ],
+                    [
+                        3,
+                        2,
+                        78
+                    ],
+                    [
+                        3,
+                        2,
+                        961
+                    ],
+                    [
+                        3,
+                        0,
+                        656
+                    ],
+                    [
+                        1,
+                        2,
+                        878
+                    ],
+                    [
+                        0,
+                        1,
+                        786
+                    ],
+                    [
+                        0,
+                        1,
+                        792
+                    ],
+                    [
+                        3,
+                        1,
+                        706
+                    ],
+                    [
+                        1,
+                        2,
+                        51
+                    ],
+                    [
+                        0,
+                        3,
+                        700
+                    ],
+                    [
+                        3,
+                        0,
+                        86
+                    ],
+                    [
+                        0,
+                        1,
+                        859
+                    ],
+                    [
+                        2,
+                        0,
+                        982
+                    ],
+                    [
+                        0,
+                        3,
+                        532
+                    ],
+                    [
+                        2,
+                        3,
+                        940
+                    ],
+                    [
+                        0,
+                        3,
+                        709
+                    ],
+                    [
+                        0,
+                        3,
+                        923
+                    ],
+                    [
+                        2,
+                        0,
+                        527
+                    ],
+                    [
+                        2,
+                        0,
+                        406
+                    ],
+                    [
+                        3,
+                        0,
+                        519
+                    ],
+                    [
+                        2,
+                        3,
+                        328
+                    ],
+                    [
+                        1,
+                        3,
+                        869
+                    ],
+                    [
+                        1,
+                        3,
+                        617
+                    ],
+                    [
+                        3,
+                        1,
+                        479
+                    ],
+                    [
+                        1,
+                        3,
+                        578
+                    ],
+                    [
+                        0,
+                        2,
+                        308
+                    ],
+                    [
+                        0,
+                        3,
+                        665
+                    ],
+                    [
+                        3,
+                        2,
+                        901
+                    ],
+                    [
+                        0,
+                        2,
+                        125
+                    ],
+                    [
+                        0,
+                        3,
+                        459
+                    ],
+                    [
+                        1,
+                        2,
+                        246
+                    ],
+                    [
+                        1,
+                        3,
+                        249
+                    ],
+                    [
+                        1,
+                        0,
+                        543
+                    ],
+                    [
+                        2,
+                        3,
+                        148
+                    ],
+                    [
+                        1,
+                        2,
+                        546
+                    ],
+                    [
+                        2,
+                        1,
+                        772
+                    ],
+                    [
+                        2,
+                        1,
+                        808
+                    ],
+                    [
+                        0,
+                        1,
+                        619
+                    ],
+                    [
+                        2,
+                        3,
+                        372
+                    ],
+                    [
+                        1,
+                        2,
+                        865
+                    ],
+                    [
+                        3,
+                        2,
+                        821
+                    ],
+                    [
+                        3,
+                        1,
+                        326
+                    ],
+                    [
+                        2,
+                        0,
+                        690
+                    ],
+                    [
+                        2,
+                        0,
+                        523
+                    ],
+                    [
+                        3,
+                        2,
+                        567
+                    ],
+                    [
+                        3,
+                        0,
+                        575
+                    ],
+                    [
+                        3,
+                        2,
+                        263
+                    ],
+                    [
+                        1,
+                        0,
+                        308
+                    ],
+                    [
+                        3,
+                        1,
+                        614
+                    ],
+                    [
+                        2,
+                        0,
+                        698
+                    ],
+                    [
+                        2,
+                        0,
+                        821
+                    ],
+                    [
+                        3,
+                        1,
+                        686
+                    ],
+                    [
+                        2,
+                        1,
+                        488
+                    ],
+                    [
+                        1,
+                        3,
+                        546
+                    ],
+                    [
+                        2,
+                        1,
+                        532
+                    ],
+                    [
+                        1,
+                        0,
+                        455
+                    ],
+                    [
+                        0,
+                        1,
+                        665
+                    ],
+                    [
+                        2,
+                        0,
+                        192
+                    ],
+                    [
+                        2,
+                        0,
+                        547
+                    ],
+                    [
+                        1,
+                        3,
+                        531
+                    ],
+                    [
+                        3,
+                        0,
+                        613
+                    ],
+                    [
+                        2,
+                        1,
+                        184
+                    ],
+                    [
+                        3,
+                        1,
+                        919
+                    ],
+                    [
+                        1,
+                        0,
+                        738
+                    ],
+                    [
+                        0,
+                        2,
+                        46
+                    ],
+                    [
+                        3,
+                        1,
+                        160
+                    ],
+                    [
+                        1,
+                        2,
+                        178
+                    ],
+                    [
+                        0,
+                        3,
+                        493
+                    ],
+                    [
+                        3,
+                        1,
+                        339
+                    ],
+                    [
+                        2,
+                        0,
+                        176
+                    ],
+                    [
+                        2,
+                        1,
+                        132
+                    ],
+                    [
+                        2,
+                        3,
+                        820
+                    ],
+                    [
+                        3,
+                        2,
+                        128
+                    ],
+                    [
+                        3,
+                        2,
+                        53
+                    ],
+                    [
+                        2,
+                        1,
+                        796
+                    ],
+                    [
+                        0,
+                        2,
+                        745
+                    ],
+                    [
+                        0,
+                        1,
+                        849
+                    ],
+                    [
+                        2,
+                        1,
+                        744
+                    ],
+                    [
+                        3,
+                        2,
+                        315
+                    ],
+                    [
+                        1,
+                        0,
+                        274
+                    ],
+                    [
+                        2,
+                        1,
+                        478
+                    ],
+                    [
+                        3,
+                        0,
+                        302
+                    ],
+                    [
+                        1,
+                        0,
+                        156
+                    ],
+                    [
+                        0,
+                        1,
+                        216
+                    ],
+                    [
+                        3,
+                        0,
+                        545
+                    ],
+                    [
+                        1,
+                        0,
+                        9
+                    ],
+                    [
+                        3,
+                        0,
+                        930
+                    ],
+                    [
+                        3,
+                        1,
+                        403
+                    ],
+                    [
+                        2,
+                        0,
+                        962
+                    ],
+                    [
+                        1,
+                        3,
+                        887
+                    ],
+                    [
+                        3,
+                        1,
+                        255
+                    ],
+                    [
+                        1,
+                        3,
+                        769
+                    ],
+                    [
+                        0,
+                        1,
+                        615
+                    ],
+                    [
+                        3,
+                        2,
+                        978
+                    ],
+                    [
+                        1,
+                        2,
+                        312
+                    ],
+                    [
+                        1,
+                        3,
+                        704
+                    ],
+                    [
+                        1,
+                        0,
+                        795
+                    ],
+                    [
+                        3,
+                        2,
+                        252
+                    ],
+                    [
+                        2,
+                        1,
+                        423
+                    ],
+                    [
+                        2,
+                        1,
+                        103
+                    ],
+                    [
+                        3,
+                        0,
+                        709
+                    ],
+                    [
+                        2,
+                        3,
+                        534
+                    ],
+                    [
+                        2,
+                        3,
+                        582
+                    ],
+                    [
+                        1,
+                        2,
+                        950
+                    ],
+                    [
+                        1,
+                        3,
+                        500
+                    ],
+                    [
+                        2,
+                        3,
+                        98
+                    ],
+                    [
+                        1,
+                        2,
+                        817
+                    ],
+                    [
+                        3,
+                        0,
+                        529
+                    ],
+                    [
+                        3,
+                        2,
+                        641
+                    ],
+                    [
+                        2,
+                        0,
+                        720
+                    ],
+                    [
+                        1,
+                        0,
+                        905
+                    ],
+                    [
+                        3,
+                        2,
+                        247
+                    ],
+                    [
+                        2,
+                        0,
+                        303
+                    ],
+                    [
+                        0,
+                        2,
+                        499
+                    ],
+                    [
+                        3,
+                        1,
+                        933
+                    ],
+                    [
+                        1,
+                        0,
+                        219
+                    ],
+                    [
+                        0,
+                        3,
+                        951
+                    ],
+                    [
+                        3,
+                        1,
+                        74
+                    ],
+                    [
+                        0,
+                        1,
+                        503
+                    ],
+                    [
+                        2,
+                        1,
+                        206
+                    ],
+                    [
+                        0,
+                        3,
+                        427
+                    ],
+                    [
+                        3,
+                        2,
+                        699
+                    ],
+                    [
+                        2,
+                        1,
+                        114
+                    ],
+                    [
+                        2,
+                        3,
+                        50
+                    ],
+                    [
+                        1,
+                        0,
+                        454
+                    ],
+                    [
+                        0,
+                        3,
+                        940
+                    ],
+                    [
+                        3,
+                        0,
+                        417
+                    ],
+                    [
+                        0,
+                        3,
+                        617
+                    ],
+                    [
+                        0,
+                        3,
+                        128
+                    ],
+                    [
+                        3,
+                        1,
+                        378
+                    ],
+                    [
+                        3,
+                        0,
+                        336
+                    ],
+                    [
+                        2,
+                        3,
+                        649
+                    ],
+                    [
+                        2,
+                        0,
+                        758
+                    ],
+                    [
+                        2,
+                        1,
+                        295
+                    ],
+                    [
+                        1,
+                        3,
+                        554
+                    ],
+                    [
+                        0,
+                        3,
+                        795
+                    ],
+                    [
+                        3,
+                        2,
+                        721
+                    ],
+                    [
+                        0,
+                        3,
+                        599
+                    ],
+                    [
+                        1,
+                        3,
+                        64
+                    ],
+                    [
+                        2,
+                        0,
+                        989
+                    ],
+                    [
+                        3,
+                        1,
+                        779
+                    ],
+                    [
+                        3,
+                        1,
+                        746
+                    ],
+                    [
+                        0,
+                        1,
+                        930
+                    ],
+                    [
+                        3,
+                        2,
+                        380
+                    ],
+                    [
+                        2,
+                        3,
+                        856
+                    ],
+                    [
+                        0,
+                        1,
+                        568
+                    ],
+                    [
+                        1,
+                        0,
+                        402
+                    ],
+                    [
+                        1,
+                        3,
+                        212
+                    ],
+                    [
+                        0,
+                        3,
+                        493
+                    ],
+                    [
+                        3,
+                        1,
+                        542
+                    ],
+                    [
+                        2,
+                        1,
+                        200
+                    ],
+                    [
+                        1,
+                        3,
+                        492
+                    ],
+                    [
+                        3,
+                        2,
+                        856
+                    ],
+                    [
+                        1,
+                        0,
+                        425
+                    ],
+                    [
+                        1,
+                        2,
+                        162
+                    ],
+                    [
+                        2,
+                        3,
+                        406
+                    ],
+                    [
+                        0,
+                        3,
+                        48
+                    ],
+                    [
+                        0,
+                        1,
+                        904
+                    ],
+                    [
+                        0,
+                        1,
+                        181
+                    ],
+                    [
+                        0,
+                        3,
+                        519
+                    ],
+                    [
+                        3,
+                        2,
+                        282
+                    ],
+                    [
+                        2,
+                        3,
+                        445
+                    ],
+                    [
+                        3,
+                        1,
+                        941
+                    ],
+                    [
+                        3,
+                        0,
+                        648
+                    ],
+                    [
+                        2,
+                        1,
+                        135
+                    ],
+                    [
+                        3,
+                        1,
+                        750
+                    ],
+                    [
+                        0,
+                        2,
+                        448
+                    ],
+                    [
+                        3,
+                        2,
+                        25
+                    ],
+                    [
+                        0,
+                        3,
+                        587
+                    ],
+                    [
+                        3,
+                        2,
+                        521
+                    ],
+                    [
+                        2,
+                        0,
+                        787
+                    ]
+                ]
+            ],
+            "output": 16
+        },
+        {
+            "input": [
+                10,
+                30571,
+                [
+                    [
+                        7,
+                        5,
+                        39
+                    ],
+                    [
+                        6,
+                        0,
+                        355
+                    ],
+                    [
+                        4,
+                        3,
+                        50
+                    ],
+                    [
+                        4,
+                        9,
+                        650
+                    ],
+                    [
+                        3,
+                        4,
+                        961
+                    ],
+                    [
+                        2,
+                        8,
+                        106
+                    ],
+                    [
+                        7,
+                        3,
+                        700
+                    ],
+                    [
+                        6,
+                        9,
+                        504
+                    ],
+                    [
+                        2,
+                        5,
+                        701
+                    ],
+                    [
+                        1,
+                        8,
+                        601
+                    ],
+                    [
+                        0,
+                        2,
+                        675
+                    ],
+                    [
+                        5,
+                        2,
+                        834
+                    ],
+                    [
+                        0,
+                        5,
+                        215
+                    ],
+                    [
+                        9,
+                        5,
+                        909
+                    ],
+                    [
+                        7,
+                        0,
+                        798
+                    ],
+                    [
+                        7,
+                        2,
+                        91
+                    ],
+                    [
+                        9,
+                        5,
+                        704
+                    ],
+                    [
+                        8,
+                        0,
+                        209
+                    ],
+                    [
+                        3,
+                        7,
+                        216
+                    ],
+                    [
+                        4,
+                        9,
+                        288
+                    ],
+                    [
+                        7,
+                        4,
+                        121
+                    ],
+                    [
+                        3,
+                        8,
+                        208
+                    ],
+                    [
+                        5,
+                        7,
+                        43
+                    ],
+                    [
+                        6,
+                        3,
+                        851
+                    ],
+                    [
+                        3,
+                        9,
+                        16
+                    ],
+                    [
+                        9,
+                        7,
+                        635
+                    ],
+                    [
+                        1,
+                        8,
+                        75
+                    ],
+                    [
+                        5,
+                        9,
+                        576
+                    ],
+                    [
+                        3,
+                        4,
+                        193
+                    ],
+                    [
+                        6,
+                        2,
+                        670
+                    ],
+                    [
+                        9,
+                        7,
+                        226
+                    ],
+                    [
+                        7,
+                        9,
+                        101
+                    ],
+                    [
+                        0,
+                        7,
+                        860
+                    ],
+                    [
+                        1,
+                        3,
+                        565
+                    ],
+                    [
+                        4,
+                        3,
+                        384
+                    ],
+                    [
+                        1,
+                        6,
+                        120
+                    ],
+                    [
+                        8,
+                        1,
+                        889
+                    ],
+                    [
+                        0,
+                        6,
+                        177
+                    ],
+                    [
+                        5,
+                        6,
+                        863
+                    ],
+                    [
+                        7,
+                        1,
+                        297
+                    ],
+                    [
+                        3,
+                        1,
+                        662
+                    ],
+                    [
+                        7,
+                        3,
+                        171
+                    ],
+                    [
+                        6,
+                        9,
+                        730
+                    ],
+                    [
+                        0,
+                        3,
+                        205
+                    ],
+                    [
+                        0,
+                        8,
+                        497
+                    ],
+                    [
+                        2,
+                        7,
+                        320
+                    ],
+                    [
+                        5,
+                        7,
+                        761
+                    ],
+                    [
+                        5,
+                        9,
+                        855
+                    ],
+                    [
+                        5,
+                        9,
+                        744
+                    ],
+                    [
+                        6,
+                        4,
+                        955
+                    ],
+                    [
+                        7,
+                        9,
+                        7
+                    ],
+                    [
+                        2,
+                        1,
+                        394
+                    ],
+                    [
+                        7,
+                        0,
+                        510
+                    ],
+                    [
+                        6,
+                        9,
+                        140
+                    ],
+                    [
+                        0,
+                        5,
+                        313
+                    ],
+                    [
+                        0,
+                        6,
+                        871
+                    ],
+                    [
+                        9,
+                        4,
+                        326
+                    ],
+                    [
+                        1,
+                        2,
+                        43
+                    ],
+                    [
+                        6,
+                        2,
+                        845
+                    ],
+                    [
+                        4,
+                        7,
+                        752
+                    ],
+                    [
+                        0,
+                        9,
+                        279
+                    ],
+                    [
+                        0,
+                        6,
+                        569
+                    ],
+                    [
+                        1,
+                        2,
+                        856
+                    ],
+                    [
+                        0,
+                        1,
+                        817
+                    ],
+                    [
+                        6,
+                        3,
+                        278
+                    ],
+                    [
+                        9,
+                        6,
+                        351
+                    ],
+                    [
+                        3,
+                        9,
+                        565
+                    ],
+                    [
+                        1,
+                        3,
+                        990
+                    ],
+                    [
+                        6,
+                        7,
+                        794
+                    ],
+                    [
+                        9,
+                        5,
+                        727
+                    ],
+                    [
+                        5,
+                        9,
+                        43
+                    ],
+                    [
+                        1,
+                        7,
+                        787
+                    ],
+                    [
+                        2,
+                        3,
+                        54
+                    ],
+                    [
+                        2,
+                        7,
+                        133
+                    ],
+                    [
+                        8,
+                        0,
+                        121
+                    ],
+                    [
+                        0,
+                        6,
+                        301
+                    ],
+                    [
+                        1,
+                        8,
+                        150
+                    ],
+                    [
+                        9,
+                        7,
+                        102
+                    ],
+                    [
+                        4,
+                        8,
+                        84
+                    ],
+                    [
+                        0,
+                        2,
+                        305
+                    ],
+                    [
+                        8,
+                        3,
+                        866
+                    ],
+                    [
+                        2,
+                        6,
+                        277
+                    ],
+                    [
+                        4,
+                        2,
+                        559
+                    ],
+                    [
+                        6,
+                        8,
+                        372
+                    ],
+                    [
+                        3,
+                        1,
+                        127
+                    ],
+                    [
+                        9,
+                        5,
+                        525
+                    ],
+                    [
+                        7,
+                        2,
+                        24
+                    ],
+                    [
+                        6,
+                        5,
+                        982
+                    ],
+                    [
+                        1,
+                        3,
+                        59
+                    ],
+                    [
+                        2,
+                        4,
+                        457
+                    ],
+                    [
+                        3,
+                        9,
+                        86
+                    ],
+                    [
+                        8,
+                        7,
+                        565
+                    ],
+                    [
+                        7,
+                        0,
+                        307
+                    ],
+                    [
+                        1,
+                        9,
+                        696
+                    ],
+                    [
+                        6,
+                        7,
+                        578
+                    ],
+                    [
+                        7,
+                        6,
+                        628
+                    ],
+                    [
+                        8,
+                        4,
+                        818
+                    ],
+                    [
+                        2,
+                        0,
+                        413
+                    ],
+                    [
+                        4,
+                        8,
+                        197
+                    ],
+                    [
+                        6,
+                        3,
+                        902
+                    ],
+                    [
+                        1,
+                        4,
+                        924
+                    ],
+                    [
+                        4,
+                        5,
+                        936
+                    ],
+                    [
+                        7,
+                        0,
+                        202
+                    ],
+                    [
+                        5,
+                        8,
+                        47
+                    ],
+                    [
+                        7,
+                        1,
+                        583
+                    ],
+                    [
+                        8,
+                        1,
+                        426
+                    ],
+                    [
+                        9,
+                        5,
+                        115
+                    ],
+                    [
+                        0,
+                        3,
+                        529
+                    ],
+                    [
+                        5,
+                        1,
+                        928
+                    ],
+                    [
+                        7,
+                        3,
+                        912
+                    ],
+                    [
+                        2,
+                        6,
+                        719
+                    ],
+                    [
+                        9,
+                        1,
+                        921
+                    ],
+                    [
+                        7,
+                        1,
+                        489
+                    ],
+                    [
+                        8,
+                        5,
+                        196
+                    ],
+                    [
+                        4,
+                        6,
+                        837
+                    ],
+                    [
+                        6,
+                        1,
+                        112
+                    ],
+                    [
+                        0,
+                        5,
+                        820
+                    ],
+                    [
+                        2,
+                        6,
+                        897
+                    ],
+                    [
+                        1,
+                        4,
+                        332
+                    ],
+                    [
+                        9,
+                        7,
+                        867
+                    ],
+                    [
+                        5,
+                        0,
+                        186
+                    ],
+                    [
+                        5,
+                        4,
+                        16
+                    ],
+                    [
+                        8,
+                        5,
+                        89
+                    ]
+                ]
+            ],
+            "output": 1019
+        },
+        {
+            "input": [
+                7,
+                85696,
+                [
+                    [
+                        4,
+                        6,
+                        374
+                    ],
+                    [
+                        2,
+                        3,
+                        736
+                    ],
+                    [
+                        5,
+                        1,
+                        930
+                    ],
+                    [
+                        1,
+                        5,
+                        892
+                    ],
+                    [
+                        4,
+                        0,
+                        846
+                    ],
+                    [
+                        6,
+                        5,
+                        380
+                    ],
+                    [
+                        0,
+                        2,
+                        479
+                    ],
+                    [
+                        4,
+                        5,
+                        411
+                    ],
+                    [
+                        4,
+                        0,
+                        198
+                    ],
+                    [
+                        3,
+                        1,
+                        770
+                    ],
+                    [
+                        2,
+                        5,
+                        26
+                    ],
+                    [
+                        1,
+                        5,
+                        989
+                    ],
+                    [
+                        5,
+                        0,
+                        911
+                    ],
+                    [
+                        6,
+                        3,
+                        189
+                    ],
+                    [
+                        4,
+                        5,
+                        108
+                    ],
+                    [
+                        3,
+                        6,
+                        34
+                    ],
+                    [
+                        2,
+                        3,
+                        246
+                    ],
+                    [
+                        4,
+                        1,
+                        966
+                    ],
+                    [
+                        4,
+                        5,
+                        599
+                    ],
+                    [
+                        6,
+                        5,
+                        1000
+                    ],
+                    [
+                        2,
+                        1,
+                        125
+                    ],
+                    [
+                        2,
+                        5,
+                        483
+                    ],
+                    [
+                        0,
+                        5,
+                        979
+                    ],
+                    [
+                        4,
+                        3,
+                        28
+                    ],
+                    [
+                        4,
+                        6,
+                        823
+                    ],
+                    [
+                        1,
+                        5,
+                        871
+                    ],
+                    [
+                        4,
+                        6,
+                        847
+                    ],
+                    [
+                        1,
+                        6,
+                        50
+                    ],
+                    [
+                        0,
+                        6,
+                        212
+                    ],
+                    [
+                        2,
+                        1,
+                        594
+                    ],
+                    [
+                        5,
+                        1,
+                        697
+                    ],
+                    [
+                        5,
+                        4,
+                        655
+                    ],
+                    [
+                        2,
+                        0,
+                        489
+                    ],
+                    [
+                        0,
+                        5,
+                        980
+                    ],
+                    [
+                        5,
+                        0,
+                        364
+                    ],
+                    [
+                        2,
+                        4,
+                        797
+                    ],
+                    [
+                        6,
+                        5,
+                        730
+                    ],
+                    [
+                        4,
+                        2,
+                        756
+                    ],
+                    [
+                        6,
+                        0,
+                        588
+                    ],
+                    [
+                        1,
+                        2,
+                        467
+                    ],
+                    [
+                        0,
+                        5,
+                        240
+                    ],
+                    [
+                        6,
+                        3,
+                        25
+                    ],
+                    [
+                        6,
+                        0,
+                        870
+                    ],
+                    [
+                        5,
+                        4,
+                        132
+                    ],
+                    [
+                        0,
+                        6,
+                        870
+                    ],
+                    [
+                        6,
+                        4,
+                        886
+                    ],
+                    [
+                        5,
+                        6,
+                        809
+                    ],
+                    [
+                        2,
+                        1,
+                        991
+                    ],
+                    [
+                        4,
+                        6,
+                        869
+                    ],
+                    [
+                        5,
+                        3,
+                        430
+                    ],
+                    [
+                        0,
+                        2,
+                        223
+                    ],
+                    [
+                        1,
+                        5,
+                        337
+                    ],
+                    [
+                        6,
+                        1,
+                        740
+                    ],
+                    [
+                        5,
+                        4,
+                        259
+                    ],
+                    [
+                        1,
+                        4,
+                        618
+                    ],
+                    [
+                        6,
+                        5,
+                        89
+                    ],
+                    [
+                        5,
+                        3,
+                        401
+                    ],
+                    [
+                        3,
+                        4,
+                        956
+                    ],
+                    [
+                        5,
+                        4,
+                        100
+                    ],
+                    [
+                        0,
+                        4,
+                        779
+                    ],
+                    [
+                        4,
+                        2,
+                        274
+                    ],
+                    [
+                        0,
+                        5,
+                        452
+                    ],
+                    [
+                        6,
+                        3,
+                        341
+                    ],
+                    [
+                        1,
+                        5,
+                        374
+                    ],
+                    [
+                        6,
+                        2,
+                        437
+                    ],
+                    [
+                        1,
+                        2,
+                        138
+                    ],
+                    [
+                        6,
+                        4,
+                        809
+                    ],
+                    [
+                        5,
+                        1,
+                        408
+                    ],
+                    [
+                        1,
+                        0,
+                        698
+                    ],
+                    [
+                        4,
+                        6,
+                        452
+                    ],
+                    [
+                        4,
+                        1,
+                        716
+                    ],
+                    [
+                        1,
+                        2,
+                        602
+                    ],
+                    [
+                        3,
+                        6,
+                        327
+                    ],
+                    [
+                        5,
+                        1,
+                        709
+                    ],
+                    [
+                        6,
+                        2,
+                        542
+                    ],
+                    [
+                        5,
+                        2,
+                        470
+                    ],
+                    [
+                        2,
+                        0,
+                        252
+                    ],
+                    [
+                        5,
+                        0,
+                        16
+                    ],
+                    [
+                        1,
+                        5,
+                        49
+                    ],
+                    [
+                        5,
+                        2,
+                        355
+                    ],
+                    [
+                        5,
+                        0,
+                        773
+                    ],
+                    [
+                        2,
+                        5,
+                        926
+                    ],
+                    [
+                        1,
+                        6,
+                        400
+                    ],
+                    [
+                        5,
+                        0,
+                        996
+                    ],
+                    [
+                        1,
+                        5,
+                        880
+                    ],
+                    [
+                        1,
+                        4,
+                        322
+                    ],
+                    [
+                        0,
+                        3,
+                        234
+                    ],
+                    [
+                        6,
+                        4,
+                        181
+                    ],
+                    [
+                        3,
+                        2,
+                        723
+                    ],
+                    [
+                        6,
+                        3,
+                        122
+                    ],
+                    [
+                        2,
+                        6,
+                        340
+                    ],
+                    [
+                        6,
+                        5,
+                        624
+                    ],
+                    [
+                        0,
+                        1,
+                        913
+                    ],
+                    [
+                        0,
+                        2,
+                        663
+                    ],
+                    [
+                        5,
+                        0,
+                        523
+                    ],
+                    [
+                        0,
+                        3,
+                        805
+                    ],
+                    [
+                        0,
+                        6,
+                        250
+                    ],
+                    [
+                        3,
+                        2,
+                        896
+                    ],
+                    [
+                        1,
+                        5,
+                        106
+                    ],
+                    [
+                        0,
+                        2,
+                        529
+                    ],
+                    [
+                        4,
+                        5,
+                        375
+                    ],
+                    [
+                        6,
+                        5,
+                        591
+                    ],
+                    [
+                        5,
+                        2,
+                        725
+                    ],
+                    [
+                        3,
+                        2,
+                        577
+                    ],
+                    [
+                        4,
+                        1,
+                        97
+                    ],
+                    [
+                        2,
+                        5,
+                        537
+                    ],
+                    [
+                        6,
+                        5,
+                        835
+                    ],
+                    [
+                        0,
+                        5,
+                        398
+                    ],
+                    [
+                        3,
+                        4,
+                        442
+                    ],
+                    [
+                        1,
+                        2,
+                        901
+                    ],
+                    [
+                        0,
+                        5,
+                        738
+                    ],
+                    [
+                        6,
+                        0,
+                        537
+                    ],
+                    [
+                        5,
+                        1,
+                        527
+                    ],
+                    [
+                        1,
+                        5,
+                        709
+                    ],
+                    [
+                        2,
+                        5,
+                        38
+                    ],
+                    [
+                        3,
+                        0,
+                        48
+                    ],
+                    [
+                        5,
+                        1,
+                        278
+                    ],
+                    [
+                        2,
+                        0,
+                        799
+                    ],
+                    [
+                        6,
+                        4,
+                        792
+                    ],
+                    [
+                        2,
+                        1,
+                        274
+                    ],
+                    [
+                        1,
+                        5,
+                        136
+                    ],
+                    [
+                        5,
+                        0,
+                        145
+                    ],
+                    [
+                        0,
+                        3,
+                        466
+                    ],
+                    [
+                        5,
+                        3,
+                        833
+                    ],
+                    [
+                        4,
+                        1,
+                        915
+                    ],
+                    [
+                        2,
+                        4,
+                        843
+                    ],
+                    [
+                        3,
+                        2,
+                        100
+                    ],
+                    [
+                        2,
+                        6,
+                        279
+                    ],
+                    [
+                        2,
+                        5,
+                        483
+                    ],
+                    [
+                        6,
+                        3,
+                        950
+                    ],
+                    [
+                        5,
+                        4,
+                        16
+                    ],
+                    [
+                        0,
+                        1,
+                        951
+                    ],
+                    [
+                        2,
+                        6,
+                        171
+                    ],
+                    [
+                        2,
+                        0,
+                        95
+                    ],
+                    [
+                        4,
+                        5,
+                        349
+                    ],
+                    [
+                        0,
+                        5,
+                        170
+                    ],
+                    [
+                        0,
+                        1,
+                        287
+                    ],
+                    [
+                        6,
+                        4,
+                        526
+                    ],
+                    [
+                        1,
+                        5,
+                        613
+                    ],
+                    [
+                        6,
+                        5,
+                        887
+                    ],
+                    [
+                        0,
+                        2,
+                        100
+                    ],
+                    [
+                        1,
+                        0,
+                        717
+                    ],
+                    [
+                        3,
+                        4,
+                        965
+                    ],
+                    [
+                        2,
+                        5,
+                        601
+                    ],
+                    [
+                        3,
+                        6,
+                        594
+                    ],
+                    [
+                        2,
+                        3,
+                        473
+                    ],
+                    [
+                        3,
+                        0,
+                        205
+                    ],
+                    [
+                        4,
+                        2,
+                        713
+                    ],
+                    [
+                        1,
+                        2,
+                        664
+                    ],
+                    [
+                        4,
+                        0,
+                        107
+                    ],
+                    [
+                        4,
+                        2,
+                        894
+                    ],
+                    [
+                        2,
+                        4,
+                        77
+                    ],
+                    [
+                        5,
+                        2,
+                        437
+                    ],
+                    [
+                        5,
+                        0,
+                        379
+                    ],
+                    [
+                        4,
+                        3,
+                        553
+                    ],
+                    [
+                        0,
+                        2,
+                        576
+                    ],
+                    [
+                        0,
+                        4,
+                        105
+                    ],
+                    [
+                        3,
+                        5,
+                        843
+                    ],
+                    [
+                        6,
+                        5,
+                        706
+                    ],
+                    [
+                        2,
+                        4,
+                        276
+                    ],
+                    [
+                        0,
+                        1,
+                        301
+                    ],
+                    [
+                        0,
+                        2,
+                        190
+                    ],
+                    [
+                        2,
+                        6,
+                        617
+                    ],
+                    [
+                        4,
+                        0,
+                        898
+                    ],
+                    [
+                        5,
+                        6,
+                        247
+                    ],
+                    [
+                        4,
+                        1,
+                        914
+                    ],
+                    [
+                        5,
+                        2,
+                        423
+                    ],
+                    [
+                        1,
+                        5,
+                        253
+                    ],
+                    [
+                        6,
+                        0,
+                        978
+                    ],
+                    [
+                        2,
+                        0,
+                        538
+                    ],
+                    [
+                        2,
+                        6,
+                        693
+                    ],
+                    [
+                        0,
+                        3,
+                        661
+                    ],
+                    [
+                        4,
+                        1,
+                        403
+                    ],
+                    [
+                        6,
+                        4,
+                        332
+                    ],
+                    [
+                        1,
+                        2,
+                        563
+                    ],
+                    [
+                        4,
+                        1,
+                        645
+                    ],
+                    [
+                        6,
+                        0,
+                        202
+                    ],
+                    [
+                        6,
+                        4,
+                        761
+                    ],
+                    [
+                        2,
+                        0,
+                        672
+                    ],
+                    [
+                        4,
+                        1,
+                        904
+                    ],
+                    [
+                        5,
+                        1,
+                        546
+                    ],
+                    [
+                        6,
+                        5,
+                        280
+                    ],
+                    [
+                        2,
+                        1,
+                        107
+                    ],
+                    [
+                        1,
+                        3,
+                        665
+                    ],
+                    [
+                        3,
+                        4,
+                        985
+                    ],
+                    [
+                        5,
+                        6,
+                        97
+                    ],
+                    [
+                        4,
+                        2,
+                        707
+                    ],
+                    [
+                        6,
+                        2,
+                        624
+                    ],
+                    [
+                        5,
+                        6,
+                        535
+                    ],
+                    [
+                        5,
+                        0,
+                        133
+                    ],
+                    [
+                        6,
+                        2,
+                        868
+                    ],
+                    [
+                        3,
+                        6,
+                        229
+                    ],
+                    [
+                        6,
+                        4,
+                        835
+                    ],
+                    [
+                        5,
+                        0,
+                        278
+                    ],
+                    [
+                        2,
+                        5,
+                        105
+                    ],
+                    [
+                        4,
+                        6,
+                        102
+                    ],
+                    [
+                        4,
+                        0,
+                        699
+                    ],
+                    [
+                        0,
+                        3,
+                        365
+                    ],
+                    [
+                        4,
+                        6,
+                        791
+                    ],
+                    [
+                        4,
+                        0,
+                        708
+                    ],
+                    [
+                        1,
+                        0,
+                        824
+                    ],
+                    [
+                        2,
+                        6,
+                        358
+                    ],
+                    [
+                        6,
+                        4,
+                        669
+                    ],
+                    [
+                        0,
+                        3,
+                        951
+                    ],
+                    [
+                        5,
+                        0,
+                        546
+                    ],
+                    [
+                        1,
+                        5,
+                        566
+                    ],
+                    [
+                        3,
+                        2,
+                        674
+                    ],
+                    [
+                        4,
+                        3,
+                        544
+                    ],
+                    [
+                        3,
+                        5,
+                        104
+                    ],
+                    [
+                        6,
+                        2,
+                        180
+                    ],
+                    [
+                        3,
+                        2,
+                        196
+                    ],
+                    [
+                        3,
+                        6,
+                        472
+                    ],
+                    [
+                        0,
+                        5,
+                        605
+                    ],
+                    [
+                        3,
+                        6,
+                        382
+                    ],
+                    [
+                        2,
+                        0,
+                        772
+                    ],
+                    [
+                        0,
+                        2,
+                        660
+                    ],
+                    [
+                        3,
+                        5,
+                        249
+                    ],
+                    [
+                        6,
+                        5,
+                        577
+                    ],
+                    [
+                        5,
+                        0,
+                        551
+                    ],
+                    [
+                        3,
+                        6,
+                        5
+                    ],
+                    [
+                        1,
+                        6,
+                        460
+                    ],
+                    [
+                        1,
+                        0,
+                        303
+                    ],
+                    [
+                        6,
+                        4,
+                        746
+                    ],
+                    [
+                        2,
+                        4,
+                        53
+                    ],
+                    [
+                        2,
+                        4,
+                        946
+                    ],
+                    [
+                        6,
+                        1,
+                        563
+                    ],
+                    [
+                        6,
+                        5,
+                        816
+                    ],
+                    [
+                        3,
+                        6,
+                        953
+                    ],
+                    [
+                        0,
+                        4,
+                        812
+                    ],
+                    [
+                        0,
+                        4,
+                        1
+                    ],
+                    [
+                        3,
+                        2,
+                        690
+                    ],
+                    [
+                        4,
+                        6,
+                        607
+                    ],
+                    [
+                        0,
+                        2,
+                        263
+                    ],
+                    [
+                        5,
+                        1,
+                        859
+                    ],
+                    [
+                        4,
+                        2,
+                        424
+                    ],
+                    [
+                        4,
+                        6,
+                        350
+                    ],
+                    [
+                        0,
+                        2,
+                        760
+                    ],
+                    [
+                        5,
+                        6,
+                        725
+                    ],
+                    [
+                        2,
+                        4,
+                        604
+                    ],
+                    [
+                        1,
+                        0,
+                        562
+                    ],
+                    [
+                        3,
+                        5,
+                        822
+                    ],
+                    [
+                        2,
+                        5,
+                        78
+                    ],
+                    [
+                        5,
+                        6,
+                        650
+                    ],
+                    [
+                        5,
+                        0,
+                        991
+                    ],
+                    [
+                        0,
+                        2,
+                        160
+                    ],
+                    [
+                        4,
+                        2,
+                        560
+                    ],
+                    [
+                        1,
+                        4,
+                        801
+                    ],
+                    [
+                        2,
+                        5,
+                        158
+                    ],
+                    [
+                        5,
+                        4,
+                        503
+                    ],
+                    [
+                        3,
+                        6,
+                        930
+                    ],
+                    [
+                        6,
+                        3,
+                        423
+                    ],
+                    [
+                        4,
+                        3,
+                        463
+                    ],
+                    [
+                        2,
+                        1,
+                        264
+                    ],
+                    [
+                        4,
+                        3,
+                        886
+                    ],
+                    [
+                        0,
+                        3,
+                        336
+                    ],
+                    [
+                        1,
+                        6,
+                        413
+                    ],
+                    [
+                        0,
+                        6,
+                        723
+                    ],
+                    [
+                        4,
+                        5,
+                        954
+                    ],
+                    [
+                        2,
+                        6,
+                        689
+                    ],
+                    [
+                        0,
+                        1,
+                        189
+                    ],
+                    [
+                        4,
+                        0,
+                        384
+                    ],
+                    [
+                        5,
+                        3,
+                        603
+                    ],
+                    [
+                        4,
+                        3,
+                        29
+                    ],
+                    [
+                        3,
+                        6,
+                        926
+                    ],
+                    [
+                        0,
+                        2,
+                        390
+                    ],
+                    [
+                        3,
+                        0,
+                        965
+                    ],
+                    [
+                        3,
+                        6,
+                        57
+                    ],
+                    [
+                        5,
+                        6,
+                        919
+                    ],
+                    [
+                        4,
+                        3,
+                        711
+                    ],
+                    [
+                        1,
+                        2,
+                        579
+                    ],
+                    [
+                        2,
+                        6,
+                        950
+                    ],
+                    [
+                        4,
+                        5,
+                        783
+                    ],
+                    [
+                        5,
+                        4,
+                        687
+                    ],
+                    [
+                        3,
+                        4,
+                        167
+                    ],
+                    [
+                        3,
+                        1,
+                        214
+                    ],
+                    [
+                        4,
+                        2,
+                        629
+                    ],
+                    [
+                        2,
+                        0,
+                        512
+                    ],
+                    [
+                        6,
+                        1,
+                        913
+                    ],
+                    [
+                        6,
+                        3,
+                        42
+                    ],
+                    [
+                        1,
+                        6,
+                        190
+                    ],
+                    [
+                        6,
+                        5,
+                        891
+                    ],
+                    [
+                        4,
+                        6,
+                        20
+                    ],
+                    [
+                        3,
+                        4,
+                        182
+                    ],
+                    [
+                        2,
+                        1,
+                        123
+                    ],
+                    [
+                        0,
+                        2,
+                        749
+                    ],
+                    [
+                        6,
+                        5,
+                        621
+                    ],
+                    [
+                        4,
+                        2,
+                        162
+                    ],
+                    [
+                        6,
+                        5,
+                        240
+                    ],
+                    [
+                        1,
+                        0,
+                        702
+                    ],
+                    [
+                        3,
+                        2,
+                        638
+                    ],
+                    [
+                        0,
+                        6,
+                        728
+                    ],
+                    [
+                        0,
+                        5,
+                        324
+                    ],
+                    [
+                        4,
+                        0,
+                        982
+                    ],
+                    [
+                        6,
+                        2,
+                        378
+                    ],
+                    [
+                        4,
+                        2,
+                        175
+                    ],
+                    [
+                        3,
+                        4,
+                        505
+                    ],
+                    [
+                        6,
+                        4,
+                        91
+                    ],
+                    [
+                        6,
+                        3,
+                        69
+                    ],
+                    [
+                        3,
+                        1,
+                        619
+                    ],
+                    [
+                        1,
+                        2,
+                        726
+                    ],
+                    [
+                        4,
+                        6,
+                        606
+                    ],
+                    [
+                        3,
+                        2,
+                        785
+                    ],
+                    [
+                        4,
+                        5,
+                        849
+                    ],
+                    [
+                        6,
+                        4,
+                        796
+                    ],
+                    [
+                        2,
+                        6,
+                        430
+                    ],
+                    [
+                        2,
+                        4,
+                        358
+                    ],
+                    [
+                        5,
+                        1,
+                        175
+                    ],
+                    [
+                        5,
+                        6,
+                        188
+                    ],
+                    [
+                        4,
+                        1,
+                        848
+                    ],
+                    [
+                        5,
+                        4,
+                        543
+                    ],
+                    [
+                        2,
+                        1,
+                        77
+                    ],
+                    [
+                        1,
+                        2,
+                        25
+                    ],
+                    [
+                        2,
+                        0,
+                        339
+                    ],
+                    [
+                        1,
+                        4,
+                        986
+                    ],
+                    [
+                        0,
+                        6,
+                        418
+                    ],
+                    [
+                        3,
+                        6,
+                        718
+                    ],
+                    [
+                        2,
+                        5,
+                        742
+                    ],
+                    [
+                        4,
+                        2,
+                        498
+                    ],
+                    [
+                        1,
+                        6,
+                        255
+                    ],
+                    [
+                        2,
+                        3,
+                        666
+                    ],
+                    [
+                        0,
+                        1,
+                        257
+                    ],
+                    [
+                        5,
+                        1,
+                        989
+                    ],
+                    [
+                        1,
+                        0,
+                        157
+                    ],
+                    [
+                        6,
+                        2,
+                        48
+                    ],
+                    [
+                        5,
+                        6,
+                        596
+                    ],
+                    [
+                        0,
+                        1,
+                        331
+                    ],
+                    [
+                        5,
+                        2,
+                        607
+                    ],
+                    [
+                        1,
+                        3,
+                        352
+                    ],
+                    [
+                        6,
+                        4,
+                        331
+                    ],
+                    [
+                        5,
+                        1,
+                        959
+                    ],
+                    [
+                        5,
+                        4,
+                        82
+                    ],
+                    [
+                        0,
+                        4,
+                        480
+                    ],
+                    [
+                        1,
+                        0,
+                        282
+                    ],
+                    [
+                        5,
+                        0,
+                        763
+                    ],
+                    [
+                        3,
+                        6,
+                        856
+                    ],
+                    [
+                        4,
+                        2,
+                        883
+                    ],
+                    [
+                        4,
+                        6,
+                        232
+                    ],
+                    [
+                        4,
+                        2,
+                        708
+                    ],
+                    [
+                        5,
+                        3,
+                        595
+                    ],
+                    [
+                        4,
+                        6,
+                        467
+                    ],
+                    [
+                        6,
+                        0,
+                        303
+                    ],
+                    [
+                        3,
+                        2,
+                        531
+                    ],
+                    [
+                        6,
+                        0,
+                        1
+                    ],
+                    [
+                        4,
+                        3,
+                        560
+                    ],
+                    [
+                        0,
+                        3,
+                        284
+                    ],
+                    [
+                        4,
+                        3,
+                        977
+                    ],
+                    [
+                        2,
+                        5,
+                        853
+                    ],
+                    [
+                        2,
+                        4,
+                        179
+                    ],
+                    [
+                        6,
+                        3,
+                        936
+                    ],
+                    [
+                        1,
+                        2,
+                        699
+                    ],
+                    [
+                        2,
+                        4,
+                        601
+                    ],
+                    [
+                        5,
+                        1,
+                        486
+                    ],
+                    [
+                        2,
+                        0,
+                        352
+                    ],
+                    [
+                        3,
+                        6,
+                        480
+                    ],
+                    [
+                        4,
+                        3,
+                        614
+                    ],
+                    [
+                        2,
+                        4,
+                        913
+                    ],
+                    [
+                        2,
+                        4,
+                        310
+                    ],
+                    [
+                        3,
+                        6,
+                        840
+                    ],
+                    [
+                        1,
+                        5,
+                        568
+                    ],
+                    [
+                        4,
+                        5,
+                        155
+                    ],
+                    [
+                        5,
+                        2,
+                        272
+                    ],
+                    [
+                        0,
+                        6,
+                        97
+                    ],
+                    [
+                        5,
+                        3,
+                        26
+                    ],
+                    [
+                        0,
+                        4,
+                        950
+                    ],
+                    [
+                        5,
+                        0,
+                        995
+                    ],
+                    [
+                        2,
+                        4,
+                        359
+                    ],
+                    [
+                        2,
+                        1,
+                        124
+                    ],
+                    [
+                        2,
+                        3,
+                        856
+                    ],
+                    [
+                        4,
+                        1,
+                        895
+                    ],
+                    [
+                        3,
+                        0,
+                        456
+                    ],
+                    [
+                        3,
+                        5,
+                        79
+                    ],
+                    [
+                        0,
+                        1,
+                        979
+                    ],
+                    [
+                        3,
+                        6,
+                        522
+                    ],
+                    [
+                        1,
+                        5,
+                        805
+                    ],
+                    [
+                        0,
+                        3,
+                        943
+                    ],
+                    [
+                        2,
+                        3,
+                        741
+                    ],
+                    [
+                        2,
+                        1,
+                        223
+                    ],
+                    [
+                        1,
+                        3,
+                        715
+                    ],
+                    [
+                        5,
+                        2,
+                        470
+                    ],
+                    [
+                        6,
+                        5,
+                        616
+                    ],
+                    [
+                        1,
+                        3,
+                        513
+                    ],
+                    [
+                        3,
+                        6,
+                        633
+                    ],
+                    [
+                        0,
+                        6,
+                        501
+                    ],
+                    [
+                        5,
+                        0,
+                        804
+                    ],
+                    [
+                        5,
+                        0,
+                        39
+                    ],
+                    [
+                        6,
+                        1,
+                        722
+                    ],
+                    [
+                        5,
+                        6,
+                        561
+                    ],
+                    [
+                        4,
+                        1,
+                        384
+                    ],
+                    [
+                        6,
+                        4,
+                        423
+                    ],
+                    [
+                        0,
+                        1,
+                        321
+                    ],
+                    [
+                        3,
+                        2,
+                        904
+                    ],
+                    [
+                        6,
+                        1,
+                        619
+                    ],
+                    [
+                        5,
+                        2,
+                        492
+                    ],
+                    [
+                        2,
+                        5,
+                        886
+                    ],
+                    [
+                        5,
+                        4,
+                        495
+                    ],
+                    [
+                        1,
+                        2,
+                        835
+                    ],
+                    [
+                        5,
+                        4,
+                        806
+                    ],
+                    [
+                        1,
+                        6,
+                        696
+                    ],
+                    [
+                        5,
+                        0,
+                        735
+                    ],
+                    [
+                        5,
+                        2,
+                        528
+                    ],
+                    [
+                        1,
+                        0,
+                        696
+                    ],
+                    [
+                        3,
+                        2,
+                        298
+                    ],
+                    [
+                        2,
+                        3,
+                        373
+                    ],
+                    [
+                        6,
+                        0,
+                        939
+                    ],
+                    [
+                        1,
+                        5,
+                        403
+                    ],
+                    [
+                        2,
+                        4,
+                        507
+                    ],
+                    [
+                        2,
+                        0,
+                        705
+                    ],
+                    [
+                        3,
+                        5,
+                        531
+                    ],
+                    [
+                        5,
+                        0,
+                        328
+                    ],
+                    [
+                        4,
+                        6,
+                        754
+                    ],
+                    [
+                        2,
+                        6,
+                        542
+                    ],
+                    [
+                        0,
+                        5,
+                        614
+                    ],
+                    [
+                        0,
+                        2,
+                        56
+                    ],
+                    [
+                        2,
+                        5,
+                        898
+                    ],
+                    [
+                        0,
+                        5,
+                        903
+                    ],
+                    [
+                        6,
+                        5,
+                        306
+                    ],
+                    [
+                        6,
+                        1,
+                        911
+                    ],
+                    [
+                        4,
+                        5,
+                        729
+                    ],
+                    [
+                        1,
+                        6,
+                        194
+                    ],
+                    [
+                        2,
+                        1,
+                        375
+                    ],
+                    [
+                        6,
+                        5,
+                        261
+                    ],
+                    [
+                        2,
+                        4,
+                        1000
+                    ],
+                    [
+                        3,
+                        5,
+                        794
+                    ],
+                    [
+                        0,
+                        3,
+                        278
+                    ],
+                    [
+                        0,
+                        3,
+                        808
+                    ],
+                    [
+                        1,
+                        4,
+                        648
+                    ],
+                    [
+                        4,
+                        5,
+                        2
+                    ],
+                    [
+                        6,
+                        2,
+                        128
+                    ],
+                    [
+                        5,
+                        2,
+                        581
+                    ],
+                    [
+                        5,
+                        2,
+                        236
+                    ],
+                    [
+                        2,
+                        3,
+                        638
+                    ],
+                    [
+                        6,
+                        1,
+                        761
+                    ],
+                    [
+                        5,
+                        3,
+                        767
+                    ],
+                    [
+                        0,
+                        4,
+                        822
+                    ],
+                    [
+                        0,
+                        3,
+                        621
+                    ],
+                    [
+                        5,
+                        3,
+                        977
+                    ],
+                    [
+                        4,
+                        1,
+                        134
+                    ],
+                    [
+                        0,
+                        2,
+                        865
+                    ],
+                    [
+                        1,
+                        6,
+                        70
+                    ],
+                    [
+                        3,
+                        4,
+                        631
+                    ],
+                    [
+                        5,
+                        4,
+                        574
+                    ],
+                    [
+                        3,
+                        0,
+                        304
+                    ],
+                    [
+                        3,
+                        2,
+                        680
+                    ],
+                    [
+                        4,
+                        1,
+                        1
+                    ],
+                    [
+                        3,
+                        1,
+                        614
+                    ],
+                    [
+                        2,
+                        3,
+                        230
+                    ],
+                    [
+                        0,
+                        2,
+                        451
+                    ],
+                    [
+                        5,
+                        3,
+                        279
+                    ],
+                    [
+                        2,
+                        1,
+                        592
+                    ],
+                    [
+                        1,
+                        4,
+                        357
+                    ],
+                    [
+                        1,
+                        2,
+                        238
+                    ],
+                    [
+                        5,
+                        0,
+                        214
+                    ],
+                    [
+                        5,
+                        6,
+                        528
+                    ],
+                    [
+                        4,
+                        0,
+                        265
+                    ],
+                    [
+                        2,
+                        3,
+                        621
+                    ],
+                    [
+                        6,
+                        1,
+                        904
+                    ],
+                    [
+                        3,
+                        5,
+                        345
+                    ],
+                    [
+                        5,
+                        4,
+                        730
+                    ],
+                    [
+                        0,
+                        2,
+                        711
+                    ],
+                    [
+                        5,
+                        1,
+                        641
+                    ],
+                    [
+                        5,
+                        0,
+                        997
+                    ],
+                    [
+                        1,
+                        6,
+                        20
+                    ],
+                    [
+                        0,
+                        4,
+                        853
+                    ],
+                    [
+                        3,
+                        4,
+                        847
+                    ],
+                    [
+                        6,
+                        4,
+                        704
+                    ],
+                    [
+                        2,
+                        0,
+                        514
+                    ],
+                    [
+                        6,
+                        2,
+                        590
+                    ],
+                    [
+                        1,
+                        3,
+                        660
+                    ],
+                    [
+                        4,
+                        5,
+                        481
+                    ],
+                    [
+                        1,
+                        3,
+                        647
+                    ],
+                    [
+                        4,
+                        1,
+                        54
+                    ],
+                    [
+                        2,
+                        6,
+                        953
+                    ],
+                    [
+                        1,
+                        0,
+                        131
+                    ],
+                    [
+                        3,
+                        1,
+                        953
+                    ],
+                    [
+                        6,
+                        5,
+                        489
+                    ],
+                    [
+                        1,
+                        2,
+                        567
+                    ],
+                    [
+                        5,
+                        0,
+                        113
+                    ],
+                    [
+                        3,
+                        5,
+                        182
+                    ],
+                    [
+                        1,
+                        3,
+                        96
+                    ],
+                    [
+                        2,
+                        0,
+                        37
+                    ],
+                    [
+                        3,
+                        5,
+                        126
+                    ],
+                    [
+                        2,
+                        6,
+                        315
+                    ],
+                    [
+                        6,
+                        1,
+                        387
+                    ],
+                    [
+                        3,
+                        4,
+                        112
+                    ],
+                    [
+                        1,
+                        2,
+                        56
+                    ],
+                    [
+                        6,
+                        3,
+                        851
+                    ],
+                    [
+                        5,
+                        2,
+                        176
+                    ],
+                    [
+                        5,
+                        0,
+                        560
+                    ],
+                    [
+                        6,
+                        2,
+                        3
+                    ],
+                    [
+                        5,
+                        6,
+                        489
+                    ],
+                    [
+                        1,
+                        3,
+                        910
+                    ],
+                    [
+                        2,
+                        6,
+                        560
+                    ],
+                    [
+                        6,
+                        2,
+                        361
+                    ],
+                    [
+                        2,
+                        6,
+                        528
+                    ],
+                    [
+                        3,
+                        2,
+                        70
+                    ],
+                    [
+                        4,
+                        2,
+                        646
+                    ],
+                    [
+                        6,
+                        0,
+                        52
+                    ],
+                    [
+                        4,
+                        5,
+                        598
+                    ],
+                    [
+                        4,
+                        5,
+                        771
+                    ],
+                    [
+                        1,
+                        5,
+                        716
+                    ],
+                    [
+                        4,
+                        1,
+                        704
+                    ],
+                    [
+                        2,
+                        1,
+                        74
+                    ],
+                    [
+                        3,
+                        0,
+                        659
+                    ],
+                    [
+                        4,
+                        3,
+                        698
+                    ],
+                    [
+                        2,
+                        6,
+                        498
+                    ],
+                    [
+                        3,
+                        0,
+                        39
+                    ],
+                    [
+                        5,
+                        4,
+                        47
+                    ],
+                    [
+                        0,
+                        2,
+                        379
+                    ],
+                    [
+                        3,
+                        5,
+                        116
+                    ],
+                    [
+                        5,
+                        2,
+                        590
+                    ],
+                    [
+                        1,
+                        2,
+                        955
+                    ],
+                    [
+                        4,
+                        6,
+                        942
+                    ],
+                    [
+                        5,
+                        2,
+                        246
+                    ],
+                    [
+                        1,
+                        6,
+                        720
+                    ],
+                    [
+                        1,
+                        4,
+                        304
+                    ],
+                    [
+                        4,
+                        2,
+                        600
+                    ],
+                    [
+                        0,
+                        1,
+                        490
+                    ],
+                    [
+                        2,
+                        6,
+                        170
+                    ],
+                    [
+                        6,
+                        0,
+                        941
+                    ],
+                    [
+                        5,
+                        4,
+                        488
+                    ],
+                    [
+                        2,
+                        4,
+                        20
+                    ],
+                    [
+                        5,
+                        6,
+                        762
+                    ],
+                    [
+                        5,
+                        4,
+                        629
+                    ],
+                    [
+                        1,
+                        4,
+                        983
+                    ],
+                    [
+                        6,
+                        4,
+                        201
+                    ],
+                    [
+                        2,
+                        4,
+                        119
+                    ],
+                    [
+                        5,
+                        1,
+                        74
+                    ],
+                    [
+                        1,
+                        2,
+                        953
+                    ],
+                    [
+                        4,
+                        1,
+                        364
+                    ],
+                    [
+                        5,
+                        2,
+                        246
+                    ],
+                    [
+                        0,
+                        3,
+                        360
+                    ],
+                    [
+                        2,
+                        6,
+                        861
+                    ],
+                    [
+                        3,
+                        6,
+                        201
+                    ],
+                    [
+                        3,
+                        1,
+                        2
+                    ],
+                    [
+                        5,
+                        1,
+                        849
+                    ],
+                    [
+                        1,
+                        0,
+                        631
+                    ],
+                    [
+                        6,
+                        5,
+                        315
+                    ],
+                    [
+                        3,
+                        1,
+                        148
+                    ],
+                    [
+                        0,
+                        6,
+                        40
+                    ],
+                    [
+                        5,
+                        1,
+                        423
+                    ],
+                    [
+                        6,
+                        1,
+                        662
+                    ],
+                    [
+                        3,
+                        6,
+                        868
+                    ],
+                    [
+                        4,
+                        6,
+                        678
+                    ],
+                    [
+                        2,
+                        0,
+                        907
+                    ],
+                    [
+                        1,
+                        3,
+                        184
+                    ],
+                    [
+                        1,
+                        2,
+                        697
+                    ],
+                    [
+                        1,
+                        4,
+                        768
+                    ],
+                    [
+                        6,
+                        0,
+                        34
+                    ],
+                    [
+                        5,
+                        4,
+                        423
+                    ],
+                    [
+                        3,
+                        4,
+                        547
+                    ],
+                    [
+                        1,
+                        0,
+                        312
+                    ],
+                    [
+                        6,
+                        3,
+                        26
+                    ],
+                    [
+                        5,
+                        3,
+                        729
+                    ],
+                    [
+                        5,
+                        3,
+                        935
+                    ],
+                    [
+                        2,
+                        4,
+                        948
+                    ],
+                    [
+                        3,
+                        2,
+                        688
+                    ],
+                    [
+                        1,
+                        6,
+                        891
+                    ],
+                    [
+                        1,
+                        6,
+                        361
+                    ],
+                    [
+                        2,
+                        3,
+                        965
+                    ],
+                    [
+                        3,
+                        6,
+                        537
+                    ],
+                    [
+                        1,
+                        6,
+                        204
+                    ],
+                    [
+                        0,
+                        5,
+                        138
+                    ],
+                    [
+                        0,
+                        4,
+                        764
+                    ],
+                    [
+                        4,
+                        1,
+                        241
+                    ],
+                    [
+                        3,
+                        4,
+                        299
+                    ],
+                    [
+                        4,
+                        6,
+                        70
+                    ],
+                    [
+                        4,
+                        1,
+                        403
+                    ],
+                    [
+                        5,
+                        4,
+                        278
+                    ],
+                    [
+                        5,
+                        4,
+                        339
+                    ],
+                    [
+                        2,
+                        0,
+                        571
+                    ],
+                    [
+                        2,
+                        3,
+                        443
+                    ],
+                    [
+                        6,
+                        1,
+                        175
+                    ],
+                    [
+                        0,
+                        4,
+                        598
+                    ],
+                    [
+                        3,
+                        4,
+                        859
+                    ],
+                    [
+                        4,
+                        2,
+                        635
+                    ],
+                    [
+                        2,
+                        0,
+                        498
+                    ],
+                    [
+                        1,
+                        6,
+                        65
+                    ],
+                    [
+                        6,
+                        3,
+                        273
+                    ],
+                    [
+                        3,
+                        5,
+                        1000
+                    ],
+                    [
+                        5,
+                        1,
+                        336
+                    ],
+                    [
+                        0,
+                        6,
+                        493
+                    ],
+                    [
+                        6,
+                        0,
+                        493
+                    ],
+                    [
+                        4,
+                        1,
+                        691
+                    ],
+                    [
+                        6,
+                        3,
+                        843
+                    ],
+                    [
+                        4,
+                        1,
+                        524
+                    ],
+                    [
+                        3,
+                        4,
+                        971
+                    ],
+                    [
+                        0,
+                        2,
+                        387
+                    ],
+                    [
+                        0,
+                        3,
+                        632
+                    ],
+                    [
+                        6,
+                        2,
+                        70
+                    ],
+                    [
+                        5,
+                        4,
+                        869
+                    ],
+                    [
+                        2,
+                        6,
+                        487
+                    ],
+                    [
+                        2,
+                        1,
+                        294
+                    ],
+                    [
+                        2,
+                        3,
+                        822
+                    ],
+                    [
+                        2,
+                        3,
+                        329
+                    ],
+                    [
+                        5,
+                        3,
+                        881
+                    ],
+                    [
+                        1,
+                        3,
+                        795
+                    ],
+                    [
+                        5,
+                        0,
+                        206
+                    ],
+                    [
+                        5,
+                        4,
+                        540
+                    ],
+                    [
+                        1,
+                        0,
+                        731
+                    ],
+                    [
+                        0,
+                        5,
+                        423
+                    ],
+                    [
+                        4,
+                        6,
+                        547
+                    ],
+                    [
+                        5,
+                        3,
+                        893
+                    ],
+                    [
+                        6,
+                        3,
+                        678
+                    ],
+                    [
+                        0,
+                        5,
+                        747
+                    ],
+                    [
+                        0,
+                        3,
+                        109
+                    ],
+                    [
+                        0,
+                        6,
+                        250
+                    ],
+                    [
+                        6,
+                        0,
+                        160
+                    ],
+                    [
+                        0,
+                        4,
+                        969
+                    ],
+                    [
+                        3,
+                        5,
+                        717
+                    ],
+                    [
+                        5,
+                        6,
+                        229
+                    ],
+                    [
+                        5,
+                        2,
+                        792
+                    ],
+                    [
+                        4,
+                        6,
+                        598
+                    ],
+                    [
+                        3,
+                        1,
+                        738
+                    ],
+                    [
+                        5,
+                        6,
+                        248
+                    ],
+                    [
+                        1,
+                        6,
+                        48
+                    ],
+                    [
+                        4,
+                        6,
+                        336
+                    ],
+                    [
+                        3,
+                        6,
+                        705
+                    ],
+                    [
+                        0,
+                        2,
+                        379
+                    ],
+                    [
+                        4,
+                        3,
+                        820
+                    ],
+                    [
+                        6,
+                        1,
+                        509
+                    ],
+                    [
+                        3,
+                        5,
+                        454
+                    ],
+                    [
+                        4,
+                        1,
+                        684
+                    ],
+                    [
+                        3,
+                        1,
+                        341
+                    ],
+                    [
+                        4,
+                        3,
+                        372
+                    ],
+                    [
+                        2,
+                        4,
+                        399
+                    ],
+                    [
+                        3,
+                        4,
+                        160
+                    ],
+                    [
+                        5,
+                        3,
+                        694
+                    ],
+                    [
+                        6,
+                        1,
+                        404
+                    ],
+                    [
+                        0,
+                        1,
+                        465
+                    ],
+                    [
+                        1,
+                        5,
+                        985
+                    ],
+                    [
+                        4,
+                        6,
+                        894
+                    ],
+                    [
+                        6,
+                        0,
+                        794
+                    ],
+                    [
+                        0,
+                        4,
+                        170
+                    ],
+                    [
+                        2,
+                        6,
+                        289
+                    ],
+                    [
+                        4,
+                        1,
+                        260
+                    ],
+                    [
+                        2,
+                        4,
+                        458
+                    ],
+                    [
+                        5,
+                        1,
+                        831
+                    ],
+                    [
+                        4,
+                        1,
+                        908
+                    ],
+                    [
+                        3,
+                        5,
+                        477
+                    ],
+                    [
+                        6,
+                        3,
+                        35
+                    ],
+                    [
+                        1,
+                        0,
+                        11
+                    ],
+                    [
+                        5,
+                        3,
+                        912
+                    ],
+                    [
+                        1,
+                        0,
+                        36
+                    ],
+                    [
+                        5,
+                        6,
+                        894
+                    ],
+                    [
+                        6,
+                        2,
+                        913
+                    ],
+                    [
+                        2,
+                        5,
+                        490
+                    ],
+                    [
+                        4,
+                        5,
+                        314
+                    ],
+                    [
+                        2,
+                        3,
+                        497
+                    ],
+                    [
+                        6,
+                        3,
+                        333
+                    ],
+                    [
+                        0,
+                        1,
+                        893
+                    ],
+                    [
+                        1,
+                        0,
+                        269
+                    ],
+                    [
+                        5,
+                        3,
+                        635
+                    ],
+                    [
+                        2,
+                        3,
+                        643
+                    ],
+                    [
+                        6,
+                        2,
+                        468
+                    ],
+                    [
+                        6,
+                        3,
+                        262
+                    ],
+                    [
+                        5,
+                        0,
+                        812
+                    ],
+                    [
+                        3,
+                        0,
+                        535
+                    ],
+                    [
+                        6,
+                        3,
+                        407
+                    ],
+                    [
+                        3,
+                        6,
+                        299
+                    ],
+                    [
+                        0,
+                        4,
+                        114
+                    ],
+                    [
+                        2,
+                        6,
+                        521
+                    ],
+                    [
+                        4,
+                        2,
+                        618
+                    ],
+                    [
+                        6,
+                        5,
+                        201
+                    ],
+                    [
+                        1,
+                        5,
+                        781
+                    ],
+                    [
+                        5,
+                        3,
+                        248
+                    ],
+                    [
+                        6,
+                        0,
+                        328
+                    ],
+                    [
+                        3,
+                        0,
+                        455
+                    ],
+                    [
+                        1,
+                        2,
+                        483
+                    ],
+                    [
+                        3,
+                        2,
+                        643
+                    ],
+                    [
+                        3,
+                        0,
+                        695
+                    ],
+                    [
+                        2,
+                        6,
+                        502
+                    ],
+                    [
+                        6,
+                        0,
+                        194
+                    ],
+                    [
+                        4,
+                        6,
+                        640
+                    ],
+                    [
+                        4,
+                        3,
+                        12
+                    ],
+                    [
+                        6,
+                        2,
+                        20
+                    ],
+                    [
+                        5,
+                        0,
+                        5
+                    ],
+                    [
+                        3,
+                        0,
+                        256
+                    ],
+                    [
+                        3,
+                        5,
+                        719
+                    ],
+                    [
+                        1,
+                        0,
+                        902
+                    ],
+                    [
+                        5,
+                        1,
+                        344
+                    ],
+                    [
+                        0,
+                        5,
+                        198
+                    ],
+                    [
+                        0,
+                        6,
+                        609
+                    ],
+                    [
+                        0,
+                        3,
+                        741
+                    ],
+                    [
+                        4,
+                        3,
+                        710
+                    ],
+                    [
+                        6,
+                        2,
+                        812
+                    ],
+                    [
+                        2,
+                        5,
+                        530
+                    ],
+                    [
+                        2,
+                        3,
+                        304
+                    ],
+                    [
+                        4,
+                        5,
+                        895
+                    ],
+                    [
+                        6,
+                        3,
+                        955
+                    ],
+                    [
+                        6,
+                        3,
+                        145
+                    ],
+                    [
+                        4,
+                        0,
+                        268
+                    ],
+                    [
+                        6,
+                        3,
+                        518
+                    ],
+                    [
+                        0,
+                        2,
+                        903
+                    ],
+                    [
+                        2,
+                        6,
+                        627
+                    ],
+                    [
+                        2,
+                        5,
+                        69
+                    ],
+                    [
+                        5,
+                        1,
+                        117
+                    ],
+                    [
+                        6,
+                        5,
+                        904
+                    ],
+                    [
+                        2,
+                        5,
+                        977
+                    ],
+                    [
+                        1,
+                        5,
+                        649
+                    ],
+                    [
+                        4,
+                        0,
+                        192
+                    ],
+                    [
+                        5,
+                        6,
+                        913
+                    ],
+                    [
+                        1,
+                        6,
+                        972
+                    ],
+                    [
+                        2,
+                        1,
+                        494
+                    ],
+                    [
+                        0,
+                        5,
+                        240
+                    ],
+                    [
+                        4,
+                        2,
+                        460
+                    ],
+                    [
+                        2,
+                        0,
+                        356
+                    ],
+                    [
+                        0,
+                        6,
+                        720
+                    ],
+                    [
+                        6,
+                        3,
+                        281
+                    ],
+                    [
+                        2,
+                        3,
+                        327
+                    ],
+                    [
+                        6,
+                        3,
+                        792
+                    ],
+                    [
+                        5,
+                        0,
+                        852
+                    ],
+                    [
+                        6,
+                        1,
+                        302
+                    ],
+                    [
+                        3,
+                        2,
+                        331
+                    ],
+                    [
+                        0,
+                        2,
+                        126
+                    ],
+                    [
+                        0,
+                        3,
+                        31
+                    ],
+                    [
+                        0,
+                        1,
+                        387
+                    ],
+                    [
+                        4,
+                        5,
+                        695
+                    ],
+                    [
+                        1,
+                        4,
+                        68
+                    ],
+                    [
+                        2,
+                        3,
+                        118
+                    ],
+                    [
+                        4,
+                        0,
+                        1
+                    ],
+                    [
+                        1,
+                        0,
+                        993
+                    ],
+                    [
+                        1,
+                        2,
+                        661
+                    ],
+                    [
+                        6,
+                        5,
+                        91
+                    ],
+                    [
+                        0,
+                        3,
+                        147
+                    ],
+                    [
+                        0,
+                        5,
+                        984
+                    ],
+                    [
+                        4,
+                        5,
+                        621
+                    ],
+                    [
+                        5,
+                        2,
+                        583
+                    ],
+                    [
+                        1,
+                        2,
+                        537
+                    ],
+                    [
+                        1,
+                        6,
+                        882
+                    ],
+                    [
+                        4,
+                        2,
+                        46
+                    ],
+                    [
+                        4,
+                        5,
+                        112
+                    ],
+                    [
+                        6,
+                        0,
+                        418
+                    ],
+                    [
+                        0,
+                        2,
+                        1000
+                    ],
+                    [
+                        5,
+                        2,
+                        514
+                    ],
+                    [
+                        0,
+                        3,
+                        798
+                    ],
+                    [
+                        6,
+                        1,
+                        883
+                    ],
+                    [
+                        4,
+                        6,
+                        444
+                    ],
+                    [
+                        4,
+                        5,
+                        154
+                    ],
+                    [
+                        3,
+                        0,
+                        23
+                    ],
+                    [
+                        5,
+                        0,
+                        495
+                    ],
+                    [
+                        4,
+                        3,
+                        676
+                    ],
+                    [
+                        1,
+                        3,
+                        539
+                    ],
+                    [
+                        1,
+                        6,
+                        653
+                    ],
+                    [
+                        6,
+                        2,
+                        464
+                    ],
+                    [
+                        6,
+                        1,
+                        322
+                    ],
+                    [
+                        3,
+                        6,
+                        126
+                    ],
+                    [
+                        4,
+                        0,
+                        644
+                    ],
+                    [
+                        2,
+                        0,
+                        472
+                    ],
+                    [
+                        5,
+                        3,
+                        601
+                    ],
+                    [
+                        5,
+                        3,
+                        643
+                    ],
+                    [
+                        5,
+                        4,
+                        885
+                    ],
+                    [
+                        0,
+                        5,
+                        360
+                    ],
+                    [
+                        1,
+                        5,
+                        672
+                    ],
+                    [
+                        5,
+                        1,
+                        861
+                    ],
+                    [
+                        1,
+                        3,
+                        951
+                    ],
+                    [
+                        5,
+                        0,
+                        135
+                    ],
+                    [
+                        2,
+                        6,
+                        852
+                    ],
+                    [
+                        0,
+                        6,
+                        265
+                    ],
+                    [
+                        3,
+                        5,
+                        454
+                    ],
+                    [
+                        3,
+                        5,
+                        479
+                    ],
+                    [
+                        0,
+                        2,
+                        8
+                    ],
+                    [
+                        1,
+                        6,
+                        571
+                    ],
+                    [
+                        3,
+                        5,
+                        83
+                    ],
+                    [
+                        1,
+                        4,
+                        238
+                    ],
+                    [
+                        4,
+                        3,
+                        477
+                    ],
+                    [
+                        4,
+                        3,
+                        120
+                    ],
+                    [
+                        3,
+                        1,
+                        521
+                    ],
+                    [
+                        3,
+                        5,
+                        88
+                    ],
+                    [
+                        6,
+                        4,
+                        510
+                    ],
+                    [
+                        5,
+                        4,
+                        311
+                    ],
+                    [
+                        6,
+                        5,
+                        321
+                    ],
+                    [
+                        2,
+                        4,
+                        430
+                    ],
+                    [
+                        2,
+                        4,
+                        763
+                    ],
+                    [
+                        1,
+                        6,
+                        353
+                    ],
+                    [
+                        1,
+                        3,
+                        435
+                    ],
+                    [
+                        5,
+                        6,
+                        95
+                    ],
+                    [
+                        2,
+                        4,
+                        809
+                    ],
+                    [
+                        6,
+                        1,
+                        870
+                    ],
+                    [
+                        0,
+                        4,
+                        249
+                    ],
+                    [
+                        1,
+                        2,
+                        393
+                    ],
+                    [
+                        5,
+                        6,
+                        315
+                    ],
+                    [
+                        3,
+                        1,
+                        222
+                    ],
+                    [
+                        2,
+                        0,
+                        410
+                    ],
+                    [
+                        2,
+                        0,
+                        686
+                    ],
+                    [
+                        6,
+                        5,
+                        478
+                    ],
+                    [
+                        0,
+                        4,
+                        621
+                    ],
+                    [
+                        5,
+                        3,
+                        662
+                    ],
+                    [
+                        5,
+                        2,
+                        300
+                    ],
+                    [
+                        0,
+                        3,
+                        591
+                    ],
+                    [
+                        1,
+                        6,
+                        850
+                    ],
+                    [
+                        6,
+                        0,
+                        919
+                    ],
+                    [
+                        1,
+                        4,
+                        182
+                    ],
+                    [
+                        1,
+                        6,
+                        639
+                    ],
+                    [
+                        6,
+                        3,
+                        606
+                    ],
+                    [
+                        5,
+                        4,
+                        590
+                    ],
+                    [
+                        1,
+                        0,
+                        360
+                    ],
+                    [
+                        1,
+                        2,
+                        189
+                    ],
+                    [
+                        6,
+                        5,
+                        734
+                    ],
+                    [
+                        1,
+                        5,
+                        130
+                    ],
+                    [
+                        0,
+                        2,
+                        638
+                    ],
+                    [
+                        6,
+                        5,
+                        803
+                    ],
+                    [
+                        2,
+                        3,
+                        80
+                    ],
+                    [
+                        5,
+                        6,
+                        350
+                    ],
+                    [
+                        2,
+                        3,
+                        935
+                    ],
+                    [
+                        4,
+                        3,
+                        175
+                    ],
+                    [
+                        4,
+                        6,
+                        584
+                    ],
+                    [
+                        2,
+                        4,
+                        266
+                    ],
+                    [
+                        5,
+                        3,
+                        223
+                    ],
+                    [
+                        1,
+                        4,
+                        471
+                    ],
+                    [
+                        1,
+                        6,
+                        351
+                    ],
+                    [
+                        4,
+                        0,
+                        623
+                    ],
+                    [
+                        6,
+                        5,
+                        777
+                    ],
+                    [
+                        3,
+                        2,
+                        887
+                    ],
+                    [
+                        1,
+                        5,
+                        681
+                    ],
+                    [
+                        5,
+                        6,
+                        223
+                    ],
+                    [
+                        3,
+                        2,
+                        931
+                    ],
+                    [
+                        1,
+                        6,
+                        283
+                    ],
+                    [
+                        1,
+                        3,
+                        59
+                    ],
+                    [
+                        4,
+                        5,
+                        190
+                    ],
+                    [
+                        5,
+                        1,
+                        1000
+                    ],
+                    [
+                        5,
+                        2,
+                        168
+                    ],
+                    [
+                        1,
+                        5,
+                        936
+                    ],
+                    [
+                        1,
+                        6,
+                        826
+                    ],
+                    [
+                        2,
+                        3,
+                        295
+                    ],
+                    [
+                        1,
+                        5,
+                        937
+                    ],
+                    [
+                        2,
+                        6,
+                        213
+                    ],
+                    [
+                        2,
+                        6,
+                        843
+                    ],
+                    [
+                        5,
+                        4,
+                        57
+                    ],
+                    [
+                        2,
+                        0,
+                        98
+                    ],
+                    [
+                        0,
+                        5,
+                        576
+                    ],
+                    [
+                        3,
+                        6,
+                        130
+                    ],
+                    [
+                        0,
+                        2,
+                        140
+                    ],
+                    [
+                        4,
+                        6,
+                        499
+                    ],
+                    [
+                        2,
+                        0,
+                        508
+                    ],
+                    [
+                        6,
+                        4,
+                        219
+                    ],
+                    [
+                        4,
+                        0,
+                        71
+                    ],
+                    [
+                        4,
+                        3,
+                        71
+                    ],
+                    [
+                        4,
+                        0,
+                        817
+                    ],
+                    [
+                        3,
+                        5,
+                        913
+                    ],
+                    [
+                        1,
+                        2,
+                        149
+                    ],
+                    [
+                        3,
+                        6,
+                        550
+                    ],
+                    [
+                        4,
+                        0,
+                        908
+                    ],
+                    [
+                        5,
+                        2,
+                        125
+                    ],
+                    [
+                        5,
+                        1,
+                        792
+                    ],
+                    [
+                        3,
+                        6,
+                        191
+                    ],
+                    [
+                        3,
+                        0,
+                        826
+                    ],
+                    [
+                        1,
+                        4,
+                        460
+                    ],
+                    [
+                        1,
+                        5,
+                        912
+                    ],
+                    [
+                        5,
+                        1,
+                        640
+                    ],
+                    [
+                        2,
+                        1,
+                        723
+                    ],
+                    [
+                        6,
+                        5,
+                        993
+                    ],
+                    [
+                        1,
+                        4,
+                        169
+                    ],
+                    [
+                        0,
+                        4,
+                        250
+                    ]
+                ]
+            ],
+            "output": 128
+        },
+        {
+            "input": [
+                6,
+                30727,
+                [
+                    [
+                        3,
+                        2,
+                        83
+                    ],
+                    [
+                        4,
+                        2,
+                        676
+                    ],
+                    [
+                        4,
+                        0,
+                        914
+                    ],
+                    [
+                        2,
+                        3,
+                        401
+                    ],
+                    [
+                        4,
+                        2,
+                        78
+                    ],
+                    [
+                        0,
+                        4,
+                        633
+                    ],
+                    [
+                        0,
+                        3,
+                        603
+                    ],
+                    [
+                        1,
+                        3,
+                        802
+                    ],
+                    [
+                        3,
+                        1,
+                        21
+                    ],
+                    [
+                        2,
+                        1,
+                        393
+                    ],
+                    [
+                        3,
+                        1,
+                        608
+                    ],
+                    [
+                        5,
+                        3,
+                        551
+                    ],
+                    [
+                        1,
+                        4,
+                        12
+                    ],
+                    [
+                        4,
+                        3,
+                        458
+                    ],
+                    [
+                        4,
+                        0,
+                        48
+                    ],
+                    [
+                        4,
+                        0,
+                        757
+                    ],
+                    [
+                        1,
+                        2,
+                        659
+                    ],
+                    [
+                        2,
+                        5,
+                        880
+                    ],
+                    [
+                        1,
+                        0,
+                        307
+                    ],
+                    [
+                        4,
+                        3,
+                        70
+                    ],
+                    [
+                        3,
+                        1,
+                        181
+                    ],
+                    [
+                        0,
+                        2,
+                        778
+                    ],
+                    [
+                        0,
+                        3,
+                        575
+                    ],
+                    [
+                        0,
+                        5,
+                        826
+                    ],
+                    [
+                        0,
+                        2,
+                        452
+                    ],
+                    [
+                        0,
+                        4,
+                        99
+                    ],
+                    [
+                        1,
+                        0,
+                        18
+                    ],
+                    [
+                        1,
+                        2,
+                        760
+                    ],
+                    [
+                        3,
+                        4,
+                        668
+                    ],
+                    [
+                        5,
+                        1,
+                        960
+                    ],
+                    [
+                        0,
+                        3,
+                        134
+                    ],
+                    [
+                        3,
+                        0,
+                        402
+                    ],
+                    [
+                        5,
+                        2,
+                        883
+                    ],
+                    [
+                        1,
+                        4,
+                        825
+                    ],
+                    [
+                        5,
+                        1,
+                        300
+                    ],
+                    [
+                        2,
+                        0,
+                        208
+                    ],
+                    [
+                        4,
+                        5,
+                        205
+                    ],
+                    [
+                        0,
+                        1,
+                        482
+                    ],
+                    [
+                        1,
+                        3,
+                        16
+                    ],
+                    [
+                        2,
+                        1,
+                        545
+                    ],
+                    [
+                        4,
+                        1,
+                        220
+                    ],
+                    [
+                        3,
+                        0,
+                        888
+                    ],
+                    [
+                        2,
+                        5,
+                        937
+                    ],
+                    [
+                        5,
+                        4,
+                        170
+                    ],
+                    [
+                        2,
+                        3,
+                        572
+                    ],
+                    [
+                        3,
+                        2,
+                        118
+                    ],
+                    [
+                        2,
+                        4,
+                        406
+                    ],
+                    [
+                        1,
+                        3,
+                        692
+                    ],
+                    [
+                        5,
+                        3,
+                        346
+                    ],
+                    [
+                        0,
+                        1,
+                        659
+                    ],
+                    [
+                        3,
+                        5,
+                        277
+                    ],
+                    [
+                        1,
+                        2,
+                        688
+                    ],
+                    [
+                        2,
+                        4,
+                        31
+                    ],
+                    [
+                        1,
+                        0,
+                        699
+                    ],
+                    [
+                        2,
+                        4,
+                        63
+                    ],
+                    [
+                        4,
+                        3,
+                        911
+                    ],
+                    [
+                        5,
+                        4,
+                        278
+                    ],
+                    [
+                        4,
+                        0,
+                        78
+                    ],
+                    [
+                        4,
+                        5,
+                        291
+                    ],
+                    [
+                        4,
+                        0,
+                        264
+                    ],
+                    [
+                        0,
+                        5,
+                        826
+                    ],
+                    [
+                        3,
+                        0,
+                        883
+                    ],
+                    [
+                        3,
+                        0,
+                        677
+                    ],
+                    [
+                        1,
+                        2,
+                        66
+                    ],
+                    [
+                        3,
+                        0,
+                        347
+                    ],
+                    [
+                        5,
+                        1,
+                        172
+                    ],
+                    [
+                        2,
+                        5,
+                        33
+                    ],
+                    [
+                        5,
+                        2,
+                        630
+                    ],
+                    [
+                        0,
+                        1,
+                        560
+                    ],
+                    [
+                        5,
+                        2,
+                        425
+                    ],
+                    [
+                        4,
+                        1,
+                        99
+                    ],
+                    [
+                        0,
+                        3,
+                        613
+                    ],
+                    [
+                        3,
+                        5,
+                        529
+                    ],
+                    [
+                        3,
+                        5,
+                        570
+                    ],
+                    [
+                        5,
+                        2,
+                        589
+                    ],
+                    [
+                        1,
+                        5,
+                        285
+                    ],
+                    [
+                        5,
+                        4,
+                        394
+                    ],
+                    [
+                        1,
+                        3,
+                        504
+                    ],
+                    [
+                        2,
+                        3,
+                        105
+                    ],
+                    [
+                        3,
+                        4,
+                        736
+                    ],
+                    [
+                        1,
+                        0,
+                        52
+                    ],
+                    [
+                        1,
+                        5,
+                        257
+                    ],
+                    [
+                        1,
+                        3,
+                        348
+                    ],
+                    [
+                        5,
+                        0,
+                        83
+                    ],
+                    [
+                        4,
+                        5,
+                        338
+                    ],
+                    [
+                        0,
+                        4,
+                        584
+                    ],
+                    [
+                        2,
+                        3,
+                        792
+                    ],
+                    [
+                        1,
+                        3,
+                        744
+                    ],
+                    [
+                        3,
+                        1,
+                        456
+                    ],
+                    [
+                        0,
+                        3,
+                        1
+                    ],
+                    [
+                        4,
+                        2,
+                        607
+                    ],
+                    [
+                        5,
+                        4,
+                        726
+                    ],
+                    [
+                        0,
+                        4,
+                        425
+                    ],
+                    [
+                        2,
+                        3,
+                        211
+                    ],
+                    [
+                        0,
+                        1,
+                        834
+                    ],
+                    [
+                        2,
+                        5,
+                        28
+                    ],
+                    [
+                        3,
+                        2,
+                        808
+                    ],
+                    [
+                        2,
+                        3,
+                        86
+                    ],
+                    [
+                        0,
+                        2,
+                        50
+                    ],
+                    [
+                        2,
+                        3,
+                        963
+                    ],
+                    [
+                        0,
+                        3,
+                        1
+                    ],
+                    [
+                        3,
+                        0,
+                        124
+                    ],
+                    [
+                        3,
+                        2,
+                        244
+                    ],
+                    [
+                        4,
+                        0,
+                        657
+                    ],
+                    [
+                        5,
+                        2,
+                        983
+                    ],
+                    [
+                        0,
+                        3,
+                        772
+                    ],
+                    [
+                        4,
+                        1,
+                        196
+                    ],
+                    [
+                        3,
+                        1,
+                        543
+                    ],
+                    [
+                        5,
+                        4,
+                        974
+                    ],
+                    [
+                        4,
+                        0,
+                        241
+                    ],
+                    [
+                        0,
+                        5,
+                        755
+                    ],
+                    [
+                        1,
+                        0,
+                        893
+                    ],
+                    [
+                        1,
+                        3,
+                        611
+                    ],
+                    [
+                        3,
+                        1,
+                        875
+                    ],
+                    [
+                        0,
+                        1,
+                        681
+                    ],
+                    [
+                        4,
+                        3,
+                        424
+                    ],
+                    [
+                        5,
+                        2,
+                        697
+                    ],
+                    [
+                        2,
+                        1,
+                        6
+                    ],
+                    [
+                        2,
+                        3,
+                        738
+                    ],
+                    [
+                        2,
+                        3,
+                        62
+                    ],
+                    [
+                        5,
+                        0,
+                        152
+                    ],
+                    [
+                        3,
+                        4,
+                        305
+                    ],
+                    [
+                        2,
+                        0,
+                        542
+                    ],
+                    [
+                        0,
+                        5,
+                        861
+                    ],
+                    [
+                        2,
+                        0,
+                        903
+                    ],
+                    [
+                        0,
+                        5,
+                        853
+                    ],
+                    [
+                        0,
+                        3,
+                        206
+                    ],
+                    [
+                        0,
+                        4,
+                        432
+                    ],
+                    [
+                        2,
+                        5,
+                        444
+                    ],
+                    [
+                        0,
+                        1,
+                        621
+                    ],
+                    [
+                        5,
+                        3,
+                        976
+                    ],
+                    [
+                        5,
+                        0,
+                        450
+                    ],
+                    [
+                        5,
+                        4,
+                        255
+                    ],
+                    [
+                        3,
+                        5,
+                        141
+                    ],
+                    [
+                        4,
+                        5,
+                        181
+                    ],
+                    [
+                        5,
+                        3,
+                        815
+                    ],
+                    [
+                        5,
+                        0,
+                        773
+                    ],
+                    [
+                        4,
+                        3,
+                        528
+                    ],
+                    [
+                        5,
+                        4,
+                        862
+                    ],
+                    [
+                        1,
+                        2,
+                        8
+                    ],
+                    [
+                        4,
+                        2,
+                        798
+                    ],
+                    [
+                        5,
+                        2,
+                        960
+                    ],
+                    [
+                        1,
+                        5,
+                        255
+                    ],
+                    [
+                        0,
+                        4,
+                        700
+                    ],
+                    [
+                        3,
+                        4,
+                        223
+                    ],
+                    [
+                        1,
+                        2,
+                        775
+                    ],
+                    [
+                        5,
+                        3,
+                        109
+                    ],
+                    [
+                        1,
+                        5,
+                        828
+                    ],
+                    [
+                        3,
+                        0,
+                        559
+                    ],
+                    [
+                        1,
+                        3,
+                        830
+                    ],
+                    [
+                        0,
+                        2,
+                        595
+                    ],
+                    [
+                        5,
+                        0,
+                        474
+                    ],
+                    [
+                        4,
+                        5,
+                        290
+                    ],
+                    [
+                        4,
+                        1,
+                        23
+                    ],
+                    [
+                        3,
+                        0,
+                        947
+                    ],
+                    [
+                        2,
+                        1,
+                        578
+                    ],
+                    [
+                        4,
+                        3,
+                        151
+                    ],
+                    [
+                        2,
+                        1,
+                        40
+                    ],
+                    [
+                        1,
+                        4,
+                        808
+                    ],
+                    [
+                        0,
+                        5,
+                        590
+                    ],
+                    [
+                        4,
+                        5,
+                        455
+                    ],
+                    [
+                        5,
+                        2,
+                        847
+                    ],
+                    [
+                        1,
+                        4,
+                        504
+                    ],
+                    [
+                        2,
+                        5,
+                        11
+                    ],
+                    [
+                        3,
+                        5,
+                        60
+                    ],
+                    [
+                        3,
+                        4,
+                        236
+                    ],
+                    [
+                        5,
+                        3,
+                        257
+                    ],
+                    [
+                        4,
+                        0,
+                        313
+                    ],
+                    [
+                        4,
+                        3,
+                        513
+                    ],
+                    [
+                        0,
+                        3,
+                        782
+                    ],
+                    [
+                        2,
+                        0,
+                        975
+                    ],
+                    [
+                        5,
+                        2,
+                        461
+                    ],
+                    [
+                        5,
+                        0,
+                        420
+                    ],
+                    [
+                        0,
+                        5,
+                        817
+                    ],
+                    [
+                        4,
+                        0,
+                        773
+                    ],
+                    [
+                        4,
+                        3,
+                        756
+                    ],
+                    [
+                        4,
+                        1,
+                        44
+                    ],
+                    [
+                        1,
+                        4,
+                        577
+                    ],
+                    [
+                        5,
+                        0,
+                        168
+                    ],
+                    [
+                        0,
+                        5,
+                        323
+                    ],
+                    [
+                        1,
+                        4,
+                        497
+                    ],
+                    [
+                        4,
+                        5,
+                        890
+                    ],
+                    [
+                        2,
+                        3,
+                        348
+                    ],
+                    [
+                        0,
+                        3,
+                        142
+                    ],
+                    [
+                        4,
+                        2,
+                        822
+                    ],
+                    [
+                        1,
+                        0,
+                        954
+                    ],
+                    [
+                        0,
+                        2,
+                        918
+                    ],
+                    [
+                        3,
+                        1,
+                        617
+                    ],
+                    [
+                        5,
+                        1,
+                        175
+                    ],
+                    [
+                        5,
+                        3,
+                        694
+                    ],
+                    [
+                        2,
+                        1,
+                        829
+                    ],
+                    [
+                        1,
+                        3,
+                        604
+                    ],
+                    [
+                        3,
+                        0,
+                        467
+                    ],
+                    [
+                        1,
+                        2,
+                        22
+                    ],
+                    [
+                        0,
+                        4,
+                        583
+                    ],
+                    [
+                        0,
+                        5,
+                        479
+                    ],
+                    [
+                        5,
+                        2,
+                        873
+                    ],
+                    [
+                        5,
+                        2,
+                        603
+                    ],
+                    [
+                        4,
+                        5,
+                        315
+                    ],
+                    [
+                        5,
+                        3,
+                        814
+                    ],
+                    [
+                        1,
+                        4,
+                        737
+                    ],
+                    [
+                        3,
+                        2,
+                        157
+                    ],
+                    [
+                        0,
+                        4,
+                        453
+                    ],
+                    [
+                        1,
+                        4,
+                        440
+                    ],
+                    [
+                        2,
+                        3,
+                        265
+                    ],
+                    [
+                        3,
+                        2,
+                        525
+                    ],
+                    [
+                        4,
+                        0,
+                        920
+                    ],
+                    [
+                        0,
+                        3,
+                        470
+                    ],
+                    [
+                        4,
+                        5,
+                        549
+                    ],
+                    [
+                        2,
+                        0,
+                        503
+                    ],
+                    [
+                        2,
+                        5,
+                        568
+                    ],
+                    [
+                        0,
+                        4,
+                        307
+                    ],
+                    [
+                        3,
+                        5,
+                        740
+                    ],
+                    [
+                        5,
+                        4,
+                        46
+                    ],
+                    [
+                        5,
+                        0,
+                        447
+                    ],
+                    [
+                        3,
+                        5,
+                        395
+                    ],
+                    [
+                        1,
+                        3,
+                        227
+                    ],
+                    [
+                        1,
+                        0,
+                        435
+                    ],
+                    [
+                        5,
+                        3,
+                        328
+                    ],
+                    [
+                        1,
+                        5,
+                        637
+                    ],
+                    [
+                        2,
+                        0,
+                        952
+                    ],
+                    [
+                        5,
+                        1,
+                        22
+                    ],
+                    [
+                        3,
+                        0,
+                        571
+                    ],
+                    [
+                        5,
+                        1,
+                        474
+                    ],
+                    [
+                        5,
+                        2,
+                        35
+                    ],
+                    [
+                        5,
+                        2,
+                        626
+                    ],
+                    [
+                        3,
+                        0,
+                        535
+                    ],
+                    [
+                        0,
+                        5,
+                        63
+                    ],
+                    [
+                        1,
+                        0,
+                        63
+                    ],
+                    [
+                        2,
+                        3,
+                        679
+                    ],
+                    [
+                        3,
+                        0,
+                        520
+                    ],
+                    [
+                        2,
+                        3,
+                        886
+                    ],
+                    [
+                        0,
+                        1,
+                        958
+                    ],
+                    [
+                        0,
+                        1,
+                        665
+                    ],
+                    [
+                        1,
+                        2,
+                        122
+                    ],
+                    [
+                        0,
+                        1,
+                        830
+                    ],
+                    [
+                        3,
+                        1,
+                        326
+                    ],
+                    [
+                        5,
+                        2,
+                        7
+                    ],
+                    [
+                        4,
+                        3,
+                        73
+                    ],
+                    [
+                        4,
+                        0,
+                        496
+                    ],
+                    [
+                        5,
+                        4,
+                        946
+                    ],
+                    [
+                        1,
+                        3,
+                        488
+                    ],
+                    [
+                        5,
+                        0,
+                        480
+                    ],
+                    [
+                        2,
+                        5,
+                        517
+                    ],
+                    [
+                        2,
+                        4,
+                        750
+                    ],
+                    [
+                        4,
+                        5,
+                        614
+                    ],
+                    [
+                        2,
+                        5,
+                        279
+                    ],
+                    [
+                        0,
+                        1,
+                        714
+                    ],
+                    [
+                        3,
+                        4,
+                        186
+                    ],
+                    [
+                        1,
+                        2,
+                        276
+                    ],
+                    [
+                        2,
+                        4,
+                        883
+                    ],
+                    [
+                        2,
+                        5,
+                        774
+                    ],
+                    [
+                        3,
+                        0,
+                        891
+                    ],
+                    [
+                        5,
+                        4,
+                        799
+                    ],
+                    [
+                        3,
+                        2,
+                        635
+                    ],
+                    [
+                        4,
+                        0,
+                        468
+                    ],
+                    [
+                        0,
+                        1,
+                        562
+                    ],
+                    [
+                        0,
+                        4,
+                        751
+                    ],
+                    [
+                        0,
+                        3,
+                        180
+                    ],
+                    [
+                        2,
+                        0,
+                        291
+                    ],
+                    [
+                        3,
+                        0,
+                        395
+                    ],
+                    [
+                        1,
+                        2,
+                        442
+                    ],
+                    [
+                        3,
+                        5,
+                        895
+                    ],
+                    [
+                        2,
+                        3,
+                        108
+                    ],
+                    [
+                        5,
+                        2,
+                        430
+                    ],
+                    [
+                        3,
+                        2,
+                        657
+                    ],
+                    [
+                        2,
+                        1,
+                        764
+                    ],
+                    [
+                        4,
+                        2,
+                        246
+                    ],
+                    [
+                        5,
+                        1,
+                        646
+                    ],
+                    [
+                        3,
+                        0,
+                        76
+                    ],
+                    [
+                        3,
+                        5,
+                        801
+                    ],
+                    [
+                        0,
+                        3,
+                        476
+                    ],
+                    [
+                        3,
+                        0,
+                        62
+                    ],
+                    [
+                        1,
+                        0,
+                        891
+                    ],
+                    [
+                        3,
+                        0,
+                        210
+                    ],
+                    [
+                        1,
+                        0,
+                        610
+                    ],
+                    [
+                        0,
+                        2,
+                        978
+                    ],
+                    [
+                        1,
+                        3,
+                        470
+                    ],
+                    [
+                        2,
+                        5,
+                        691
+                    ],
+                    [
+                        3,
+                        0,
+                        636
+                    ],
+                    [
+                        5,
+                        2,
+                        624
+                    ],
+                    [
+                        0,
+                        1,
+                        1
+                    ],
+                    [
+                        3,
+                        2,
+                        630
+                    ],
+                    [
+                        0,
+                        4,
+                        579
+                    ],
+                    [
+                        1,
+                        3,
+                        63
+                    ],
+                    [
+                        4,
+                        0,
+                        243
+                    ],
+                    [
+                        2,
+                        0,
+                        914
+                    ],
+                    [
+                        3,
+                        0,
+                        275
+                    ],
+                    [
+                        4,
+                        1,
+                        625
+                    ],
+                    [
+                        1,
+                        0,
+                        621
+                    ],
+                    [
+                        3,
+                        1,
+                        704
+                    ],
+                    [
+                        2,
+                        4,
+                        934
+                    ],
+                    [
+                        0,
+                        3,
+                        900
+                    ],
+                    [
+                        1,
+                        5,
+                        245
+                    ],
+                    [
+                        1,
+                        2,
+                        768
+                    ],
+                    [
+                        5,
+                        2,
+                        412
+                    ],
+                    [
+                        5,
+                        3,
+                        952
+                    ],
+                    [
+                        3,
+                        1,
+                        303
+                    ],
+                    [
+                        1,
+                        4,
+                        369
+                    ],
+                    [
+                        4,
+                        0,
+                        976
+                    ],
+                    [
+                        2,
+                        5,
+                        86
+                    ],
+                    [
+                        4,
+                        0,
+                        309
+                    ],
+                    [
+                        5,
+                        2,
+                        341
+                    ],
+                    [
+                        1,
+                        5,
+                        143
+                    ],
+                    [
+                        1,
+                        3,
+                        122
+                    ],
+                    [
+                        3,
+                        0,
+                        847
+                    ],
+                    [
+                        3,
+                        2,
+                        75
+                    ],
+                    [
+                        2,
+                        1,
+                        340
+                    ],
+                    [
+                        1,
+                        2,
+                        224
+                    ],
+                    [
+                        5,
+                        1,
+                        509
+                    ],
+                    [
+                        0,
+                        4,
+                        619
+                    ],
+                    [
+                        1,
+                        5,
+                        197
+                    ],
+                    [
+                        3,
+                        1,
+                        936
+                    ],
+                    [
+                        1,
+                        4,
+                        634
+                    ],
+                    [
+                        1,
+                        5,
+                        455
+                    ],
+                    [
+                        2,
+                        3,
+                        541
+                    ],
+                    [
+                        5,
+                        1,
+                        126
+                    ],
+                    [
+                        0,
+                        5,
+                        42
+                    ],
+                    [
+                        0,
+                        1,
+                        445
+                    ],
+                    [
+                        3,
+                        5,
+                        913
+                    ],
+                    [
+                        2,
+                        1,
+                        104
+                    ],
+                    [
+                        2,
+                        3,
+                        88
+                    ],
+                    [
+                        0,
+                        4,
+                        373
+                    ],
+                    [
+                        5,
+                        3,
+                        449
+                    ],
+                    [
+                        1,
+                        0,
+                        674
+                    ],
+                    [
+                        1,
+                        3,
+                        710
+                    ],
+                    [
+                        5,
+                        4,
+                        273
+                    ],
+                    [
+                        4,
+                        3,
+                        664
+                    ],
+                    [
+                        2,
+                        5,
+                        520
+                    ],
+                    [
+                        5,
+                        3,
+                        910
+                    ],
+                    [
+                        2,
+                        4,
+                        676
+                    ],
+                    [
+                        3,
+                        5,
+                        3
+                    ],
+                    [
+                        5,
+                        2,
+                        619
+                    ],
+                    [
+                        0,
+                        3,
+                        402
+                    ],
+                    [
+                        2,
+                        1,
+                        813
+                    ],
+                    [
+                        1,
+                        3,
+                        560
+                    ],
+                    [
+                        5,
+                        2,
+                        314
+                    ],
+                    [
+                        2,
+                        5,
+                        51
+                    ],
+                    [
+                        3,
+                        1,
+                        10
+                    ],
+                    [
+                        3,
+                        5,
+                        542
+                    ],
+                    [
+                        0,
+                        3,
+                        689
+                    ],
+                    [
+                        0,
+                        2,
+                        414
+                    ],
+                    [
+                        3,
+                        5,
+                        249
+                    ],
+                    [
+                        3,
+                        0,
+                        449
+                    ],
+                    [
+                        0,
+                        2,
+                        745
+                    ],
+                    [
+                        1,
+                        3,
+                        51
+                    ],
+                    [
+                        5,
+                        4,
+                        941
+                    ],
+                    [
+                        4,
+                        5,
+                        658
+                    ],
+                    [
+                        0,
+                        4,
+                        281
+                    ],
+                    [
+                        0,
+                        3,
+                        416
+                    ],
+                    [
+                        3,
+                        5,
+                        539
+                    ],
+                    [
+                        5,
+                        1,
+                        772
+                    ],
+                    [
+                        3,
+                        2,
+                        393
+                    ],
+                    [
+                        1,
+                        4,
+                        784
+                    ],
+                    [
+                        1,
+                        0,
+                        328
+                    ],
+                    [
+                        1,
+                        0,
+                        310
+                    ],
+                    [
+                        2,
+                        5,
+                        319
+                    ],
+                    [
+                        2,
+                        1,
+                        598
+                    ],
+                    [
+                        3,
+                        0,
+                        398
+                    ],
+                    [
+                        1,
+                        5,
+                        114
+                    ],
+                    [
+                        4,
+                        2,
+                        801
+                    ],
+                    [
+                        0,
+                        2,
+                        486
+                    ],
+                    [
+                        4,
+                        2,
+                        582
+                    ],
+                    [
+                        1,
+                        3,
+                        885
+                    ],
+                    [
+                        0,
+                        2,
+                        683
+                    ],
+                    [
+                        5,
+                        1,
+                        152
+                    ],
+                    [
+                        5,
+                        2,
+                        431
+                    ],
+                    [
+                        2,
+                        1,
+                        645
+                    ],
+                    [
+                        0,
+                        4,
+                        920
+                    ],
+                    [
+                        3,
+                        5,
+                        881
+                    ],
+                    [
+                        2,
+                        5,
+                        683
+                    ],
+                    [
+                        4,
+                        3,
+                        485
+                    ],
+                    [
+                        3,
+                        2,
+                        143
+                    ],
+                    [
+                        0,
+                        1,
+                        89
+                    ],
+                    [
+                        2,
+                        3,
+                        267
+                    ],
+                    [
+                        2,
+                        1,
+                        561
+                    ],
+                    [
+                        2,
+                        1,
+                        137
+                    ],
+                    [
+                        1,
+                        4,
+                        194
+                    ],
+                    [
+                        1,
+                        0,
+                        805
+                    ],
+                    [
+                        2,
+                        3,
+                        166
+                    ],
+                    [
+                        4,
+                        0,
+                        767
+                    ],
+                    [
+                        4,
+                        3,
+                        394
+                    ],
+                    [
+                        4,
+                        2,
+                        490
+                    ],
+                    [
+                        5,
+                        4,
+                        675
+                    ],
+                    [
+                        1,
+                        5,
+                        647
+                    ],
+                    [
+                        1,
+                        2,
+                        417
+                    ],
+                    [
+                        0,
+                        5,
+                        196
+                    ],
+                    [
+                        5,
+                        2,
+                        760
+                    ],
+                    [
+                        0,
+                        5,
+                        63
+                    ],
+                    [
+                        3,
+                        1,
+                        622
+                    ],
+                    [
+                        3,
+                        0,
+                        665
+                    ],
+                    [
+                        2,
+                        3,
+                        354
+                    ],
+                    [
+                        3,
+                        0,
+                        501
+                    ],
+                    [
+                        1,
+                        0,
+                        684
+                    ],
+                    [
+                        4,
+                        2,
+                        668
+                    ],
+                    [
+                        0,
+                        5,
+                        773
+                    ],
+                    [
+                        3,
+                        0,
+                        3
+                    ],
+                    [
+                        3,
+                        2,
+                        57
+                    ],
+                    [
+                        4,
+                        3,
+                        693
+                    ],
+                    [
+                        2,
+                        1,
+                        730
+                    ],
+                    [
+                        0,
+                        4,
+                        778
+                    ],
+                    [
+                        4,
+                        1,
+                        946
+                    ],
+                    [
+                        2,
+                        5,
+                        892
+                    ],
+                    [
+                        0,
+                        4,
+                        393
+                    ],
+                    [
+                        0,
+                        2,
+                        40
+                    ],
+                    [
+                        3,
+                        5,
+                        720
+                    ],
+                    [
+                        4,
+                        1,
+                        281
+                    ],
+                    [
+                        1,
+                        4,
+                        682
+                    ],
+                    [
+                        2,
+                        4,
+                        686
+                    ],
+                    [
+                        5,
+                        2,
+                        100
+                    ],
+                    [
+                        0,
+                        1,
+                        869
+                    ],
+                    [
+                        1,
+                        4,
+                        451
+                    ],
+                    [
+                        0,
+                        1,
+                        960
+                    ],
+                    [
+                        2,
+                        0,
+                        880
+                    ],
+                    [
+                        0,
+                        2,
+                        421
+                    ],
+                    [
+                        0,
+                        4,
+                        744
+                    ],
+                    [
+                        4,
+                        3,
+                        900
+                    ],
+                    [
+                        3,
+                        2,
+                        40
+                    ],
+                    [
+                        3,
+                        5,
+                        512
+                    ],
+                    [
+                        5,
+                        2,
+                        892
+                    ],
+                    [
+                        1,
+                        0,
+                        938
+                    ],
+                    [
+                        5,
+                        0,
+                        209
+                    ],
+                    [
+                        2,
+                        3,
+                        302
+                    ],
+                    [
+                        2,
+                        4,
+                        600
+                    ],
+                    [
+                        2,
+                        4,
+                        528
+                    ],
+                    [
+                        3,
+                        2,
+                        465
+                    ],
+                    [
+                        5,
+                        0,
+                        176
+                    ],
+                    [
+                        1,
+                        0,
+                        496
+                    ],
+                    [
+                        3,
+                        2,
+                        143
+                    ],
+                    [
+                        4,
+                        0,
+                        387
+                    ],
+                    [
+                        2,
+                        4,
+                        394
+                    ],
+                    [
+                        3,
+                        5,
+                        527
+                    ],
+                    [
+                        0,
+                        1,
+                        910
+                    ],
+                    [
+                        3,
+                        1,
+                        667
+                    ],
+                    [
+                        5,
+                        1,
+                        741
+                    ],
+                    [
+                        3,
+                        2,
+                        853
+                    ],
+                    [
+                        5,
+                        3,
+                        481
+                    ],
+                    [
+                        0,
+                        3,
+                        738
+                    ],
+                    [
+                        5,
+                        2,
+                        247
+                    ],
+                    [
+                        3,
+                        2,
+                        940
+                    ],
+                    [
+                        3,
+                        1,
+                        58
+                    ],
+                    [
+                        3,
+                        0,
+                        791
+                    ],
+                    [
+                        4,
+                        2,
+                        302
+                    ],
+                    [
+                        0,
+                        1,
+                        643
+                    ],
+                    [
+                        4,
+                        5,
+                        175
+                    ],
+                    [
+                        5,
+                        3,
+                        689
+                    ],
+                    [
+                        2,
+                        5,
+                        548
+                    ],
+                    [
+                        0,
+                        1,
+                        851
+                    ],
+                    [
+                        3,
+                        0,
+                        64
+                    ],
+                    [
+                        1,
+                        0,
+                        923
+                    ],
+                    [
+                        1,
+                        4,
+                        520
+                    ],
+                    [
+                        1,
+                        3,
+                        990
+                    ],
+                    [
+                        4,
+                        1,
+                        98
+                    ],
+                    [
+                        4,
+                        5,
+                        541
+                    ],
+                    [
+                        2,
+                        3,
+                        429
+                    ],
+                    [
+                        0,
+                        5,
+                        875
+                    ],
+                    [
+                        1,
+                        4,
+                        516
+                    ],
+                    [
+                        5,
+                        0,
+                        268
+                    ],
+                    [
+                        1,
+                        0,
+                        679
+                    ],
+                    [
+                        3,
+                        5,
+                        763
+                    ],
+                    [
+                        1,
+                        0,
+                        665
+                    ],
+                    [
+                        0,
+                        5,
+                        138
+                    ],
+                    [
+                        0,
+                        2,
+                        66
+                    ],
+                    [
+                        5,
+                        1,
+                        493
+                    ],
+                    [
+                        2,
+                        3,
+                        411
+                    ],
+                    [
+                        3,
+                        2,
+                        628
+                    ],
+                    [
+                        4,
+                        2,
+                        61
+                    ],
+                    [
+                        2,
+                        5,
+                        276
+                    ],
+                    [
+                        4,
+                        1,
+                        61
+                    ],
+                    [
+                        1,
+                        0,
+                        916
+                    ],
+                    [
+                        4,
+                        3,
+                        103
+                    ],
+                    [
+                        1,
+                        2,
+                        829
+                    ],
+                    [
+                        0,
+                        2,
+                        435
+                    ],
+                    [
+                        3,
+                        5,
+                        187
+                    ],
+                    [
+                        4,
+                        2,
+                        588
+                    ],
+                    [
+                        3,
+                        4,
+                        289
+                    ],
+                    [
+                        3,
+                        5,
+                        817
+                    ],
+                    [
+                        3,
+                        0,
+                        435
+                    ],
+                    [
+                        2,
+                        4,
+                        654
+                    ],
+                    [
+                        4,
+                        2,
+                        857
+                    ],
+                    [
+                        2,
+                        1,
+                        230
+                    ],
+                    [
+                        2,
+                        5,
+                        318
+                    ],
+                    [
+                        0,
+                        5,
+                        202
+                    ],
+                    [
+                        0,
+                        4,
+                        715
+                    ],
+                    [
+                        4,
+                        0,
+                        868
+                    ],
+                    [
+                        4,
+                        0,
+                        672
+                    ],
+                    [
+                        5,
+                        3,
+                        881
+                    ],
+                    [
+                        0,
+                        5,
+                        139
+                    ],
+                    [
+                        1,
+                        2,
+                        577
+                    ],
+                    [
+                        3,
+                        4,
+                        32
+                    ],
+                    [
+                        2,
+                        5,
+                        539
+                    ],
+                    [
+                        1,
+                        2,
+                        275
+                    ],
+                    [
+                        2,
+                        3,
+                        458
+                    ],
+                    [
+                        3,
+                        1,
+                        903
+                    ],
+                    [
+                        1,
+                        4,
+                        406
+                    ],
+                    [
+                        5,
+                        0,
+                        639
+                    ],
+                    [
+                        3,
+                        1,
+                        339
+                    ],
+                    [
+                        3,
+                        1,
+                        138
+                    ],
+                    [
+                        0,
+                        2,
+                        330
+                    ],
+                    [
+                        2,
+                        1,
+                        857
+                    ],
+                    [
+                        5,
+                        4,
+                        390
+                    ],
+                    [
+                        3,
+                        2,
+                        691
+                    ],
+                    [
+                        5,
+                        1,
+                        288
+                    ],
+                    [
+                        3,
+                        5,
+                        987
+                    ],
+                    [
+                        5,
+                        1,
+                        144
+                    ],
+                    [
+                        1,
+                        4,
+                        720
+                    ],
+                    [
+                        3,
+                        1,
+                        414
+                    ],
+                    [
+                        0,
+                        1,
+                        161
+                    ],
+                    [
+                        2,
+                        1,
+                        889
+                    ],
+                    [
+                        3,
+                        1,
+                        272
+                    ],
+                    [
+                        5,
+                        2,
+                        31
+                    ],
+                    [
+                        2,
+                        1,
+                        238
+                    ],
+                    [
+                        4,
+                        3,
+                        116
+                    ],
+                    [
+                        4,
+                        5,
+                        878
+                    ],
+                    [
+                        4,
+                        3,
+                        64
+                    ],
+                    [
+                        4,
+                        3,
+                        407
+                    ],
+                    [
+                        1,
+                        2,
+                        544
+                    ],
+                    [
+                        4,
+                        1,
+                        586
+                    ],
+                    [
+                        0,
+                        4,
+                        432
+                    ],
+                    [
+                        3,
+                        5,
+                        33
+                    ],
+                    [
+                        4,
+                        1,
+                        921
+                    ],
+                    [
+                        5,
+                        2,
+                        146
+                    ],
+                    [
+                        2,
+                        0,
+                        262
+                    ],
+                    [
+                        1,
+                        2,
+                        542
+                    ],
+                    [
+                        3,
+                        4,
+                        178
+                    ],
+                    [
+                        5,
+                        2,
+                        288
+                    ],
+                    [
+                        3,
+                        0,
+                        829
+                    ],
+                    [
+                        2,
+                        3,
+                        161
+                    ],
+                    [
+                        4,
+                        3,
+                        780
+                    ],
+                    [
+                        1,
+                        0,
+                        410
+                    ],
+                    [
+                        5,
+                        0,
+                        397
+                    ],
+                    [
+                        2,
+                        5,
+                        554
+                    ],
+                    [
+                        0,
+                        4,
+                        90
+                    ],
+                    [
+                        0,
+                        3,
+                        937
+                    ],
+                    [
+                        1,
+                        0,
+                        335
+                    ],
+                    [
+                        5,
+                        0,
+                        693
+                    ],
+                    [
+                        4,
+                        2,
+                        706
+                    ],
+                    [
+                        0,
+                        2,
+                        280
+                    ],
+                    [
+                        3,
+                        0,
+                        951
+                    ],
+                    [
+                        0,
+                        5,
+                        531
+                    ],
+                    [
+                        1,
+                        3,
+                        80
+                    ],
+                    [
+                        4,
+                        5,
+                        263
+                    ],
+                    [
+                        5,
+                        1,
+                        683
+                    ],
+                    [
+                        2,
+                        3,
+                        170
+                    ],
+                    [
+                        0,
+                        1,
+                        373
+                    ],
+                    [
+                        4,
+                        1,
+                        554
+                    ],
+                    [
+                        3,
+                        5,
+                        688
+                    ],
+                    [
+                        5,
+                        0,
+                        936
+                    ],
+                    [
+                        4,
+                        1,
+                        247
+                    ],
+                    [
+                        2,
+                        1,
+                        812
+                    ],
+                    [
+                        1,
+                        5,
+                        285
+                    ],
+                    [
+                        0,
+                        1,
+                        350
+                    ],
+                    [
+                        3,
+                        1,
+                        552
+                    ],
+                    [
+                        4,
+                        2,
+                        49
+                    ],
+                    [
+                        3,
+                        5,
+                        745
+                    ],
+                    [
+                        4,
+                        0,
+                        655
+                    ],
+                    [
+                        1,
+                        3,
+                        42
+                    ],
+                    [
+                        5,
+                        3,
+                        264
+                    ],
+                    [
+                        4,
+                        0,
+                        143
+                    ],
+                    [
+                        5,
+                        2,
+                        218
+                    ],
+                    [
+                        2,
+                        5,
+                        578
+                    ],
+                    [
+                        2,
+                        0,
+                        379
+                    ],
+                    [
+                        0,
+                        3,
+                        924
+                    ],
+                    [
+                        0,
+                        4,
+                        944
+                    ],
+                    [
+                        5,
+                        0,
+                        769
+                    ],
+                    [
+                        4,
+                        3,
+                        825
+                    ],
+                    [
+                        3,
+                        4,
+                        435
+                    ],
+                    [
+                        2,
+                        0,
+                        125
+                    ],
+                    [
+                        0,
+                        4,
+                        582
+                    ],
+                    [
+                        2,
+                        0,
+                        130
+                    ],
+                    [
+                        3,
+                        0,
+                        602
+                    ],
+                    [
+                        0,
+                        3,
+                        788
+                    ],
+                    [
+                        1,
+                        5,
+                        465
+                    ],
+                    [
+                        2,
+                        1,
+                        797
+                    ],
+                    [
+                        2,
+                        0,
+                        631
+                    ],
+                    [
+                        1,
+                        3,
+                        204
+                    ],
+                    [
+                        2,
+                        0,
+                        791
+                    ],
+                    [
+                        0,
+                        5,
+                        486
+                    ],
+                    [
+                        0,
+                        2,
+                        546
+                    ],
+                    [
+                        5,
+                        4,
+                        549
+                    ],
+                    [
+                        4,
+                        1,
+                        974
+                    ],
+                    [
+                        1,
+                        2,
+                        985
+                    ],
+                    [
+                        3,
+                        5,
+                        284
+                    ],
+                    [
+                        1,
+                        4,
+                        45
+                    ],
+                    [
+                        3,
+                        1,
+                        487
+                    ],
+                    [
+                        2,
+                        0,
+                        116
+                    ],
+                    [
+                        5,
+                        1,
+                        579
+                    ],
+                    [
+                        2,
+                        4,
+                        624
+                    ],
+                    [
+                        3,
+                        0,
+                        392
+                    ],
+                    [
+                        0,
+                        5,
+                        633
+                    ],
+                    [
+                        2,
+                        0,
+                        583
+                    ],
+                    [
+                        1,
+                        2,
+                        464
+                    ],
+                    [
+                        5,
+                        3,
+                        320
+                    ],
+                    [
+                        4,
+                        0,
+                        764
+                    ],
+                    [
+                        1,
+                        0,
+                        788
+                    ],
+                    [
+                        1,
+                        5,
+                        466
+                    ],
+                    [
+                        4,
+                        5,
+                        268
+                    ],
+                    [
+                        1,
+                        0,
+                        460
+                    ],
+                    [
+                        5,
+                        0,
+                        81
+                    ],
+                    [
+                        3,
+                        2,
+                        329
+                    ],
+                    [
+                        5,
+                        3,
+                        976
+                    ],
+                    [
+                        0,
+                        4,
+                        57
+                    ],
+                    [
+                        4,
+                        2,
+                        846
+                    ],
+                    [
+                        2,
+                        3,
+                        694
+                    ],
+                    [
+                        4,
+                        0,
+                        879
+                    ],
+                    [
+                        3,
+                        1,
+                        927
+                    ],
+                    [
+                        4,
+                        3,
+                        184
+                    ],
+                    [
+                        2,
+                        3,
+                        950
+                    ],
+                    [
+                        1,
+                        2,
+                        330
+                    ],
+                    [
+                        4,
+                        1,
+                        738
+                    ],
+                    [
+                        4,
+                        5,
+                        174
+                    ],
+                    [
+                        5,
+                        3,
+                        276
+                    ],
+                    [
+                        2,
+                        1,
+                        213
+                    ],
+                    [
+                        2,
+                        3,
+                        384
+                    ],
+                    [
+                        4,
+                        2,
+                        912
+                    ],
+                    [
+                        2,
+                        1,
+                        655
+                    ],
+                    [
+                        0,
+                        1,
+                        303
+                    ],
+                    [
+                        2,
+                        1,
+                        262
+                    ],
+                    [
+                        5,
+                        2,
+                        613
+                    ],
+                    [
+                        2,
+                        3,
+                        719
+                    ],
+                    [
+                        3,
+                        2,
+                        331
+                    ],
+                    [
+                        5,
+                        2,
+                        220
+                    ],
+                    [
+                        5,
+                        3,
+                        172
+                    ],
+                    [
+                        3,
+                        5,
+                        956
+                    ],
+                    [
+                        5,
+                        4,
+                        848
+                    ],
+                    [
+                        5,
+                        1,
+                        492
+                    ],
+                    [
+                        5,
+                        2,
+                        381
+                    ],
+                    [
+                        3,
+                        4,
+                        504
+                    ],
+                    [
+                        3,
+                        0,
+                        575
+                    ],
+                    [
+                        1,
+                        2,
+                        560
+                    ],
+                    [
+                        2,
+                        0,
+                        9
+                    ],
+                    [
+                        3,
+                        2,
+                        201
+                    ],
+                    [
+                        4,
+                        0,
+                        846
+                    ],
+                    [
+                        3,
+                        4,
+                        623
+                    ],
+                    [
+                        1,
+                        2,
+                        704
+                    ],
+                    [
+                        5,
+                        2,
+                        11
+                    ],
+                    [
+                        1,
+                        4,
+                        503
+                    ],
+                    [
+                        5,
+                        0,
+                        90
+                    ],
+                    [
+                        1,
+                        0,
+                        686
+                    ],
+                    [
+                        3,
+                        1,
+                        695
+                    ],
+                    [
+                        1,
+                        0,
+                        805
+                    ],
+                    [
+                        0,
+                        3,
+                        914
+                    ],
+                    [
+                        5,
+                        1,
+                        535
+                    ],
+                    [
+                        4,
+                        0,
+                        908
+                    ],
+                    [
+                        1,
+                        0,
+                        511
+                    ],
+                    [
+                        2,
+                        4,
+                        404
+                    ],
+                    [
+                        2,
+                        3,
+                        655
+                    ],
+                    [
+                        0,
+                        1,
+                        631
+                    ],
+                    [
+                        2,
+                        0,
+                        164
+                    ],
+                    [
+                        4,
+                        0,
+                        16
+                    ],
+                    [
+                        2,
+                        5,
+                        940
+                    ],
+                    [
+                        0,
+                        4,
+                        828
+                    ],
+                    [
+                        1,
+                        0,
+                        133
+                    ],
+                    [
+                        2,
+                        1,
+                        956
+                    ],
+                    [
+                        2,
+                        0,
+                        314
+                    ],
+                    [
+                        1,
+                        0,
+                        621
+                    ],
+                    [
+                        0,
+                        4,
+                        480
+                    ],
+                    [
+                        4,
+                        1,
+                        792
+                    ],
+                    [
+                        1,
+                        3,
+                        109
+                    ],
+                    [
+                        0,
+                        2,
+                        96
+                    ],
+                    [
+                        5,
+                        2,
+                        808
+                    ],
+                    [
+                        3,
+                        2,
+                        290
+                    ],
+                    [
+                        2,
+                        3,
+                        154
+                    ],
+                    [
+                        5,
+                        1,
+                        79
+                    ],
+                    [
+                        0,
+                        4,
+                        973
+                    ],
+                    [
+                        0,
+                        5,
+                        830
+                    ],
+                    [
+                        2,
+                        1,
+                        815
+                    ],
+                    [
+                        5,
+                        4,
+                        519
+                    ],
+                    [
+                        4,
+                        2,
+                        801
+                    ],
+                    [
+                        1,
+                        5,
+                        353
+                    ],
+                    [
+                        2,
+                        3,
+                        889
+                    ],
+                    [
+                        0,
+                        3,
+                        596
+                    ],
+                    [
+                        2,
+                        0,
+                        856
+                    ],
+                    [
+                        0,
+                        3,
+                        254
+                    ],
+                    [
+                        1,
+                        4,
+                        622
+                    ],
+                    [
+                        5,
+                        4,
+                        329
+                    ],
+                    [
+                        2,
+                        1,
+                        920
+                    ],
+                    [
+                        5,
+                        3,
+                        106
+                    ],
+                    [
+                        2,
+                        1,
+                        646
+                    ],
+                    [
+                        0,
+                        5,
+                        853
+                    ],
+                    [
+                        4,
+                        0,
+                        662
+                    ],
+                    [
+                        4,
+                        5,
+                        812
+                    ],
+                    [
+                        2,
+                        4,
+                        224
+                    ],
+                    [
+                        2,
+                        1,
+                        671
+                    ],
+                    [
+                        0,
+                        5,
+                        229
+                    ],
+                    [
+                        4,
+                        3,
+                        65
+                    ],
+                    [
+                        3,
+                        0,
+                        652
+                    ],
+                    [
+                        2,
+                        4,
+                        997
+                    ],
+                    [
+                        4,
+                        3,
+                        602
+                    ],
+                    [
+                        0,
+                        2,
+                        775
+                    ],
+                    [
+                        0,
+                        4,
+                        894
+                    ],
+                    [
+                        4,
+                        2,
+                        70
+                    ],
+                    [
+                        5,
+                        0,
+                        17
+                    ],
+                    [
+                        1,
+                        3,
+                        540
+                    ],
+                    [
+                        1,
+                        4,
+                        64
+                    ],
+                    [
+                        0,
+                        5,
+                        977
+                    ],
+                    [
+                        1,
+                        2,
+                        196
+                    ]
+                ]
+            ],
+            "output": 64
+        },
+        {
+            "input": [
+                8,
+                66441,
+                [
+                    [
+                        5,
+                        3,
+                        158
+                    ],
+                    [
+                        7,
+                        6,
+                        734
+                    ],
+                    [
+                        5,
+                        6,
+                        502
+                    ],
+                    [
+                        3,
+                        5,
+                        509
+                    ],
+                    [
+                        6,
+                        7,
+                        7
+                    ],
+                    [
+                        2,
+                        0,
+                        416
+                    ],
+                    [
+                        0,
+                        6,
+                        204
+                    ],
+                    [
+                        3,
+                        4,
+                        193
+                    ],
+                    [
+                        0,
+                        6,
+                        76
+                    ],
+                    [
+                        7,
+                        2,
+                        83
+                    ],
+                    [
+                        7,
+                        1,
+                        490
+                    ],
+                    [
+                        7,
+                        1,
+                        122
+                    ],
+                    [
+                        5,
+                        7,
+                        966
+                    ],
+                    [
+                        0,
+                        1,
+                        553
+                    ],
+                    [
+                        3,
+                        4,
+                        100
+                    ],
+                    [
+                        2,
+                        1,
+                        889
+                    ],
+                    [
+                        6,
+                        4,
+                        185
+                    ],
+                    [
+                        1,
+                        0,
+                        467
+                    ],
+                    [
+                        4,
+                        5,
+                        825
+                    ],
+                    [
+                        4,
+                        5,
+                        800
+                    ],
+                    [
+                        1,
+                        0,
+                        891
+                    ],
+                    [
+                        7,
+                        4,
+                        328
+                    ],
+                    [
+                        3,
+                        6,
+                        65
+                    ],
+                    [
+                        2,
+                        7,
+                        208
+                    ],
+                    [
+                        2,
+                        3,
+                        277
+                    ],
+                    [
+                        2,
+                        6,
+                        743
+                    ],
+                    [
+                        6,
+                        2,
+                        697
+                    ],
+                    [
+                        0,
+                        1,
+                        814
+                    ],
+                    [
+                        2,
+                        7,
+                        562
+                    ],
+                    [
+                        4,
+                        6,
+                        676
+                    ],
+                    [
+                        7,
+                        0,
+                        795
+                    ],
+                    [
+                        4,
+                        1,
+                        435
+                    ],
+                    [
+                        5,
+                        7,
+                        929
+                    ],
+                    [
+                        0,
+                        3,
+                        398
+                    ],
+                    [
+                        3,
+                        4,
+                        632
+                    ],
+                    [
+                        0,
+                        4,
+                        458
+                    ],
+                    [
+                        7,
+                        3,
+                        229
+                    ],
+                    [
+                        1,
+                        4,
+                        83
+                    ],
+                    [
+                        7,
+                        4,
+                        925
+                    ],
+                    [
+                        5,
+                        4,
+                        704
+                    ],
+                    [
+                        2,
+                        1,
+                        426
+                    ],
+                    [
+                        4,
+                        2,
+                        535
+                    ],
+                    [
+                        4,
+                        2,
+                        79
+                    ],
+                    [
+                        3,
+                        7,
+                        976
+                    ],
+                    [
+                        2,
+                        0,
+                        546
+                    ],
+                    [
+                        7,
+                        6,
+                        809
+                    ],
+                    [
+                        0,
+                        1,
+                        656
+                    ],
+                    [
+                        2,
+                        5,
+                        145
+                    ],
+                    [
+                        1,
+                        0,
+                        11
+                    ],
+                    [
+                        2,
+                        5,
+                        762
+                    ],
+                    [
+                        2,
+                        6,
+                        667
+                    ],
+                    [
+                        0,
+                        2,
+                        664
+                    ],
+                    [
+                        6,
+                        7,
+                        365
+                    ],
+                    [
+                        0,
+                        5,
+                        658
+                    ],
+                    [
+                        7,
+                        4,
+                        538
+                    ],
+                    [
+                        3,
+                        4,
+                        243
+                    ],
+                    [
+                        4,
+                        7,
+                        650
+                    ],
+                    [
+                        0,
+                        6,
+                        615
+                    ],
+                    [
+                        7,
+                        2,
+                        672
+                    ],
+                    [
+                        1,
+                        3,
+                        192
+                    ],
+                    [
+                        3,
+                        1,
+                        942
+                    ],
+                    [
+                        5,
+                        3,
+                        780
+                    ],
+                    [
+                        2,
+                        5,
+                        347
+                    ],
+                    [
+                        5,
+                        7,
+                        740
+                    ],
+                    [
+                        7,
+                        6,
+                        731
+                    ],
+                    [
+                        1,
+                        5,
+                        894
+                    ],
+                    [
+                        5,
+                        0,
+                        757
+                    ],
+                    [
+                        4,
+                        3,
+                        329
+                    ],
+                    [
+                        2,
+                        4,
+                        899
+                    ],
+                    [
+                        0,
+                        6,
+                        740
+                    ],
+                    [
+                        5,
+                        1,
+                        357
+                    ],
+                    [
+                        6,
+                        5,
+                        225
+                    ],
+                    [
+                        1,
+                        6,
+                        581
+                    ],
+                    [
+                        3,
+                        6,
+                        308
+                    ],
+                    [
+                        2,
+                        6,
+                        653
+                    ],
+                    [
+                        4,
+                        7,
+                        860
+                    ],
+                    [
+                        4,
+                        1,
+                        33
+                    ],
+                    [
+                        2,
+                        7,
+                        167
+                    ],
+                    [
+                        5,
+                        0,
+                        549
+                    ],
+                    [
+                        5,
+                        4,
+                        736
+                    ],
+                    [
+                        6,
+                        5,
+                        966
+                    ],
+                    [
+                        4,
+                        5,
+                        90
+                    ],
+                    [
+                        7,
+                        2,
+                        726
+                    ],
+                    [
+                        4,
+                        6,
+                        92
+                    ],
+                    [
+                        2,
+                        5,
+                        633
+                    ],
+                    [
+                        6,
+                        3,
+                        440
+                    ],
+                    [
+                        3,
+                        2,
+                        229
+                    ],
+                    [
+                        0,
+                        2,
+                        565
+                    ],
+                    [
+                        1,
+                        4,
+                        111
+                    ],
+                    [
+                        0,
+                        3,
+                        443
+                    ],
+                    [
+                        3,
+                        2,
+                        458
+                    ],
+                    [
+                        5,
+                        1,
+                        265
+                    ],
+                    [
+                        2,
+                        0,
+                        869
+                    ],
+                    [
+                        2,
+                        7,
+                        477
+                    ],
+                    [
+                        2,
+                        6,
+                        835
+                    ],
+                    [
+                        1,
+                        0,
+                        793
+                    ],
+                    [
+                        0,
+                        4,
+                        120
+                    ],
+                    [
+                        3,
+                        7,
+                        349
+                    ],
+                    [
+                        4,
+                        5,
+                        757
+                    ],
+                    [
+                        7,
+                        4,
+                        491
+                    ],
+                    [
+                        4,
+                        6,
+                        546
+                    ],
+                    [
+                        0,
+                        2,
+                        663
+                    ],
+                    [
+                        7,
+                        6,
+                        537
+                    ],
+                    [
+                        0,
+                        2,
+                        155
+                    ],
+                    [
+                        2,
+                        7,
+                        262
+                    ],
+                    [
+                        5,
+                        3,
+                        323
+                    ],
+                    [
+                        5,
+                        2,
+                        661
+                    ],
+                    [
+                        5,
+                        0,
+                        667
+                    ],
+                    [
+                        2,
+                        3,
+                        269
+                    ],
+                    [
+                        4,
+                        0,
+                        55
+                    ],
+                    [
+                        5,
+                        1,
+                        941
+                    ],
+                    [
+                        3,
+                        0,
+                        498
+                    ],
+                    [
+                        7,
+                        6,
+                        210
+                    ],
+                    [
+                        3,
+                        6,
+                        975
+                    ],
+                    [
+                        7,
+                        1,
+                        78
+                    ],
+                    [
+                        5,
+                        4,
+                        151
+                    ],
+                    [
+                        6,
+                        0,
+                        519
+                    ],
+                    [
+                        3,
+                        2,
+                        115
+                    ],
+                    [
+                        6,
+                        5,
+                        404
+                    ],
+                    [
+                        3,
+                        0,
+                        520
+                    ],
+                    [
+                        3,
+                        6,
+                        492
+                    ],
+                    [
+                        5,
+                        3,
+                        369
+                    ],
+                    [
+                        0,
+                        5,
+                        624
+                    ],
+                    [
+                        1,
+                        0,
+                        910
+                    ],
+                    [
+                        3,
+                        7,
+                        468
+                    ],
+                    [
+                        0,
+                        4,
+                        290
+                    ],
+                    [
+                        5,
+                        0,
+                        258
+                    ],
+                    [
+                        7,
+                        4,
+                        697
+                    ],
+                    [
+                        0,
+                        4,
+                        741
+                    ],
+                    [
+                        3,
+                        5,
+                        700
+                    ],
+                    [
+                        6,
+                        3,
+                        619
+                    ],
+                    [
+                        1,
+                        4,
+                        737
+                    ],
+                    [
+                        1,
+                        5,
+                        219
+                    ],
+                    [
+                        4,
+                        2,
+                        905
+                    ],
+                    [
+                        4,
+                        7,
+                        952
+                    ],
+                    [
+                        5,
+                        3,
+                        533
+                    ],
+                    [
+                        4,
+                        7,
+                        581
+                    ],
+                    [
+                        2,
+                        5,
+                        868
+                    ],
+                    [
+                        7,
+                        0,
+                        666
+                    ],
+                    [
+                        7,
+                        3,
+                        489
+                    ],
+                    [
+                        1,
+                        6,
+                        366
+                    ],
+                    [
+                        0,
+                        4,
+                        401
+                    ],
+                    [
+                        1,
+                        3,
+                        56
+                    ],
+                    [
+                        5,
+                        2,
+                        800
+                    ],
+                    [
+                        0,
+                        2,
+                        186
+                    ],
+                    [
+                        5,
+                        4,
+                        915
+                    ],
+                    [
+                        5,
+                        4,
+                        668
+                    ],
+                    [
+                        5,
+                        1,
+                        541
+                    ],
+                    [
+                        7,
+                        4,
+                        953
+                    ],
+                    [
+                        7,
+                        0,
+                        823
+                    ],
+                    [
+                        7,
+                        5,
+                        256
+                    ],
+                    [
+                        6,
+                        3,
+                        193
+                    ],
+                    [
+                        7,
+                        3,
+                        570
+                    ],
+                    [
+                        3,
+                        1,
+                        72
+                    ],
+                    [
+                        7,
+                        2,
+                        216
+                    ],
+                    [
+                        7,
+                        6,
+                        578
+                    ],
+                    [
+                        2,
+                        6,
+                        244
+                    ],
+                    [
+                        6,
+                        2,
+                        714
+                    ],
+                    [
+                        7,
+                        6,
+                        194
+                    ],
+                    [
+                        2,
+                        3,
+                        547
+                    ],
+                    [
+                        3,
+                        2,
+                        78
+                    ],
+                    [
+                        6,
+                        7,
+                        311
+                    ],
+                    [
+                        0,
+                        6,
+                        198
+                    ],
+                    [
+                        0,
+                        1,
+                        896
+                    ],
+                    [
+                        3,
+                        6,
+                        192
+                    ],
+                    [
+                        0,
+                        4,
+                        274
+                    ],
+                    [
+                        4,
+                        0,
+                        931
+                    ],
+                    [
+                        4,
+                        2,
+                        972
+                    ],
+                    [
+                        1,
+                        6,
+                        454
+                    ],
+                    [
+                        3,
+                        1,
+                        341
+                    ],
+                    [
+                        1,
+                        2,
+                        515
+                    ],
+                    [
+                        3,
+                        0,
+                        744
+                    ],
+                    [
+                        5,
+                        0,
+                        366
+                    ],
+                    [
+                        1,
+                        3,
+                        916
+                    ],
+                    [
+                        3,
+                        6,
+                        100
+                    ],
+                    [
+                        0,
+                        6,
+                        195
+                    ],
+                    [
+                        3,
+                        6,
+                        579
+                    ],
+                    [
+                        4,
+                        2,
+                        511
+                    ],
+                    [
+                        0,
+                        7,
+                        907
+                    ],
+                    [
+                        1,
+                        5,
+                        548
+                    ],
+                    [
+                        3,
+                        6,
+                        975
+                    ],
+                    [
+                        1,
+                        4,
+                        542
+                    ],
+                    [
+                        4,
+                        3,
+                        104
+                    ],
+                    [
+                        4,
+                        5,
+                        501
+                    ],
+                    [
+                        0,
+                        3,
+                        494
+                    ],
+                    [
+                        3,
+                        5,
+                        184
+                    ],
+                    [
+                        5,
+                        3,
+                        94
+                    ],
+                    [
+                        7,
+                        6,
+                        4
+                    ],
+                    [
+                        6,
+                        5,
+                        917
+                    ],
+                    [
+                        2,
+                        1,
+                        688
+                    ],
+                    [
+                        4,
+                        3,
+                        115
+                    ],
+                    [
+                        1,
+                        5,
+                        168
+                    ],
+                    [
+                        5,
+                        0,
+                        769
+                    ],
+                    [
+                        3,
+                        1,
+                        438
+                    ],
+                    [
+                        4,
+                        7,
+                        931
+                    ],
+                    [
+                        6,
+                        3,
+                        805
+                    ],
+                    [
+                        5,
+                        3,
+                        272
+                    ],
+                    [
+                        5,
+                        3,
+                        470
+                    ],
+                    [
+                        1,
+                        7,
+                        275
+                    ],
+                    [
+                        2,
+                        7,
+                        493
+                    ],
+                    [
+                        7,
+                        2,
+                        235
+                    ],
+                    [
+                        0,
+                        7,
+                        258
+                    ],
+                    [
+                        3,
+                        2,
+                        872
+                    ],
+                    [
+                        0,
+                        7,
+                        770
+                    ],
+                    [
+                        5,
+                        1,
+                        263
+                    ],
+                    [
+                        7,
+                        6,
+                        362
+                    ],
+                    [
+                        3,
+                        7,
+                        389
+                    ],
+                    [
+                        5,
+                        4,
+                        501
+                    ],
+                    [
+                        7,
+                        1,
+                        512
+                    ],
+                    [
+                        5,
+                        4,
+                        345
+                    ],
+                    [
+                        4,
+                        0,
+                        263
+                    ],
+                    [
+                        2,
+                        0,
+                        681
+                    ],
+                    [
+                        4,
+                        7,
+                        860
+                    ],
+                    [
+                        1,
+                        7,
+                        882
+                    ],
+                    [
+                        6,
+                        0,
+                        646
+                    ],
+                    [
+                        3,
+                        6,
+                        816
+                    ],
+                    [
+                        6,
+                        2,
+                        91
+                    ],
+                    [
+                        3,
+                        2,
+                        189
+                    ],
+                    [
+                        2,
+                        5,
+                        97
+                    ],
+                    [
+                        1,
+                        5,
+                        693
+                    ],
+                    [
+                        3,
+                        6,
+                        630
+                    ],
+                    [
+                        4,
+                        5,
+                        183
+                    ],
+                    [
+                        6,
+                        1,
+                        505
+                    ],
+                    [
+                        2,
+                        5,
+                        887
+                    ],
+                    [
+                        2,
+                        4,
+                        135
+                    ],
+                    [
+                        7,
+                        5,
+                        965
+                    ],
+                    [
+                        2,
+                        7,
+                        547
+                    ],
+                    [
+                        7,
+                        6,
+                        367
+                    ],
+                    [
+                        5,
+                        1,
+                        660
+                    ],
+                    [
+                        7,
+                        0,
+                        275
+                    ],
+                    [
+                        2,
+                        6,
+                        10
+                    ],
+                    [
+                        1,
+                        5,
+                        621
+                    ],
+                    [
+                        6,
+                        2,
+                        770
+                    ],
+                    [
+                        2,
+                        5,
+                        766
+                    ],
+                    [
+                        2,
+                        1,
+                        851
+                    ],
+                    [
+                        0,
+                        6,
+                        596
+                    ],
+                    [
+                        2,
+                        7,
+                        246
+                    ],
+                    [
+                        7,
+                        0,
+                        607
+                    ],
+                    [
+                        6,
+                        7,
+                        870
+                    ],
+                    [
+                        5,
+                        1,
+                        197
+                    ],
+                    [
+                        7,
+                        3,
+                        825
+                    ],
+                    [
+                        3,
+                        2,
+                        144
+                    ],
+                    [
+                        2,
+                        7,
+                        270
+                    ],
+                    [
+                        5,
+                        2,
+                        311
+                    ],
+                    [
+                        2,
+                        0,
+                        418
+                    ],
+                    [
+                        1,
+                        4,
+                        673
+                    ],
+                    [
+                        2,
+                        6,
+                        273
+                    ],
+                    [
+                        5,
+                        1,
+                        549
+                    ],
+                    [
+                        6,
+                        3,
+                        501
+                    ],
+                    [
+                        4,
+                        3,
+                        116
+                    ],
+                    [
+                        2,
+                        1,
+                        204
+                    ],
+                    [
+                        4,
+                        0,
+                        736
+                    ],
+                    [
+                        3,
+                        0,
+                        283
+                    ],
+                    [
+                        7,
+                        2,
+                        232
+                    ],
+                    [
+                        3,
+                        5,
+                        65
+                    ],
+                    [
+                        6,
+                        7,
+                        451
+                    ],
+                    [
+                        1,
+                        7,
+                        706
+                    ],
+                    [
+                        5,
+                        6,
+                        608
+                    ],
+                    [
+                        3,
+                        0,
+                        276
+                    ],
+                    [
+                        5,
+                        7,
+                        79
+                    ],
+                    [
+                        5,
+                        7,
+                        206
+                    ],
+                    [
+                        7,
+                        1,
+                        661
+                    ],
+                    [
+                        6,
+                        7,
+                        231
+                    ],
+                    [
+                        7,
+                        3,
+                        793
+                    ],
+                    [
+                        6,
+                        1,
+                        69
+                    ],
+                    [
+                        7,
+                        5,
+                        66
+                    ],
+                    [
+                        2,
+                        0,
+                        399
+                    ],
+                    [
+                        0,
+                        3,
+                        690
+                    ],
+                    [
+                        3,
+                        6,
+                        707
+                    ],
+                    [
+                        5,
+                        6,
+                        400
+                    ],
+                    [
+                        0,
+                        1,
+                        157
+                    ],
+                    [
+                        1,
+                        4,
+                        955
+                    ],
+                    [
+                        4,
+                        2,
+                        148
+                    ],
+                    [
+                        1,
+                        5,
+                        167
+                    ],
+                    [
+                        2,
+                        6,
+                        393
+                    ],
+                    [
+                        5,
+                        7,
+                        369
+                    ],
+                    [
+                        7,
+                        5,
+                        712
+                    ],
+                    [
+                        5,
+                        6,
+                        898
+                    ],
+                    [
+                        3,
+                        5,
+                        400
+                    ],
+                    [
+                        4,
+                        6,
+                        202
+                    ],
+                    [
+                        3,
+                        7,
+                        868
+                    ],
+                    [
+                        6,
+                        3,
+                        339
+                    ],
+                    [
+                        3,
+                        1,
+                        143
+                    ],
+                    [
+                        3,
+                        2,
+                        105
+                    ],
+                    [
+                        7,
+                        6,
+                        350
+                    ],
+                    [
+                        4,
+                        7,
+                        816
+                    ],
+                    [
+                        1,
+                        4,
+                        729
+                    ],
+                    [
+                        5,
+                        4,
+                        554
+                    ],
+                    [
+                        7,
+                        5,
+                        787
+                    ],
+                    [
+                        5,
+                        3,
+                        321
+                    ],
+                    [
+                        3,
+                        6,
+                        297
+                    ],
+                    [
+                        3,
+                        0,
+                        723
+                    ],
+                    [
+                        5,
+                        0,
+                        584
+                    ],
+                    [
+                        6,
+                        7,
+                        210
+                    ],
+                    [
+                        2,
+                        7,
+                        664
+                    ],
+                    [
+                        1,
+                        3,
+                        557
+                    ],
+                    [
+                        6,
+                        2,
+                        759
+                    ],
+                    [
+                        7,
+                        3,
+                        414
+                    ],
+                    [
+                        4,
+                        7,
+                        712
+                    ],
+                    [
+                        2,
+                        0,
+                        493
+                    ],
+                    [
+                        3,
+                        5,
+                        751
+                    ],
+                    [
+                        3,
+                        4,
+                        451
+                    ],
+                    [
+                        4,
+                        7,
+                        833
+                    ],
+                    [
+                        3,
+                        4,
+                        50
+                    ],
+                    [
+                        3,
+                        0,
+                        904
+                    ],
+                    [
+                        3,
+                        1,
+                        5
+                    ],
+                    [
+                        4,
+                        0,
+                        586
+                    ],
+                    [
+                        6,
+                        0,
+                        984
+                    ],
+                    [
+                        2,
+                        1,
+                        362
+                    ],
+                    [
+                        4,
+                        7,
+                        254
+                    ],
+                    [
+                        0,
+                        4,
+                        348
+                    ],
+                    [
+                        1,
+                        0,
+                        572
+                    ],
+                    [
+                        3,
+                        0,
+                        19
+                    ],
+                    [
+                        4,
+                        1,
+                        471
+                    ],
+                    [
+                        2,
+                        0,
+                        247
+                    ],
+                    [
+                        0,
+                        2,
+                        521
+                    ],
+                    [
+                        1,
+                        3,
+                        520
+                    ],
+                    [
+                        7,
+                        6,
+                        582
+                    ],
+                    [
+                        0,
+                        4,
+                        420
+                    ],
+                    [
+                        0,
+                        1,
+                        786
+                    ],
+                    [
+                        4,
+                        1,
+                        653
+                    ],
+                    [
+                        6,
+                        3,
+                        437
+                    ],
+                    [
+                        5,
+                        7,
+                        763
+                    ],
+                    [
+                        6,
+                        0,
+                        946
+                    ],
+                    [
+                        3,
+                        0,
+                        713
+                    ],
+                    [
+                        3,
+                        7,
+                        158
+                    ],
+                    [
+                        7,
+                        3,
+                        239
+                    ],
+                    [
+                        7,
+                        6,
+                        180
+                    ],
+                    [
+                        0,
+                        1,
+                        435
+                    ],
+                    [
+                        5,
+                        0,
+                        656
+                    ],
+                    [
+                        0,
+                        3,
+                        183
+                    ],
+                    [
+                        0,
+                        3,
+                        7
+                    ],
+                    [
+                        4,
+                        6,
+                        670
+                    ],
+                    [
+                        0,
+                        4,
+                        529
+                    ],
+                    [
+                        3,
+                        4,
+                        152
+                    ],
+                    [
+                        5,
+                        6,
+                        299
+                    ],
+                    [
+                        7,
+                        1,
+                        38
+                    ],
+                    [
+                        6,
+                        7,
+                        363
+                    ],
+                    [
+                        1,
+                        7,
+                        51
+                    ],
+                    [
+                        0,
+                        3,
+                        383
+                    ],
+                    [
+                        0,
+                        4,
+                        792
+                    ],
+                    [
+                        7,
+                        5,
+                        738
+                    ],
+                    [
+                        4,
+                        3,
+                        812
+                    ],
+                    [
+                        7,
+                        0,
+                        862
+                    ],
+                    [
+                        4,
+                        0,
+                        996
+                    ],
+                    [
+                        3,
+                        4,
+                        66
+                    ],
+                    [
+                        6,
+                        4,
+                        400
+                    ],
+                    [
+                        7,
+                        0,
+                        66
+                    ],
+                    [
+                        1,
+                        5,
+                        629
+                    ],
+                    [
+                        7,
+                        1,
+                        481
+                    ],
+                    [
+                        4,
+                        1,
+                        788
+                    ],
+                    [
+                        5,
+                        2,
+                        363
+                    ],
+                    [
+                        3,
+                        0,
+                        507
+                    ],
+                    [
+                        7,
+                        0,
+                        910
+                    ],
+                    [
+                        7,
+                        1,
+                        928
+                    ],
+                    [
+                        0,
+                        6,
+                        638
+                    ],
+                    [
+                        7,
+                        4,
+                        133
+                    ],
+                    [
+                        7,
+                        5,
+                        296
+                    ],
+                    [
+                        4,
+                        6,
+                        352
+                    ],
+                    [
+                        4,
+                        5,
+                        118
+                    ],
+                    [
+                        0,
+                        7,
+                        825
+                    ],
+                    [
+                        6,
+                        3,
+                        148
+                    ],
+                    [
+                        0,
+                        1,
+                        73
+                    ],
+                    [
+                        6,
+                        4,
+                        221
+                    ],
+                    [
+                        6,
+                        7,
+                        715
+                    ],
+                    [
+                        1,
+                        7,
+                        980
+                    ],
+                    [
+                        5,
+                        3,
+                        678
+                    ],
+                    [
+                        4,
+                        7,
+                        794
+                    ],
+                    [
+                        6,
+                        5,
+                        14
+                    ],
+                    [
+                        3,
+                        4,
+                        72
+                    ],
+                    [
+                        3,
+                        6,
+                        763
+                    ],
+                    [
+                        7,
+                        1,
+                        848
+                    ],
+                    [
+                        7,
+                        5,
+                        201
+                    ],
+                    [
+                        2,
+                        1,
+                        136
+                    ],
+                    [
+                        6,
+                        3,
+                        551
+                    ],
+                    [
+                        1,
+                        4,
+                        358
+                    ],
+                    [
+                        3,
+                        6,
+                        160
+                    ],
+                    [
+                        1,
+                        6,
+                        886
+                    ],
+                    [
+                        7,
+                        1,
+                        771
+                    ],
+                    [
+                        3,
+                        7,
+                        999
+                    ],
+                    [
+                        4,
+                        3,
+                        294
+                    ],
+                    [
+                        1,
+                        4,
+                        34
+                    ],
+                    [
+                        7,
+                        1,
+                        920
+                    ],
+                    [
+                        3,
+                        7,
+                        36
+                    ],
+                    [
+                        2,
+                        4,
+                        878
+                    ],
+                    [
+                        6,
+                        7,
+                        73
+                    ],
+                    [
+                        3,
+                        7,
+                        223
+                    ],
+                    [
+                        1,
+                        0,
+                        193
+                    ],
+                    [
+                        4,
+                        0,
+                        416
+                    ],
+                    [
+                        1,
+                        6,
+                        304
+                    ],
+                    [
+                        2,
+                        0,
+                        978
+                    ],
+                    [
+                        5,
+                        6,
+                        680
+                    ],
+                    [
+                        7,
+                        1,
+                        464
+                    ],
+                    [
+                        5,
+                        3,
+                        263
+                    ],
+                    [
+                        5,
+                        6,
+                        869
+                    ],
+                    [
+                        5,
+                        2,
+                        883
+                    ],
+                    [
+                        0,
+                        1,
+                        712
+                    ],
+                    [
+                        1,
+                        0,
+                        158
+                    ],
+                    [
+                        6,
+                        7,
+                        68
+                    ],
+                    [
+                        5,
+                        0,
+                        435
+                    ],
+                    [
+                        3,
+                        7,
+                        587
+                    ],
+                    [
+                        5,
+                        0,
+                        852
+                    ],
+                    [
+                        4,
+                        1,
+                        771
+                    ],
+                    [
+                        7,
+                        4,
+                        678
+                    ],
+                    [
+                        2,
+                        3,
+                        238
+                    ],
+                    [
+                        5,
+                        1,
+                        837
+                    ],
+                    [
+                        1,
+                        3,
+                        857
+                    ],
+                    [
+                        1,
+                        0,
+                        629
+                    ],
+                    [
+                        3,
+                        6,
+                        550
+                    ],
+                    [
+                        2,
+                        5,
+                        124
+                    ],
+                    [
+                        5,
+                        3,
+                        153
+                    ],
+                    [
+                        0,
+                        3,
+                        417
+                    ],
+                    [
+                        7,
+                        3,
+                        324
+                    ],
+                    [
+                        5,
+                        3,
+                        258
+                    ],
+                    [
+                        5,
+                        3,
+                        648
+                    ],
+                    [
+                        0,
+                        5,
+                        416
+                    ],
+                    [
+                        0,
+                        4,
+                        704
+                    ],
+                    [
+                        7,
+                        2,
+                        123
+                    ],
+                    [
+                        7,
+                        3,
+                        15
+                    ],
+                    [
+                        2,
+                        5,
+                        709
+                    ],
+                    [
+                        2,
+                        6,
+                        632
+                    ],
+                    [
+                        1,
+                        4,
+                        599
+                    ],
+                    [
+                        1,
+                        6,
+                        969
+                    ],
+                    [
+                        6,
+                        1,
+                        140
+                    ],
+                    [
+                        3,
+                        5,
+                        251
+                    ],
+                    [
+                        2,
+                        6,
+                        5
+                    ],
+                    [
+                        2,
+                        6,
+                        576
+                    ],
+                    [
+                        4,
+                        2,
+                        91
+                    ],
+                    [
+                        1,
+                        0,
+                        781
+                    ],
+                    [
+                        2,
+                        1,
+                        22
+                    ],
+                    [
+                        1,
+                        7,
+                        628
+                    ],
+                    [
+                        4,
+                        6,
+                        586
+                    ],
+                    [
+                        4,
+                        1,
+                        855
+                    ],
+                    [
+                        3,
+                        0,
+                        888
+                    ],
+                    [
+                        0,
+                        1,
+                        100
+                    ],
+                    [
+                        5,
+                        1,
+                        300
+                    ],
+                    [
+                        5,
+                        4,
+                        882
+                    ],
+                    [
+                        1,
+                        0,
+                        526
+                    ],
+                    [
+                        0,
+                        4,
+                        263
+                    ],
+                    [
+                        5,
+                        2,
+                        475
+                    ],
+                    [
+                        4,
+                        2,
+                        827
+                    ],
+                    [
+                        6,
+                        5,
+                        815
+                    ],
+                    [
+                        5,
+                        3,
+                        742
+                    ],
+                    [
+                        3,
+                        1,
+                        271
+                    ],
+                    [
+                        1,
+                        0,
+                        145
+                    ],
+                    [
+                        2,
+                        4,
+                        949
+                    ],
+                    [
+                        6,
+                        5,
+                        657
+                    ],
+                    [
+                        6,
+                        3,
+                        71
+                    ],
+                    [
+                        6,
+                        4,
+                        829
+                    ],
+                    [
+                        1,
+                        2,
+                        652
+                    ],
+                    [
+                        4,
+                        1,
+                        580
+                    ],
+                    [
+                        3,
+                        0,
+                        176
+                    ],
+                    [
+                        1,
+                        5,
+                        372
+                    ],
+                    [
+                        2,
+                        0,
+                        115
+                    ],
+                    [
+                        3,
+                        4,
+                        1000
+                    ],
+                    [
+                        7,
+                        0,
+                        569
+                    ],
+                    [
+                        6,
+                        2,
+                        241
+                    ],
+                    [
+                        7,
+                        6,
+                        391
+                    ],
+                    [
+                        0,
+                        5,
+                        856
+                    ],
+                    [
+                        7,
+                        2,
+                        806
+                    ],
+                    [
+                        3,
+                        1,
+                        295
+                    ],
+                    [
+                        2,
+                        0,
+                        637
+                    ],
+                    [
+                        7,
+                        1,
+                        258
+                    ],
+                    [
+                        7,
+                        5,
+                        645
+                    ],
+                    [
+                        1,
+                        3,
+                        136
+                    ],
+                    [
+                        6,
+                        4,
+                        93
+                    ],
+                    [
+                        1,
+                        6,
+                        37
+                    ],
+                    [
+                        0,
+                        7,
+                        53
+                    ],
+                    [
+                        2,
+                        6,
+                        621
+                    ],
+                    [
+                        2,
+                        1,
+                        196
+                    ],
+                    [
+                        6,
+                        0,
+                        26
+                    ],
+                    [
+                        5,
+                        7,
+                        225
+                    ],
+                    [
+                        3,
+                        1,
+                        260
+                    ],
+                    [
+                        2,
+                        3,
+                        299
+                    ],
+                    [
+                        0,
+                        1,
+                        172
+                    ],
+                    [
+                        7,
+                        5,
+                        549
+                    ]
+                ]
+            ],
+            "output": 256
+        },
+        {
+            "input": [
+                4,
+                3192,
+                [
+                    [
+                        1,
+                        0,
+                        323
+                    ],
+                    [
+                        3,
+                        2,
+                        323
+                    ],
+                    [
+                        0,
+                        1,
+                        606
+                    ],
+                    [
+                        0,
+                        2,
+                        846
+                    ],
+                    [
+                        0,
+                        3,
+                        314
+                    ],
+                    [
+                        3,
+                        0,
+                        275
+                    ],
+                    [
+                        3,
+                        2,
+                        99
+                    ],
+                    [
+                        2,
+                        0,
+                        290
+                    ],
+                    [
+                        1,
+                        0,
+                        981
+                    ],
+                    [
+                        3,
+                        2,
+                        298
+                    ],
+                    [
+                        3,
+                        1,
+                        261
+                    ],
+                    [
+                        0,
+                        3,
+                        636
+                    ],
+                    [
+                        1,
+                        2,
+                        797
+                    ],
+                    [
+                        1,
+                        3,
+                        946
+                    ],
+                    [
+                        1,
+                        2,
+                        995
+                    ],
+                    [
+                        2,
+                        1,
+                        771
+                    ],
+                    [
+                        2,
+                        1,
+                        497
+                    ],
+                    [
+                        1,
+                        2,
+                        128
+                    ],
+                    [
+                        0,
+                        3,
+                        881
+                    ],
+                    [
+                        1,
+                        0,
+                        329
+                    ],
+                    [
+                        1,
+                        0,
+                        276
+                    ],
+                    [
+                        2,
+                        0,
+                        999
+                    ],
+                    [
+                        2,
+                        0,
+                        757
+                    ],
+                    [
+                        0,
+                        1,
+                        576
+                    ],
+                    [
+                        0,
+                        2,
+                        199
+                    ],
+                    [
+                        2,
+                        1,
+                        191
+                    ],
+                    [
+                        0,
+                        1,
+                        443
+                    ],
+                    [
+                        1,
+                        3,
+                        757
+                    ],
+                    [
+                        0,
+                        1,
+                        723
+                    ],
+                    [
+                        0,
+                        3,
+                        971
+                    ],
+                    [
+                        1,
+                        3,
+                        522
+                    ],
+                    [
+                        3,
+                        2,
+                        600
+                    ],
+                    [
+                        1,
+                        2,
+                        289
+                    ],
+                    [
+                        0,
+                        1,
+                        730
+                    ],
+                    [
+                        1,
+                        3,
+                        105
+                    ],
+                    [
+                        0,
+                        2,
+                        11
+                    ],
+                    [
+                        1,
+                        3,
+                        327
+                    ],
+                    [
+                        2,
+                        3,
+                        495
+                    ],
+                    [
+                        1,
+                        3,
+                        58
+                    ],
+                    [
+                        0,
+                        2,
+                        653
+                    ],
+                    [
+                        1,
+                        2,
+                        197
+                    ],
+                    [
+                        0,
+                        2,
+                        15
+                    ],
+                    [
+                        1,
+                        0,
+                        133
+                    ],
+                    [
+                        1,
+                        2,
+                        434
+                    ],
+                    [
+                        2,
+                        1,
+                        701
+                    ],
+                    [
+                        0,
+                        1,
+                        94
+                    ],
+                    [
+                        2,
+                        1,
+                        62
+                    ],
+                    [
+                        3,
+                        0,
+                        356
+                    ],
+                    [
+                        2,
+                        3,
+                        401
+                    ],
+                    [
+                        1,
+                        0,
+                        377
+                    ],
+                    [
+                        1,
+                        0,
+                        781
+                    ],
+                    [
+                        2,
+                        3,
+                        294
+                    ],
+                    [
+                        3,
+                        1,
+                        634
+                    ],
+                    [
+                        3,
+                        1,
+                        39
+                    ],
+                    [
+                        1,
+                        2,
+                        947
+                    ],
+                    [
+                        1,
+                        2,
+                        383
+                    ],
+                    [
+                        2,
+                        0,
+                        42
+                    ],
+                    [
+                        2,
+                        1,
+                        970
+                    ],
+                    [
+                        1,
+                        3,
+                        277
+                    ],
+                    [
+                        1,
+                        2,
+                        397
+                    ],
+                    [
+                        0,
+                        2,
+                        301
+                    ],
+                    [
+                        3,
+                        1,
+                        396
+                    ],
+                    [
+                        3,
+                        1,
+                        194
+                    ],
+                    [
+                        0,
+                        2,
+                        679
+                    ],
+                    [
+                        2,
+                        0,
+                        526
+                    ],
+                    [
+                        3,
+                        1,
+                        852
+                    ],
+                    [
+                        0,
+                        2,
+                        652
+                    ],
+                    [
+                        0,
+                        2,
+                        323
+                    ],
+                    [
+                        3,
+                        2,
+                        432
+                    ],
+                    [
+                        2,
+                        1,
+                        263
+                    ],
+                    [
+                        0,
+                        1,
+                        123
+                    ],
+                    [
+                        1,
+                        2,
+                        920
+                    ],
+                    [
+                        1,
+                        3,
+                        392
+                    ],
+                    [
+                        3,
+                        0,
+                        901
+                    ],
+                    [
+                        2,
+                        3,
+                        361
+                    ],
+                    [
+                        0,
+                        2,
+                        410
+                    ],
+                    [
+                        2,
+                        3,
+                        305
+                    ],
+                    [
+                        2,
+                        3,
+                        434
+                    ],
+                    [
+                        3,
+                        1,
+                        716
+                    ],
+                    [
+                        1,
+                        0,
+                        482
+                    ],
+                    [
+                        0,
+                        1,
+                        540
+                    ],
+                    [
+                        1,
+                        3,
+                        250
+                    ],
+                    [
+                        0,
+                        2,
+                        384
+                    ],
+                    [
+                        2,
+                        1,
+                        947
+                    ],
+                    [
+                        1,
+                        2,
+                        417
+                    ],
+                    [
+                        0,
+                        3,
+                        79
+                    ],
+                    [
+                        1,
+                        3,
+                        525
+                    ],
+                    [
+                        0,
+                        3,
+                        886
+                    ],
+                    [
+                        2,
+                        1,
+                        203
+                    ],
+                    [
+                        2,
+                        0,
+                        598
+                    ],
+                    [
+                        1,
+                        0,
+                        800
+                    ],
+                    [
+                        2,
+                        1,
+                        922
+                    ],
+                    [
+                        0,
+                        3,
+                        234
+                    ],
+                    [
+                        2,
+                        1,
+                        626
+                    ],
+                    [
+                        0,
+                        1,
+                        729
+                    ],
+                    [
+                        1,
+                        3,
+                        791
+                    ],
+                    [
+                        0,
+                        1,
+                        510
+                    ],
+                    [
+                        0,
+                        1,
+                        788
+                    ],
+                    [
+                        1,
+                        2,
+                        523
+                    ],
+                    [
+                        2,
+                        0,
+                        448
+                    ],
+                    [
+                        1,
+                        3,
+                        490
+                    ],
+                    [
+                        3,
+                        2,
+                        62
+                    ],
+                    [
+                        1,
+                        2,
+                        826
+                    ],
+                    [
+                        3,
+                        2,
+                        813
+                    ],
+                    [
+                        3,
+                        2,
+                        775
+                    ],
+                    [
+                        0,
+                        1,
+                        829
+                    ],
+                    [
+                        2,
+                        3,
+                        722
+                    ],
+                    [
+                        2,
+                        3,
+                        66
+                    ],
+                    [
+                        1,
+                        2,
+                        460
+                    ],
+                    [
+                        2,
+                        1,
+                        389
+                    ],
+                    [
+                        3,
+                        0,
+                        376
+                    ],
+                    [
+                        0,
+                        2,
+                        946
+                    ],
+                    [
+                        3,
+                        1,
+                        752
+                    ],
+                    [
+                        1,
+                        0,
+                        293
+                    ],
+                    [
+                        2,
+                        3,
+                        659
+                    ],
+                    [
+                        1,
+                        0,
+                        649
+                    ],
+                    [
+                        0,
+                        1,
+                        885
+                    ],
+                    [
+                        2,
+                        1,
+                        75
+                    ],
+                    [
+                        1,
+                        2,
+                        470
+                    ],
+                    [
+                        1,
+                        2,
+                        893
+                    ],
+                    [
+                        1,
+                        2,
+                        988
+                    ],
+                    [
+                        3,
+                        2,
+                        625
+                    ],
+                    [
+                        1,
+                        2,
+                        6
+                    ],
+                    [
+                        1,
+                        2,
+                        591
+                    ],
+                    [
+                        0,
+                        2,
+                        467
+                    ],
+                    [
+                        1,
+                        2,
+                        558
+                    ],
+                    [
+                        3,
+                        1,
+                        765
+                    ],
+                    [
+                        2,
+                        3,
+                        742
+                    ],
+                    [
+                        1,
+                        2,
+                        238
+                    ],
+                    [
+                        3,
+                        2,
+                        477
+                    ],
+                    [
+                        1,
+                        2,
+                        471
+                    ],
+                    [
+                        0,
+                        2,
+                        213
+                    ],
+                    [
+                        3,
+                        0,
+                        348
+                    ],
+                    [
+                        1,
+                        3,
+                        928
+                    ],
+                    [
+                        0,
+                        2,
+                        330
+                    ],
+                    [
+                        2,
+                        0,
+                        918
+                    ],
+                    [
+                        0,
+                        3,
+                        119
+                    ],
+                    [
+                        3,
+                        1,
+                        700
+                    ],
+                    [
+                        3,
+                        0,
+                        735
+                    ],
+                    [
+                        0,
+                        3,
+                        460
+                    ],
+                    [
+                        0,
+                        3,
+                        773
+                    ],
+                    [
+                        3,
+                        0,
+                        1000
+                    ],
+                    [
+                        0,
+                        3,
+                        676
+                    ],
+                    [
+                        1,
+                        3,
+                        722
+                    ],
+                    [
+                        3,
+                        1,
+                        845
+                    ],
+                    [
+                        3,
+                        2,
+                        533
+                    ],
+                    [
+                        0,
+                        3,
+                        775
+                    ],
+                    [
+                        3,
+                        2,
+                        294
+                    ],
+                    [
+                        0,
+                        1,
+                        591
+                    ],
+                    [
+                        0,
+                        2,
+                        429
+                    ],
+                    [
+                        2,
+                        0,
+                        205
+                    ],
+                    [
+                        3,
+                        2,
+                        225
+                    ],
+                    [
+                        0,
+                        1,
+                        896
+                    ],
+                    [
+                        0,
+                        2,
+                        783
+                    ],
+                    [
+                        0,
+                        3,
+                        949
+                    ],
+                    [
+                        2,
+                        1,
+                        985
+                    ],
+                    [
+                        0,
+                        2,
+                        64
+                    ],
+                    [
+                        2,
+                        3,
+                        985
+                    ],
+                    [
+                        0,
+                        2,
+                        32
+                    ],
+                    [
+                        3,
+                        0,
+                        532
+                    ],
+                    [
+                        3,
+                        1,
+                        649
+                    ],
+                    [
+                        1,
+                        0,
+                        615
+                    ],
+                    [
+                        0,
+                        3,
+                        771
+                    ],
+                    [
+                        2,
+                        0,
+                        155
+                    ],
+                    [
+                        2,
+                        3,
+                        930
+                    ],
+                    [
+                        2,
+                        3,
+                        518
+                    ],
+                    [
+                        3,
+                        2,
+                        213
+                    ],
+                    [
+                        0,
+                        2,
+                        849
+                    ],
+                    [
+                        3,
+                        2,
+                        555
+                    ],
+                    [
+                        3,
+                        2,
+                        725
+                    ],
+                    [
+                        2,
+                        3,
+                        483
+                    ],
+                    [
+                        2,
+                        3,
+                        979
+                    ],
+                    [
+                        0,
+                        1,
+                        719
+                    ],
+                    [
+                        2,
+                        1,
+                        177
+                    ],
+                    [
+                        0,
+                        2,
+                        753
+                    ],
+                    [
+                        2,
+                        0,
+                        526
+                    ],
+                    [
+                        3,
+                        0,
+                        324
+                    ],
+                    [
+                        2,
+                        3,
+                        809
+                    ],
+                    [
+                        1,
+                        0,
+                        383
+                    ],
+                    [
+                        1,
+                        2,
+                        484
+                    ],
+                    [
+                        1,
+                        3,
+                        261
+                    ],
+                    [
+                        0,
+                        3,
+                        11
+                    ],
+                    [
+                        3,
+                        2,
+                        583
+                    ],
+                    [
+                        2,
+                        1,
+                        49
+                    ],
+                    [
+                        2,
+                        1,
+                        484
+                    ],
+                    [
+                        3,
+                        1,
+                        807
+                    ],
+                    [
+                        3,
+                        0,
+                        365
+                    ],
+                    [
+                        2,
+                        3,
+                        232
+                    ],
+                    [
+                        3,
+                        1,
+                        553
+                    ],
+                    [
+                        2,
+                        1,
+                        677
+                    ],
+                    [
+                        3,
+                        0,
+                        281
+                    ],
+                    [
+                        2,
+                        0,
+                        266
+                    ],
+                    [
+                        2,
+                        3,
+                        599
+                    ],
+                    [
+                        2,
+                        0,
+                        110
+                    ],
+                    [
+                        2,
+                        1,
+                        256
+                    ],
+                    [
+                        0,
+                        1,
+                        18
+                    ],
+                    [
+                        3,
+                        2,
+                        630
+                    ],
+                    [
+                        3,
+                        2,
+                        358
+                    ],
+                    [
+                        2,
+                        3,
+                        650
+                    ],
+                    [
+                        0,
+                        2,
+                        749
+                    ],
+                    [
+                        3,
+                        1,
+                        42
+                    ],
+                    [
+                        2,
+                        3,
+                        725
+                    ],
+                    [
+                        3,
+                        0,
+                        180
+                    ],
+                    [
+                        0,
+                        1,
+                        294
+                    ],
+                    [
+                        3,
+                        1,
+                        487
+                    ],
+                    [
+                        1,
+                        0,
+                        426
+                    ],
+                    [
+                        0,
+                        2,
+                        568
+                    ],
+                    [
+                        3,
+                        2,
+                        880
+                    ],
+                    [
+                        2,
+                        3,
+                        908
+                    ],
+                    [
+                        2,
+                        1,
+                        265
+                    ],
+                    [
+                        1,
+                        2,
+                        412
+                    ],
+                    [
+                        1,
+                        2,
+                        331
+                    ],
+                    [
+                        2,
+                        1,
+                        193
+                    ],
+                    [
+                        0,
+                        3,
+                        369
+                    ],
+                    [
+                        1,
+                        2,
+                        825
+                    ],
+                    [
+                        1,
+                        2,
+                        840
+                    ],
+                    [
+                        0,
+                        1,
+                        717
+                    ],
+                    [
+                        0,
+                        3,
+                        733
+                    ],
+                    [
+                        1,
+                        3,
+                        496
+                    ],
+                    [
+                        2,
+                        3,
+                        106
+                    ],
+                    [
+                        3,
+                        1,
+                        656
+                    ],
+                    [
+                        2,
+                        0,
+                        509
+                    ],
+                    [
+                        2,
+                        0,
+                        993
+                    ],
+                    [
+                        1,
+                        0,
+                        866
+                    ],
+                    [
+                        1,
+                        2,
+                        431
+                    ],
+                    [
+                        0,
+                        3,
+                        687
+                    ],
+                    [
+                        2,
+                        0,
+                        52
+                    ],
+                    [
+                        1,
+                        2,
+                        418
+                    ],
+                    [
+                        0,
+                        2,
+                        541
+                    ],
+                    [
+                        2,
+                        1,
+                        503
+                    ],
+                    [
+                        3,
+                        0,
+                        214
+                    ],
+                    [
+                        0,
+                        2,
+                        128
+                    ],
+                    [
+                        0,
+                        1,
+                        29
+                    ],
+                    [
+                        3,
+                        1,
+                        781
+                    ],
+                    [
+                        1,
+                        0,
+                        15
+                    ],
+                    [
+                        0,
+                        2,
+                        252
+                    ],
+                    [
+                        1,
+                        2,
+                        255
+                    ],
+                    [
+                        2,
+                        3,
+                        26
+                    ],
+                    [
+                        1,
+                        0,
+                        975
+                    ],
+                    [
+                        0,
+                        2,
+                        992
+                    ],
+                    [
+                        1,
+                        2,
+                        181
+                    ],
+                    [
+                        3,
+                        0,
+                        65
+                    ],
+                    [
+                        2,
+                        0,
+                        942
+                    ],
+                    [
+                        3,
+                        0,
+                        90
+                    ],
+                    [
+                        3,
+                        2,
+                        585
+                    ],
+                    [
+                        1,
+                        2,
+                        866
+                    ],
+                    [
+                        2,
+                        0,
+                        625
+                    ],
+                    [
+                        1,
+                        0,
+                        318
+                    ],
+                    [
+                        0,
+                        1,
+                        757
+                    ],
+                    [
+                        3,
+                        0,
+                        459
+                    ],
+                    [
+                        2,
+                        3,
+                        935
+                    ],
+                    [
+                        3,
+                        2,
+                        139
+                    ],
+                    [
+                        0,
+                        3,
+                        961
+                    ],
+                    [
+                        1,
+                        2,
+                        222
+                    ],
+                    [
+                        0,
+                        1,
+                        210
+                    ],
+                    [
+                        0,
+                        1,
+                        797
+                    ],
+                    [
+                        1,
+                        0,
+                        52
+                    ],
+                    [
+                        1,
+                        3,
+                        300
+                    ],
+                    [
+                        3,
+                        2,
+                        935
+                    ],
+                    [
+                        3,
+                        0,
+                        483
+                    ],
+                    [
+                        1,
+                        0,
+                        373
+                    ],
+                    [
+                        2,
+                        1,
+                        501
+                    ],
+                    [
+                        3,
+                        2,
+                        167
+                    ],
+                    [
+                        2,
+                        1,
+                        220
+                    ],
+                    [
+                        3,
+                        1,
+                        446
+                    ],
+                    [
+                        3,
+                        0,
+                        172
+                    ],
+                    [
+                        3,
+                        2,
+                        173
+                    ],
+                    [
+                        0,
+                        3,
+                        276
+                    ],
+                    [
+                        0,
+                        2,
+                        488
+                    ],
+                    [
+                        3,
+                        1,
+                        498
+                    ],
+                    [
+                        2,
+                        0,
+                        730
+                    ],
+                    [
+                        1,
+                        0,
+                        424
+                    ],
+                    [
+                        3,
+                        0,
+                        783
+                    ],
+                    [
+                        3,
+                        0,
+                        331
+                    ],
+                    [
+                        0,
+                        1,
+                        270
+                    ],
+                    [
+                        2,
+                        0,
+                        996
+                    ],
+                    [
+                        2,
+                        0,
+                        989
+                    ],
+                    [
+                        1,
+                        2,
+                        633
+                    ],
+                    [
+                        2,
+                        3,
+                        195
+                    ],
+                    [
+                        2,
+                        3,
+                        7
+                    ],
+                    [
+                        3,
+                        1,
+                        512
+                    ],
+                    [
+                        2,
+                        3,
+                        234
+                    ],
+                    [
+                        0,
+                        3,
+                        497
+                    ],
+                    [
+                        2,
+                        0,
+                        496
+                    ],
+                    [
+                        3,
+                        0,
+                        183
+                    ],
+                    [
+                        2,
+                        3,
+                        170
+                    ],
+                    [
+                        0,
+                        2,
+                        786
+                    ],
+                    [
+                        0,
+                        1,
+                        305
+                    ],
+                    [
+                        2,
+                        0,
+                        501
+                    ],
+                    [
+                        0,
+                        3,
+                        296
+                    ],
+                    [
+                        3,
+                        2,
+                        476
+                    ],
+                    [
+                        2,
+                        3,
+                        853
+                    ],
+                    [
+                        2,
+                        1,
+                        97
+                    ],
+                    [
+                        3,
+                        0,
+                        847
+                    ],
+                    [
+                        3,
+                        0,
+                        271
+                    ],
+                    [
+                        1,
+                        2,
+                        81
+                    ],
+                    [
+                        3,
+                        2,
+                        592
+                    ],
+                    [
+                        1,
+                        3,
+                        894
+                    ],
+                    [
+                        3,
+                        0,
+                        723
+                    ],
+                    [
+                        0,
+                        3,
+                        98
+                    ],
+                    [
+                        0,
+                        3,
+                        315
+                    ],
+                    [
+                        2,
+                        3,
+                        29
+                    ],
+                    [
+                        3,
+                        0,
+                        210
+                    ],
+                    [
+                        2,
+                        1,
+                        649
+                    ],
+                    [
+                        1,
+                        3,
+                        813
+                    ],
+                    [
+                        0,
+                        1,
+                        122
+                    ],
+                    [
+                        0,
+                        2,
+                        832
+                    ],
+                    [
+                        0,
+                        1,
+                        429
+                    ],
+                    [
+                        2,
+                        3,
+                        487
+                    ],
+                    [
+                        0,
+                        2,
+                        788
+                    ],
+                    [
+                        1,
+                        0,
+                        161
+                    ],
+                    [
+                        2,
+                        1,
+                        641
+                    ],
+                    [
+                        3,
+                        2,
+                        585
+                    ],
+                    [
+                        1,
+                        3,
+                        463
+                    ],
+                    [
+                        0,
+                        3,
+                        537
+                    ],
+                    [
+                        2,
+                        3,
+                        366
+                    ],
+                    [
+                        3,
+                        1,
+                        634
+                    ],
+                    [
+                        0,
+                        2,
+                        269
+                    ],
+                    [
+                        3,
+                        0,
+                        105
+                    ],
+                    [
+                        0,
+                        1,
+                        601
+                    ],
+                    [
+                        3,
+                        0,
+                        193
+                    ],
+                    [
+                        0,
+                        1,
+                        363
+                    ],
+                    [
+                        0,
+                        1,
+                        570
+                    ],
+                    [
+                        2,
+                        1,
+                        117
+                    ],
+                    [
+                        3,
+                        2,
+                        725
+                    ],
+                    [
+                        0,
+                        2,
+                        883
+                    ],
+                    [
+                        0,
+                        2,
+                        52
+                    ],
+                    [
+                        0,
+                        3,
+                        184
+                    ],
+                    [
+                        0,
+                        3,
+                        924
+                    ],
+                    [
+                        0,
+                        3,
+                        157
+                    ],
+                    [
+                        0,
+                        3,
+                        832
+                    ],
+                    [
+                        1,
+                        2,
+                        776
+                    ],
+                    [
+                        2,
+                        3,
+                        804
+                    ],
+                    [
+                        0,
+                        3,
+                        656
+                    ],
+                    [
+                        3,
+                        1,
+                        24
+                    ],
+                    [
+                        0,
+                        3,
+                        194
+                    ],
+                    [
+                        1,
+                        0,
+                        638
+                    ],
+                    [
+                        2,
+                        1,
+                        413
+                    ],
+                    [
+                        1,
+                        2,
+                        689
+                    ],
+                    [
+                        1,
+                        3,
+                        842
+                    ],
+                    [
+                        0,
+                        1,
+                        636
+                    ],
+                    [
+                        2,
+                        1,
+                        300
+                    ],
+                    [
+                        2,
+                        3,
+                        49
+                    ],
+                    [
+                        0,
+                        1,
+                        118
+                    ],
+                    [
+                        1,
+                        0,
+                        864
+                    ],
+                    [
+                        3,
+                        1,
+                        393
+                    ],
+                    [
+                        2,
+                        0,
+                        265
+                    ],
+                    [
+                        3,
+                        0,
+                        145
+                    ],
+                    [
+                        2,
+                        1,
+                        791
+                    ],
+                    [
+                        1,
+                        3,
+                        563
+                    ],
+                    [
+                        1,
+                        0,
+                        675
+                    ],
+                    [
+                        3,
+                        1,
+                        948
+                    ],
+                    [
+                        3,
+                        0,
+                        327
+                    ],
+                    [
+                        1,
+                        0,
+                        665
+                    ],
+                    [
+                        3,
+                        1,
+                        189
+                    ],
+                    [
+                        0,
+                        3,
+                        913
+                    ],
+                    [
+                        1,
+                        0,
+                        370
+                    ],
+                    [
+                        2,
+                        0,
+                        284
+                    ],
+                    [
+                        2,
+                        1,
+                        10
+                    ],
+                    [
+                        2,
+                        1,
+                        553
+                    ],
+                    [
+                        1,
+                        0,
+                        470
+                    ],
+                    [
+                        1,
+                        2,
+                        51
+                    ],
+                    [
+                        0,
+                        1,
+                        745
+                    ],
+                    [
+                        2,
+                        3,
+                        350
+                    ],
+                    [
+                        2,
+                        3,
+                        223
+                    ],
+                    [
+                        1,
+                        2,
+                        609
+                    ],
+                    [
+                        0,
+                        2,
+                        259
+                    ],
+                    [
+                        2,
+                        1,
+                        268
+                    ],
+                    [
+                        1,
+                        0,
+                        21
+                    ],
+                    [
+                        0,
+                        3,
+                        362
+                    ],
+                    [
+                        2,
+                        0,
+                        513
+                    ],
+                    [
+                        0,
+                        1,
+                        371
+                    ],
+                    [
+                        2,
+                        1,
+                        290
+                    ],
+                    [
+                        0,
+                        1,
+                        784
+                    ],
+                    [
+                        3,
+                        1,
+                        262
+                    ],
+                    [
+                        1,
+                        3,
+                        557
+                    ],
+                    [
+                        0,
+                        3,
+                        618
+                    ],
+                    [
+                        1,
+                        3,
+                        652
+                    ],
+                    [
+                        2,
+                        3,
+                        782
+                    ],
+                    [
+                        1,
+                        3,
+                        845
+                    ],
+                    [
+                        1,
+                        0,
+                        636
+                    ],
+                    [
+                        3,
+                        1,
+                        891
+                    ],
+                    [
+                        1,
+                        0,
+                        451
+                    ],
+                    [
+                        1,
+                        3,
+                        505
+                    ],
+                    [
+                        3,
+                        0,
+                        289
+                    ],
+                    [
+                        3,
+                        2,
+                        400
+                    ],
+                    [
+                        2,
+                        3,
+                        697
+                    ],
+                    [
+                        3,
+                        1,
+                        160
+                    ],
+                    [
+                        0,
+                        1,
+                        366
+                    ],
+                    [
+                        1,
+                        3,
+                        923
+                    ],
+                    [
+                        3,
+                        2,
+                        553
+                    ],
+                    [
+                        2,
+                        1,
+                        91
+                    ],
+                    [
+                        0,
+                        3,
+                        269
+                    ],
+                    [
+                        0,
+                        3,
+                        909
+                    ],
+                    [
+                        2,
+                        1,
+                        363
+                    ],
+                    [
+                        1,
+                        2,
+                        940
+                    ],
+                    [
+                        0,
+                        1,
+                        812
+                    ],
+                    [
+                        2,
+                        3,
+                        803
+                    ],
+                    [
+                        2,
+                        0,
+                        366
+                    ],
+                    [
+                        1,
+                        2,
+                        335
+                    ],
+                    [
+                        3,
+                        0,
+                        796
+                    ],
+                    [
+                        0,
+                        3,
+                        76
+                    ],
+                    [
+                        2,
+                        1,
+                        444
+                    ],
+                    [
+                        0,
+                        2,
+                        356
+                    ],
+                    [
+                        3,
+                        2,
+                        922
+                    ],
+                    [
+                        0,
+                        2,
+                        923
+                    ],
+                    [
+                        1,
+                        2,
+                        5
+                    ],
+                    [
+                        1,
+                        3,
+                        298
+                    ],
+                    [
+                        0,
+                        3,
+                        398
+                    ],
+                    [
+                        1,
+                        2,
+                        947
+                    ],
+                    [
+                        0,
+                        1,
+                        377
+                    ],
+                    [
+                        1,
+                        2,
+                        696
+                    ],
+                    [
+                        0,
+                        2,
+                        666
+                    ],
+                    [
+                        2,
+                        3,
+                        246
+                    ],
+                    [
+                        1,
+                        2,
+                        161
+                    ],
+                    [
+                        1,
+                        3,
+                        439
+                    ],
+                    [
+                        3,
+                        1,
+                        931
+                    ],
+                    [
+                        3,
+                        1,
+                        232
+                    ],
+                    [
+                        1,
+                        0,
+                        126
+                    ],
+                    [
+                        0,
+                        2,
+                        225
+                    ],
+                    [
+                        0,
+                        1,
+                        484
+                    ],
+                    [
+                        2,
+                        3,
+                        103
+                    ],
+                    [
+                        1,
+                        0,
+                        227
+                    ],
+                    [
+                        2,
+                        1,
+                        263
+                    ],
+                    [
+                        2,
+                        3,
+                        549
+                    ],
+                    [
+                        1,
+                        3,
+                        611
+                    ],
+                    [
+                        1,
+                        2,
+                        904
+                    ],
+                    [
+                        2,
+                        1,
+                        208
+                    ],
+                    [
+                        1,
+                        2,
+                        372
+                    ],
+                    [
+                        0,
+                        2,
+                        17
+                    ],
+                    [
+                        3,
+                        2,
+                        745
+                    ],
+                    [
+                        0,
+                        2,
+                        441
+                    ],
+                    [
+                        2,
+                        3,
+                        410
+                    ],
+                    [
+                        1,
+                        3,
+                        458
+                    ],
+                    [
+                        0,
+                        3,
+                        427
+                    ],
+                    [
+                        1,
+                        2,
+                        417
+                    ],
+                    [
+                        2,
+                        1,
+                        86
+                    ],
+                    [
+                        3,
+                        2,
+                        408
+                    ],
+                    [
+                        2,
+                        0,
+                        93
+                    ],
+                    [
+                        1,
+                        3,
+                        787
+                    ],
+                    [
+                        1,
+                        2,
+                        462
+                    ],
+                    [
+                        2,
+                        1,
+                        395
+                    ],
+                    [
+                        3,
+                        0,
+                        353
+                    ],
+                    [
+                        2,
+                        1,
+                        26
+                    ],
+                    [
+                        1,
+                        2,
+                        415
+                    ],
+                    [
+                        3,
+                        0,
+                        918
+                    ],
+                    [
+                        1,
+                        0,
+                        25
+                    ],
+                    [
+                        3,
+                        1,
+                        448
+                    ],
+                    [
+                        2,
+                        0,
+                        223
+                    ],
+                    [
+                        3,
+                        0,
+                        214
+                    ],
+                    [
+                        0,
+                        3,
+                        957
+                    ],
+                    [
+                        2,
+                        3,
+                        480
+                    ],
+                    [
+                        1,
+                        2,
+                        163
+                    ],
+                    [
+                        1,
+                        3,
+                        750
+                    ],
+                    [
+                        2,
+                        3,
+                        443
+                    ],
+                    [
+                        3,
+                        0,
+                        656
+                    ],
+                    [
+                        2,
+                        0,
+                        730
+                    ],
+                    [
+                        0,
+                        3,
+                        613
+                    ],
+                    [
+                        3,
+                        1,
+                        865
+                    ],
+                    [
+                        2,
+                        3,
+                        977
+                    ],
+                    [
+                        3,
+                        1,
+                        692
+                    ],
+                    [
+                        3,
+                        0,
+                        767
+                    ],
+                    [
+                        1,
+                        2,
+                        487
+                    ],
+                    [
+                        0,
+                        2,
+                        554
+                    ],
+                    [
+                        0,
+                        1,
+                        915
+                    ],
+                    [
+                        1,
+                        0,
+                        939
+                    ],
+                    [
+                        0,
+                        2,
+                        632
+                    ],
+                    [
+                        0,
+                        1,
+                        506
+                    ],
+                    [
+                        0,
+                        1,
+                        407
+                    ],
+                    [
+                        2,
+                        1,
+                        898
+                    ],
+                    [
+                        2,
+                        1,
+                        729
+                    ],
+                    [
+                        0,
+                        2,
+                        56
+                    ],
+                    [
+                        0,
+                        1,
+                        56
+                    ],
+                    [
+                        1,
+                        3,
+                        145
+                    ],
+                    [
+                        1,
+                        0,
+                        86
+                    ],
+                    [
+                        2,
+                        0,
+                        252
+                    ],
+                    [
+                        2,
+                        0,
+                        496
+                    ],
+                    [
+                        1,
+                        3,
+                        547
+                    ],
+                    [
+                        2,
+                        3,
+                        275
+                    ],
+                    [
+                        0,
+                        2,
+                        466
+                    ],
+                    [
+                        1,
+                        2,
+                        720
+                    ],
+                    [
+                        3,
+                        1,
+                        522
+                    ],
+                    [
+                        2,
+                        1,
+                        929
+                    ],
+                    [
+                        3,
+                        2,
+                        54
+                    ],
+                    [
+                        1,
+                        2,
+                        761
+                    ],
+                    [
+                        3,
+                        0,
+                        484
+                    ],
+                    [
+                        3,
+                        1,
+                        129
+                    ],
+                    [
+                        1,
+                        0,
+                        247
+                    ],
+                    [
+                        3,
+                        2,
+                        592
+                    ],
+                    [
+                        2,
+                        3,
+                        654
+                    ],
+                    [
+                        2,
+                        1,
+                        793
+                    ],
+                    [
+                        2,
+                        3,
+                        353
+                    ],
+                    [
+                        3,
+                        1,
+                        687
+                    ],
+                    [
+                        3,
+                        2,
+                        183
+                    ],
+                    [
+                        2,
+                        0,
+                        692
+                    ],
+                    [
+                        0,
+                        2,
+                        241
+                    ],
+                    [
+                        0,
+                        3,
+                        859
+                    ],
+                    [
+                        1,
+                        2,
+                        367
+                    ],
+                    [
+                        0,
+                        1,
+                        906
+                    ],
+                    [
+                        2,
+                        0,
+                        549
+                    ],
+                    [
+                        3,
+                        2,
+                        88
+                    ],
+                    [
+                        2,
+                        1,
+                        148
+                    ],
+                    [
+                        2,
+                        3,
+                        564
+                    ],
+                    [
+                        2,
+                        3,
+                        523
+                    ],
+                    [
+                        3,
+                        2,
+                        791
+                    ],
+                    [
+                        3,
+                        1,
+                        245
+                    ],
+                    [
+                        1,
+                        2,
+                        713
+                    ],
+                    [
+                        2,
+                        3,
+                        422
+                    ],
+                    [
+                        0,
+                        2,
+                        397
+                    ],
+                    [
+                        0,
+                        1,
+                        897
+                    ],
+                    [
+                        2,
+                        0,
+                        259
+                    ],
+                    [
+                        1,
+                        0,
+                        856
+                    ],
+                    [
+                        1,
+                        0,
+                        431
+                    ],
+                    [
+                        3,
+                        0,
+                        663
+                    ],
+                    [
+                        2,
+                        3,
+                        820
+                    ],
+                    [
+                        1,
+                        3,
+                        376
+                    ],
+                    [
+                        0,
+                        1,
+                        839
+                    ],
+                    [
+                        0,
+                        1,
+                        483
+                    ],
+                    [
+                        2,
+                        3,
+                        559
+                    ],
+                    [
+                        1,
+                        2,
+                        81
+                    ],
+                    [
+                        0,
+                        3,
+                        864
+                    ],
+                    [
+                        2,
+                        0,
+                        107
+                    ],
+                    [
+                        3,
+                        2,
+                        258
+                    ],
+                    [
+                        2,
+                        1,
+                        493
+                    ],
+                    [
+                        0,
+                        3,
+                        735
+                    ],
+                    [
+                        1,
+                        2,
+                        332
+                    ],
+                    [
+                        2,
+                        3,
+                        912
+                    ],
+                    [
+                        2,
+                        1,
+                        816
+                    ],
+                    [
+                        2,
+                        1,
+                        301
+                    ],
+                    [
+                        0,
+                        2,
+                        761
+                    ],
+                    [
+                        1,
+                        3,
+                        372
+                    ],
+                    [
+                        0,
+                        3,
+                        690
+                    ],
+                    [
+                        2,
+                        3,
+                        381
+                    ],
+                    [
+                        2,
+                        0,
+                        297
+                    ],
+                    [
+                        3,
+                        0,
+                        697
+                    ],
+                    [
+                        3,
+                        0,
+                        814
+                    ],
+                    [
+                        1,
+                        2,
+                        554
+                    ],
+                    [
+                        1,
+                        2,
+                        146
+                    ],
+                    [
+                        2,
+                        1,
+                        910
+                    ],
+                    [
+                        0,
+                        1,
+                        454
+                    ],
+                    [
+                        0,
+                        2,
+                        216
+                    ],
+                    [
+                        3,
+                        0,
+                        132
+                    ],
+                    [
+                        1,
+                        0,
+                        842
+                    ],
+                    [
+                        0,
+                        3,
+                        647
+                    ],
+                    [
+                        0,
+                        2,
+                        824
+                    ],
+                    [
+                        2,
+                        3,
+                        617
+                    ],
+                    [
+                        3,
+                        2,
+                        895
+                    ],
+                    [
+                        2,
+                        1,
+                        84
+                    ],
+                    [
+                        0,
+                        3,
+                        583
+                    ],
+                    [
+                        3,
+                        0,
+                        455
+                    ],
+                    [
+                        2,
+                        1,
+                        840
+                    ],
+                    [
+                        3,
+                        0,
+                        546
+                    ],
+                    [
+                        0,
+                        2,
+                        228
+                    ],
+                    [
+                        0,
+                        1,
+                        230
+                    ],
+                    [
+                        0,
+                        1,
+                        981
+                    ],
+                    [
+                        0,
+                        3,
+                        125
+                    ],
+                    [
+                        2,
+                        0,
+                        577
+                    ],
+                    [
+                        1,
+                        0,
+                        768
+                    ],
+                    [
+                        2,
+                        1,
+                        632
+                    ],
+                    [
+                        0,
+                        1,
+                        884
+                    ],
+                    [
+                        2,
+                        1,
+                        456
+                    ],
+                    [
+                        0,
+                        1,
+                        439
+                    ],
+                    [
+                        0,
+                        2,
+                        107
+                    ],
+                    [
+                        1,
+                        2,
+                        648
+                    ],
+                    [
+                        0,
+                        2,
+                        240
+                    ],
+                    [
+                        3,
+                        2,
+                        77
+                    ],
+                    [
+                        0,
+                        1,
+                        444
+                    ],
+                    [
+                        0,
+                        3,
+                        742
+                    ],
+                    [
+                        3,
+                        2,
+                        494
+                    ],
+                    [
+                        1,
+                        3,
+                        962
+                    ],
+                    [
+                        3,
+                        1,
+                        942
+                    ],
+                    [
+                        1,
+                        3,
+                        336
+                    ],
+                    [
+                        1,
+                        2,
+                        459
+                    ],
+                    [
+                        2,
+                        3,
+                        976
+                    ],
+                    [
+                        2,
+                        0,
+                        267
+                    ],
+                    [
+                        3,
+                        2,
+                        298
+                    ],
+                    [
+                        1,
+                        3,
+                        432
+                    ],
+                    [
+                        2,
+                        0,
+                        834
+                    ],
+                    [
+                        3,
+                        1,
+                        861
+                    ],
+                    [
+                        0,
+                        3,
+                        83
+                    ],
+                    [
+                        2,
+                        1,
+                        657
+                    ],
+                    [
+                        3,
+                        0,
+                        404
+                    ],
+                    [
+                        3,
+                        2,
+                        718
+                    ],
+                    [
+                        0,
+                        3,
+                        532
+                    ],
+                    [
+                        3,
+                        2,
+                        765
+                    ],
+                    [
+                        1,
+                        2,
+                        129
+                    ],
+                    [
+                        0,
+                        2,
+                        971
+                    ],
+                    [
+                        3,
+                        0,
+                        624
+                    ],
+                    [
+                        2,
+                        1,
+                        217
+                    ],
+                    [
+                        3,
+                        0,
+                        728
+                    ],
+                    [
+                        0,
+                        1,
+                        32
+                    ],
+                    [
+                        2,
+                        3,
+                        583
+                    ],
+                    [
+                        1,
+                        0,
+                        17
+                    ],
+                    [
+                        0,
+                        1,
+                        181
+                    ],
+                    [
+                        2,
+                        3,
+                        439
+                    ],
+                    [
+                        2,
+                        1,
+                        771
+                    ],
+                    [
+                        0,
+                        1,
+                        494
+                    ],
+                    [
+                        3,
+                        2,
+                        28
+                    ],
+                    [
+                        2,
+                        3,
+                        680
+                    ],
+                    [
+                        1,
+                        0,
+                        729
+                    ],
+                    [
+                        0,
+                        1,
+                        692
+                    ],
+                    [
+                        0,
+                        3,
+                        529
+                    ],
+                    [
+                        0,
+                        1,
+                        107
+                    ],
+                    [
+                        3,
+                        1,
+                        861
+                    ],
+                    [
+                        3,
+                        1,
+                        678
+                    ],
+                    [
+                        3,
+                        1,
+                        885
+                    ],
+                    [
+                        0,
+                        2,
+                        591
+                    ],
+                    [
+                        1,
+                        3,
+                        3
+                    ],
+                    [
+                        0,
+                        2,
+                        441
+                    ],
+                    [
+                        3,
+                        0,
+                        260
+                    ],
+                    [
+                        2,
+                        3,
+                        822
+                    ],
+                    [
+                        1,
+                        0,
+                        18
+                    ],
+                    [
+                        1,
+                        3,
+                        160
+                    ],
+                    [
+                        3,
+                        0,
+                        791
+                    ],
+                    [
+                        0,
+                        1,
+                        357
+                    ],
+                    [
+                        2,
+                        3,
+                        543
+                    ],
+                    [
+                        3,
+                        0,
+                        826
+                    ],
+                    [
+                        3,
+                        0,
+                        174
+                    ],
+                    [
+                        3,
+                        0,
+                        689
+                    ],
+                    [
+                        3,
+                        2,
+                        983
+                    ],
+                    [
+                        1,
+                        2,
+                        402
+                    ],
+                    [
+                        2,
+                        3,
+                        455
+                    ],
+                    [
+                        1,
+                        2,
+                        90
+                    ],
+                    [
+                        1,
+                        3,
+                        820
+                    ],
+                    [
+                        2,
+                        3,
+                        477
+                    ],
+                    [
+                        3,
+                        0,
+                        253
+                    ],
+                    [
+                        1,
+                        0,
+                        994
+                    ],
+                    [
+                        3,
+                        1,
+                        179
+                    ],
+                    [
+                        0,
+                        1,
+                        512
+                    ],
+                    [
+                        2,
+                        3,
+                        649
+                    ],
+                    [
+                        2,
+                        1,
+                        859
+                    ],
+                    [
+                        2,
+                        1,
+                        878
+                    ],
+                    [
+                        3,
+                        0,
+                        276
+                    ],
+                    [
+                        0,
+                        1,
+                        351
+                    ],
+                    [
+                        2,
+                        0,
+                        870
+                    ],
+                    [
+                        1,
+                        2,
+                        185
+                    ],
+                    [
+                        2,
+                        1,
+                        964
+                    ],
+                    [
+                        2,
+                        3,
+                        185
+                    ],
+                    [
+                        2,
+                        0,
+                        546
+                    ],
+                    [
+                        1,
+                        3,
+                        908
+                    ],
+                    [
+                        3,
+                        0,
+                        18
+                    ],
+                    [
+                        2,
+                        0,
+                        658
+                    ],
+                    [
+                        2,
+                        1,
+                        211
+                    ],
+                    [
+                        2,
+                        3,
+                        883
+                    ],
+                    [
+                        1,
+                        3,
+                        405
+                    ],
+                    [
+                        1,
+                        2,
+                        399
+                    ],
+                    [
+                        1,
+                        2,
+                        325
+                    ],
+                    [
+                        1,
+                        2,
+                        763
+                    ],
+                    [
+                        3,
+                        0,
+                        465
+                    ],
+                    [
+                        2,
+                        0,
+                        242
+                    ],
+                    [
+                        1,
+                        2,
+                        6
+                    ],
+                    [
+                        3,
+                        2,
+                        227
+                    ],
+                    [
+                        2,
+                        1,
+                        426
+                    ],
+                    [
+                        1,
+                        0,
+                        605
+                    ],
+                    [
+                        2,
+                        1,
+                        811
+                    ],
+                    [
+                        3,
+                        1,
+                        757
+                    ],
+                    [
+                        3,
+                        2,
+                        783
+                    ],
+                    [
+                        0,
+                        1,
+                        986
+                    ],
+                    [
+                        2,
+                        3,
+                        983
+                    ],
+                    [
+                        1,
+                        2,
+                        476
+                    ],
+                    [
+                        2,
+                        3,
+                        815
+                    ],
+                    [
+                        3,
+                        2,
+                        170
+                    ],
+                    [
+                        3,
+                        1,
+                        255
+                    ],
+                    [
+                        0,
+                        3,
+                        974
+                    ],
+                    [
+                        1,
+                        2,
+                        836
+                    ],
+                    [
+                        1,
+                        3,
+                        721
+                    ],
+                    [
+                        3,
+                        1,
+                        822
+                    ],
+                    [
+                        2,
+                        0,
+                        374
+                    ],
+                    [
+                        2,
+                        1,
+                        354
+                    ],
+                    [
+                        2,
+                        3,
+                        686
+                    ],
+                    [
+                        3,
+                        2,
+                        513
+                    ],
+                    [
+                        3,
+                        1,
+                        841
+                    ],
+                    [
+                        3,
+                        2,
+                        261
+                    ],
+                    [
+                        0,
+                        3,
+                        662
+                    ],
+                    [
+                        1,
+                        0,
+                        670
+                    ],
+                    [
+                        3,
+                        0,
+                        569
+                    ],
+                    [
+                        3,
+                        1,
+                        980
+                    ],
+                    [
+                        3,
+                        0,
+                        636
+                    ],
+                    [
+                        0,
+                        2,
+                        678
+                    ],
+                    [
+                        2,
+                        1,
+                        455
+                    ],
+                    [
+                        3,
+                        1,
+                        340
+                    ],
+                    [
+                        3,
+                        2,
+                        521
+                    ],
+                    [
+                        3,
+                        0,
+                        211
+                    ],
+                    [
+                        0,
+                        3,
+                        915
+                    ],
+                    [
+                        0,
+                        1,
+                        473
+                    ],
+                    [
+                        1,
+                        0,
+                        544
+                    ],
+                    [
+                        2,
+                        0,
+                        103
+                    ],
+                    [
+                        0,
+                        1,
+                        728
+                    ],
+                    [
+                        3,
+                        2,
+                        75
+                    ],
+                    [
+                        2,
+                        1,
+                        514
+                    ],
+                    [
+                        2,
+                        3,
+                        550
+                    ],
+                    [
+                        1,
+                        2,
+                        97
+                    ],
+                    [
+                        0,
+                        2,
+                        656
+                    ],
+                    [
+                        2,
+                        1,
+                        47
+                    ],
+                    [
+                        1,
+                        2,
+                        72
+                    ],
+                    [
+                        1,
+                        3,
+                        414
+                    ],
+                    [
+                        2,
+                        0,
+                        901
+                    ],
+                    [
+                        2,
+                        3,
+                        625
+                    ],
+                    [
+                        2,
+                        1,
+                        947
+                    ],
+                    [
+                        1,
+                        2,
+                        455
+                    ],
+                    [
+                        0,
+                        2,
+                        270
+                    ],
+                    [
+                        0,
+                        2,
+                        789
+                    ],
+                    [
+                        0,
+                        2,
+                        271
+                    ],
+                    [
+                        1,
+                        2,
+                        844
+                    ],
+                    [
+                        0,
+                        1,
+                        372
+                    ],
+                    [
+                        1,
+                        3,
+                        830
+                    ],
+                    [
+                        2,
+                        0,
+                        996
+                    ],
+                    [
+                        0,
+                        3,
+                        675
+                    ],
+                    [
+                        1,
+                        2,
+                        141
+                    ],
+                    [
+                        2,
+                        1,
+                        916
+                    ],
+                    [
+                        2,
+                        1,
+                        721
+                    ],
+                    [
+                        0,
+                        1,
+                        864
+                    ],
+                    [
+                        2,
+                        1,
+                        508
+                    ],
+                    [
+                        1,
+                        3,
+                        740
+                    ],
+                    [
+                        3,
+                        1,
+                        663
+                    ],
+                    [
+                        2,
+                        3,
+                        255
+                    ],
+                    [
+                        1,
+                        3,
+                        172
+                    ],
+                    [
+                        0,
+                        2,
+                        553
+                    ],
+                    [
+                        1,
+                        3,
+                        97
+                    ],
+                    [
+                        1,
+                        2,
+                        500
+                    ],
+                    [
+                        3,
+                        2,
+                        786
+                    ],
+                    [
+                        0,
+                        1,
+                        775
+                    ],
+                    [
+                        0,
+                        1,
+                        436
+                    ],
+                    [
+                        0,
+                        2,
+                        933
+                    ],
+                    [
+                        2,
+                        0,
+                        828
+                    ],
+                    [
+                        2,
+                        1,
+                        414
+                    ],
+                    [
+                        1,
+                        3,
+                        178
+                    ],
+                    [
+                        3,
+                        0,
+                        612
+                    ],
+                    [
+                        2,
+                        3,
+                        303
+                    ],
+                    [
+                        0,
+                        2,
+                        390
+                    ],
+                    [
+                        2,
+                        0,
+                        972
+                    ],
+                    [
+                        3,
+                        2,
+                        167
+                    ],
+                    [
+                        3,
+                        1,
+                        457
+                    ],
+                    [
+                        2,
+                        0,
+                        372
+                    ],
+                    [
+                        1,
+                        0,
+                        735
+                    ],
+                    [
+                        0,
+                        3,
+                        884
+                    ],
+                    [
+                        1,
+                        2,
+                        499
+                    ],
+                    [
+                        0,
+                        2,
+                        473
+                    ],
+                    [
+                        2,
+                        1,
+                        883
+                    ],
+                    [
+                        1,
+                        3,
+                        76
+                    ],
+                    [
+                        0,
+                        3,
+                        853
+                    ],
+                    [
+                        3,
+                        1,
+                        217
+                    ],
+                    [
+                        2,
+                        0,
+                        192
+                    ],
+                    [
+                        2,
+                        0,
+                        848
+                    ],
+                    [
+                        3,
+                        0,
+                        720
+                    ],
+                    [
+                        0,
+                        1,
+                        373
+                    ],
+                    [
+                        2,
+                        1,
+                        542
+                    ],
+                    [
+                        1,
+                        2,
+                        316
+                    ],
+                    [
+                        2,
+                        0,
+                        318
+                    ],
+                    [
+                        1,
+                        2,
+                        841
+                    ],
+                    [
+                        1,
+                        0,
+                        981
+                    ],
+                    [
+                        1,
+                        0,
+                        201
+                    ],
+                    [
+                        2,
+                        3,
+                        776
+                    ],
+                    [
+                        1,
+                        3,
+                        588
+                    ],
+                    [
+                        3,
+                        2,
+                        669
+                    ],
+                    [
+                        2,
+                        1,
+                        185
+                    ],
+                    [
+                        1,
+                        0,
+                        817
+                    ],
+                    [
+                        0,
+                        1,
+                        34
+                    ],
+                    [
+                        2,
+                        0,
+                        16
+                    ],
+                    [
+                        3,
+                        0,
+                        609
+                    ],
+                    [
+                        0,
+                        2,
+                        80
+                    ],
+                    [
+                        2,
+                        3,
+                        554
+                    ],
+                    [
+                        1,
+                        2,
+                        813
+                    ],
+                    [
+                        3,
+                        2,
+                        159
+                    ],
+                    [
+                        2,
+                        0,
+                        806
+                    ],
+                    [
+                        3,
+                        1,
+                        189
+                    ],
+                    [
+                        0,
+                        3,
+                        553
+                    ],
+                    [
+                        1,
+                        0,
+                        388
+                    ],
+                    [
+                        1,
+                        0,
+                        816
+                    ],
+                    [
+                        2,
+                        0,
+                        965
+                    ],
+                    [
+                        3,
+                        0,
+                        855
+                    ],
+                    [
+                        0,
+                        3,
+                        584
+                    ],
+                    [
+                        1,
+                        2,
+                        777
+                    ],
+                    [
+                        3,
+                        1,
+                        964
+                    ],
+                    [
+                        2,
+                        1,
+                        467
+                    ],
+                    [
+                        1,
+                        0,
+                        703
+                    ],
+                    [
+                        0,
+                        3,
+                        684
+                    ],
+                    [
+                        2,
+                        1,
+                        875
+                    ],
+                    [
+                        1,
+                        0,
+                        547
+                    ],
+                    [
+                        2,
+                        1,
+                        780
+                    ],
+                    [
+                        1,
+                        3,
+                        406
+                    ],
+                    [
+                        3,
+                        0,
+                        874
+                    ],
+                    [
+                        2,
+                        3,
+                        294
+                    ],
+                    [
+                        1,
+                        2,
+                        738
+                    ],
+                    [
+                        2,
+                        1,
+                        723
+                    ],
+                    [
+                        3,
+                        0,
+                        524
+                    ],
+                    [
+                        1,
+                        2,
+                        500
+                    ],
+                    [
+                        2,
+                        0,
+                        304
+                    ],
+                    [
+                        3,
+                        0,
+                        621
+                    ],
+                    [
+                        0,
+                        1,
+                        12
+                    ],
+                    [
+                        3,
+                        1,
+                        572
+                    ],
+                    [
+                        3,
+                        2,
+                        603
+                    ],
+                    [
+                        0,
+                        1,
+                        415
+                    ],
+                    [
+                        3,
+                        2,
+                        301
+                    ],
+                    [
+                        2,
+                        3,
+                        869
+                    ],
+                    [
+                        1,
+                        0,
+                        735
+                    ],
+                    [
+                        0,
+                        2,
+                        255
+                    ],
+                    [
+                        3,
+                        1,
+                        726
+                    ],
+                    [
+                        0,
+                        3,
+                        307
+                    ],
+                    [
+                        3,
+                        2,
+                        344
+                    ],
+                    [
+                        2,
+                        3,
+                        88
+                    ],
+                    [
+                        2,
+                        3,
+                        209
+                    ],
+                    [
+                        1,
+                        0,
+                        575
+                    ],
+                    [
+                        2,
+                        1,
+                        741
+                    ],
+                    [
+                        1,
+                        0,
+                        220
+                    ],
+                    [
+                        1,
+                        0,
+                        380
+                    ],
+                    [
+                        2,
+                        0,
+                        690
+                    ],
+                    [
+                        1,
+                        3,
+                        900
+                    ],
+                    [
+                        1,
+                        2,
+                        851
+                    ],
+                    [
+                        3,
+                        0,
+                        506
+                    ],
+                    [
+                        3,
+                        2,
+                        468
+                    ],
+                    [
+                        0,
+                        3,
+                        130
+                    ],
+                    [
+                        1,
+                        2,
+                        744
+                    ],
+                    [
+                        3,
+                        0,
+                        912
+                    ],
+                    [
+                        3,
+                        0,
+                        216
+                    ],
+                    [
+                        0,
+                        2,
+                        576
+                    ],
+                    [
+                        1,
+                        2,
+                        136
+                    ],
+                    [
+                        0,
+                        2,
+                        133
+                    ],
+                    [
+                        0,
+                        3,
+                        527
+                    ],
+                    [
+                        2,
+                        3,
+                        295
+                    ],
+                    [
+                        2,
+                        0,
+                        928
+                    ],
+                    [
+                        0,
+                        3,
+                        78
+                    ],
+                    [
+                        1,
+                        0,
+                        582
+                    ],
+                    [
+                        1,
+                        3,
+                        900
+                    ],
+                    [
+                        3,
+                        2,
+                        252
+                    ],
+                    [
+                        0,
+                        3,
+                        499
+                    ],
+                    [
+                        1,
+                        0,
+                        366
+                    ],
+                    [
+                        3,
+                        1,
+                        776
+                    ],
+                    [
+                        0,
+                        1,
+                        852
+                    ],
+                    [
+                        3,
+                        1,
+                        531
+                    ]
+                ]
+            ],
+            "output": 16
+        },
+        {
+            "input": [
+                3,
+                62946,
+                [
+                    [
+                        0,
+                        2,
+                        729
+                    ],
+                    [
+                        0,
+                        1,
+                        852
+                    ],
+                    [
+                        0,
+                        2,
+                        517
+                    ],
+                    [
+                        1,
+                        2,
+                        908
+                    ],
+                    [
+                        1,
+                        2,
+                        153
+                    ],
+                    [
+                        1,
+                        0,
+                        196
+                    ],
+                    [
+                        0,
+                        2,
+                        282
+                    ],
+                    [
+                        1,
+                        2,
+                        78
+                    ],
+                    [
+                        2,
+                        1,
+                        38
+                    ],
+                    [
+                        1,
+                        2,
+                        984
+                    ],
+                    [
+                        1,
+                        0,
+                        538
+                    ],
+                    [
+                        2,
+                        0,
+                        295
+                    ],
+                    [
+                        0,
+                        1,
+                        549
+                    ],
+                    [
+                        0,
+                        2,
+                        575
+                    ],
+                    [
+                        2,
+                        0,
+                        976
+                    ],
+                    [
+                        2,
+                        1,
+                        216
+                    ],
+                    [
+                        2,
+                        0,
+                        620
+                    ],
+                    [
+                        0,
+                        2,
+                        181
+                    ],
+                    [
+                        1,
+                        2,
+                        815
+                    ],
+                    [
+                        2,
+                        1,
+                        671
+                    ],
+                    [
+                        1,
+                        0,
+                        716
+                    ],
+                    [
+                        2,
+                        1,
+                        487
+                    ],
+                    [
+                        2,
+                        0,
+                        676
+                    ],
+                    [
+                        2,
+                        0,
+                        201
+                    ],
+                    [
+                        1,
+                        0,
+                        681
+                    ],
+                    [
+                        0,
+                        2,
+                        5
+                    ],
+                    [
+                        2,
+                        1,
+                        733
+                    ],
+                    [
+                        0,
+                        1,
+                        349
+                    ],
+                    [
+                        1,
+                        2,
+                        591
+                    ],
+                    [
+                        0,
+                        1,
+                        304
+                    ],
+                    [
+                        2,
+                        1,
+                        333
+                    ],
+                    [
+                        1,
+                        2,
+                        342
+                    ],
+                    [
+                        2,
+                        0,
+                        158
+                    ],
+                    [
+                        2,
+                        0,
+                        908
+                    ],
+                    [
+                        2,
+                        0,
+                        426
+                    ],
+                    [
+                        2,
+                        1,
+                        551
+                    ],
+                    [
+                        2,
+                        0,
+                        629
+                    ],
+                    [
+                        0,
+                        2,
+                        326
+                    ],
+                    [
+                        1,
+                        0,
+                        688
+                    ],
+                    [
+                        1,
+                        2,
+                        871
+                    ],
+                    [
+                        2,
+                        1,
+                        7
+                    ],
+                    [
+                        0,
+                        1,
+                        48
+                    ],
+                    [
+                        0,
+                        2,
+                        268
+                    ],
+                    [
+                        0,
+                        1,
+                        862
+                    ],
+                    [
+                        0,
+                        1,
+                        623
+                    ],
+                    [
+                        2,
+                        1,
+                        749
+                    ],
+                    [
+                        2,
+                        1,
+                        461
+                    ],
+                    [
+                        2,
+                        1,
+                        130
+                    ],
+                    [
+                        1,
+                        2,
+                        84
+                    ],
+                    [
+                        2,
+                        0,
+                        750
+                    ],
+                    [
+                        1,
+                        0,
+                        795
+                    ],
+                    [
+                        1,
+                        2,
+                        176
+                    ],
+                    [
+                        0,
+                        2,
+                        402
+                    ],
+                    [
+                        0,
+                        1,
+                        515
+                    ],
+                    [
+                        2,
+                        1,
+                        364
+                    ],
+                    [
+                        2,
+                        1,
+                        244
+                    ],
+                    [
+                        0,
+                        2,
+                        979
+                    ],
+                    [
+                        2,
+                        0,
+                        389
+                    ],
+                    [
+                        2,
+                        0,
+                        96
+                    ],
+                    [
+                        2,
+                        1,
+                        306
+                    ],
+                    [
+                        1,
+                        2,
+                        956
+                    ],
+                    [
+                        2,
+                        1,
+                        444
+                    ],
+                    [
+                        0,
+                        1,
+                        98
+                    ],
+                    [
+                        2,
+                        0,
+                        415
+                    ],
+                    [
+                        1,
+                        2,
+                        487
+                    ],
+                    [
+                        1,
+                        2,
+                        841
+                    ],
+                    [
+                        1,
+                        0,
+                        60
+                    ],
+                    [
+                        0,
+                        2,
+                        995
+                    ],
+                    [
+                        0,
+                        1,
+                        466
+                    ],
+                    [
+                        0,
+                        1,
+                        783
+                    ],
+                    [
+                        1,
+                        0,
+                        323
+                    ],
+                    [
+                        0,
+                        2,
+                        625
+                    ],
+                    [
+                        2,
+                        0,
+                        612
+                    ],
+                    [
+                        1,
+                        0,
+                        133
+                    ],
+                    [
+                        2,
+                        0,
+                        695
+                    ],
+                    [
+                        0,
+                        2,
+                        560
+                    ],
+                    [
+                        0,
+                        1,
+                        420
+                    ],
+                    [
+                        1,
+                        0,
+                        233
+                    ],
+                    [
+                        0,
+                        1,
+                        39
+                    ],
+                    [
+                        1,
+                        0,
+                        251
+                    ],
+                    [
+                        1,
+                        2,
+                        747
+                    ],
+                    [
+                        2,
+                        0,
+                        392
+                    ],
+                    [
+                        1,
+                        0,
+                        459
+                    ],
+                    [
+                        1,
+                        0,
+                        326
+                    ],
+                    [
+                        1,
+                        2,
+                        811
+                    ],
+                    [
+                        0,
+                        2,
+                        438
+                    ],
+                    [
+                        2,
+                        1,
+                        431
+                    ],
+                    [
+                        2,
+                        0,
+                        677
+                    ],
+                    [
+                        0,
+                        1,
+                        127
+                    ],
+                    [
+                        1,
+                        0,
+                        843
+                    ],
+                    [
+                        0,
+                        2,
+                        281
+                    ],
+                    [
+                        1,
+                        2,
+                        529
+                    ],
+                    [
+                        1,
+                        2,
+                        803
+                    ],
+                    [
+                        2,
+                        1,
+                        800
+                    ],
+                    [
+                        0,
+                        1,
+                        959
+                    ],
+                    [
+                        1,
+                        2,
+                        64
+                    ],
+                    [
+                        2,
+                        0,
+                        994
+                    ],
+                    [
+                        1,
+                        2,
+                        294
+                    ],
+                    [
+                        2,
+                        0,
+                        101
+                    ],
+                    [
+                        1,
+                        0,
+                        869
+                    ],
+                    [
+                        2,
+                        0,
+                        503
+                    ],
+                    [
+                        1,
+                        2,
+                        60
+                    ],
+                    [
+                        0,
+                        1,
+                        606
+                    ],
+                    [
+                        2,
+                        0,
+                        839
+                    ],
+                    [
+                        0,
+                        2,
+                        34
+                    ],
+                    [
+                        1,
+                        0,
+                        177
+                    ],
+                    [
+                        0,
+                        2,
+                        822
+                    ],
+                    [
+                        0,
+                        2,
+                        743
+                    ],
+                    [
+                        1,
+                        0,
+                        873
+                    ],
+                    [
+                        2,
+                        0,
+                        945
+                    ],
+                    [
+                        2,
+                        1,
+                        608
+                    ],
+                    [
+                        2,
+                        1,
+                        56
+                    ],
+                    [
+                        2,
+                        0,
+                        936
+                    ],
+                    [
+                        2,
+                        0,
+                        224
+                    ],
+                    [
+                        2,
+                        1,
+                        954
+                    ],
+                    [
+                        2,
+                        1,
+                        562
+                    ],
+                    [
+                        0,
+                        1,
+                        500
+                    ],
+                    [
+                        1,
+                        2,
+                        34
+                    ],
+                    [
+                        1,
+                        0,
+                        859
+                    ],
+                    [
+                        2,
+                        0,
+                        610
+                    ],
+                    [
+                        0,
+                        1,
+                        970
+                    ],
+                    [
+                        1,
+                        0,
+                        769
+                    ],
+                    [
+                        0,
+                        2,
+                        486
+                    ],
+                    [
+                        0,
+                        2,
+                        221
+                    ],
+                    [
+                        2,
+                        1,
+                        766
+                    ],
+                    [
+                        0,
+                        1,
+                        525
+                    ],
+                    [
+                        2,
+                        1,
+                        797
+                    ],
+                    [
+                        0,
+                        2,
+                        956
+                    ],
+                    [
+                        2,
+                        1,
+                        13
+                    ],
+                    [
+                        2,
+                        0,
+                        623
+                    ],
+                    [
+                        0,
+                        1,
+                        324
+                    ],
+                    [
+                        0,
+                        1,
+                        904
+                    ],
+                    [
+                        2,
+                        1,
+                        717
+                    ],
+                    [
+                        1,
+                        2,
+                        677
+                    ],
+                    [
+                        0,
+                        1,
+                        121
+                    ],
+                    [
+                        1,
+                        0,
+                        732
+                    ],
+                    [
+                        2,
+                        1,
+                        391
+                    ],
+                    [
+                        1,
+                        0,
+                        335
+                    ],
+                    [
+                        0,
+                        2,
+                        375
+                    ],
+                    [
+                        2,
+                        1,
+                        557
+                    ],
+                    [
+                        2,
+                        1,
+                        585
+                    ],
+                    [
+                        2,
+                        0,
+                        768
+                    ],
+                    [
+                        0,
+                        1,
+                        583
+                    ],
+                    [
+                        1,
+                        2,
+                        645
+                    ],
+                    [
+                        2,
+                        0,
+                        903
+                    ],
+                    [
+                        0,
+                        1,
+                        459
+                    ],
+                    [
+                        0,
+                        1,
+                        171
+                    ],
+                    [
+                        2,
+                        1,
+                        477
+                    ],
+                    [
+                        0,
+                        1,
+                        118
+                    ],
+                    [
+                        0,
+                        2,
+                        897
+                    ],
+                    [
+                        1,
+                        2,
+                        724
+                    ],
+                    [
+                        1,
+                        0,
+                        814
+                    ],
+                    [
+                        1,
+                        0,
+                        116
+                    ],
+                    [
+                        2,
+                        1,
+                        95
+                    ],
+                    [
+                        0,
+                        1,
+                        460
+                    ],
+                    [
+                        2,
+                        0,
+                        32
+                    ],
+                    [
+                        1,
+                        2,
+                        985
+                    ],
+                    [
+                        0,
+                        1,
+                        26
+                    ],
+                    [
+                        1,
+                        0,
+                        119
+                    ],
+                    [
+                        1,
+                        0,
+                        856
+                    ],
+                    [
+                        0,
+                        2,
+                        755
+                    ],
+                    [
+                        1,
+                        0,
+                        878
+                    ],
+                    [
+                        0,
+                        2,
+                        954
+                    ],
+                    [
+                        1,
+                        2,
+                        582
+                    ],
+                    [
+                        0,
+                        1,
+                        957
+                    ],
+                    [
+                        0,
+                        1,
+                        575
+                    ],
+                    [
+                        0,
+                        2,
+                        857
+                    ],
+                    [
+                        0,
+                        2,
+                        563
+                    ],
+                    [
+                        1,
+                        0,
+                        945
+                    ],
+                    [
+                        2,
+                        1,
+                        629
+                    ],
+                    [
+                        0,
+                        1,
+                        56
+                    ],
+                    [
+                        2,
+                        1,
+                        721
+                    ],
+                    [
+                        2,
+                        0,
+                        648
+                    ],
+                    [
+                        2,
+                        0,
+                        655
+                    ],
+                    [
+                        0,
+                        2,
+                        288
+                    ],
+                    [
+                        2,
+                        0,
+                        703
+                    ],
+                    [
+                        0,
+                        1,
+                        993
+                    ],
+                    [
+                        0,
+                        1,
+                        448
+                    ],
+                    [
+                        0,
+                        1,
+                        970
+                    ],
+                    [
+                        1,
+                        2,
+                        875
+                    ],
+                    [
+                        1,
+                        0,
+                        533
+                    ],
+                    [
+                        1,
+                        2,
+                        900
+                    ],
+                    [
+                        0,
+                        1,
+                        191
+                    ],
+                    [
+                        0,
+                        1,
+                        534
+                    ],
+                    [
+                        0,
+                        1,
+                        84
+                    ],
+                    [
+                        2,
+                        0,
+                        390
+                    ],
+                    [
+                        1,
+                        2,
+                        182
+                    ],
+                    [
+                        0,
+                        2,
+                        145
+                    ],
+                    [
+                        0,
+                        2,
+                        743
+                    ],
+                    [
+                        1,
+                        0,
+                        748
+                    ],
+                    [
+                        1,
+                        2,
+                        400
+                    ],
+                    [
+                        2,
+                        0,
+                        179
+                    ],
+                    [
+                        1,
+                        2,
+                        94
+                    ],
+                    [
+                        0,
+                        1,
+                        252
+                    ],
+                    [
+                        0,
+                        1,
+                        253
+                    ],
+                    [
+                        2,
+                        1,
+                        238
+                    ],
+                    [
+                        2,
+                        0,
+                        987
+                    ],
+                    [
+                        2,
+                        0,
+                        90
+                    ],
+                    [
+                        1,
+                        0,
+                        296
+                    ],
+                    [
+                        2,
+                        1,
+                        203
+                    ],
+                    [
+                        0,
+                        1,
+                        43
+                    ],
+                    [
+                        2,
+                        0,
+                        26
+                    ],
+                    [
+                        2,
+                        0,
+                        551
+                    ],
+                    [
+                        2,
+                        0,
+                        292
+                    ],
+                    [
+                        0,
+                        1,
+                        946
+                    ],
+                    [
+                        0,
+                        2,
+                        864
+                    ],
+                    [
+                        2,
+                        1,
+                        935
+                    ],
+                    [
+                        1,
+                        0,
+                        406
+                    ],
+                    [
+                        0,
+                        2,
+                        880
+                    ],
+                    [
+                        2,
+                        0,
+                        340
+                    ],
+                    [
+                        0,
+                        1,
+                        244
+                    ],
+                    [
+                        0,
+                        2,
+                        337
+                    ],
+                    [
+                        2,
+                        1,
+                        255
+                    ],
+                    [
+                        2,
+                        1,
+                        312
+                    ],
+                    [
+                        2,
+                        0,
+                        372
+                    ],
+                    [
+                        2,
+                        0,
+                        691
+                    ],
+                    [
+                        0,
+                        2,
+                        978
+                    ],
+                    [
+                        0,
+                        2,
+                        802
+                    ],
+                    [
+                        1,
+                        0,
+                        514
+                    ],
+                    [
+                        1,
+                        0,
+                        151
+                    ],
+                    [
+                        2,
+                        1,
+                        317
+                    ],
+                    [
+                        2,
+                        0,
+                        239
+                    ],
+                    [
+                        1,
+                        0,
+                        779
+                    ],
+                    [
+                        1,
+                        0,
+                        881
+                    ],
+                    [
+                        0,
+                        2,
+                        273
+                    ],
+                    [
+                        1,
+                        0,
+                        466
+                    ],
+                    [
+                        0,
+                        1,
+                        120
+                    ],
+                    [
+                        2,
+                        1,
+                        837
+                    ],
+                    [
+                        2,
+                        1,
+                        47
+                    ],
+                    [
+                        2,
+                        1,
+                        579
+                    ],
+                    [
+                        0,
+                        2,
+                        747
+                    ],
+                    [
+                        0,
+                        1,
+                        684
+                    ],
+                    [
+                        0,
+                        1,
+                        55
+                    ],
+                    [
+                        1,
+                        2,
+                        46
+                    ],
+                    [
+                        2,
+                        0,
+                        534
+                    ],
+                    [
+                        2,
+                        0,
+                        486
+                    ],
+                    [
+                        2,
+                        1,
+                        986
+                    ],
+                    [
+                        1,
+                        2,
+                        499
+                    ],
+                    [
+                        1,
+                        0,
+                        141
+                    ],
+                    [
+                        2,
+                        1,
+                        498
+                    ],
+                    [
+                        2,
+                        0,
+                        585
+                    ],
+                    [
+                        0,
+                        2,
+                        250
+                    ],
+                    [
+                        1,
+                        2,
+                        392
+                    ],
+                    [
+                        2,
+                        1,
+                        475
+                    ],
+                    [
+                        2,
+                        1,
+                        919
+                    ],
+                    [
+                        2,
+                        1,
+                        842
+                    ],
+                    [
+                        0,
+                        2,
+                        712
+                    ],
+                    [
+                        2,
+                        1,
+                        900
+                    ],
+                    [
+                        2,
+                        1,
+                        55
+                    ],
+                    [
+                        1,
+                        2,
+                        420
+                    ],
+                    [
+                        0,
+                        2,
+                        592
+                    ],
+                    [
+                        2,
+                        0,
+                        781
+                    ],
+                    [
+                        0,
+                        1,
+                        639
+                    ],
+                    [
+                        2,
+                        0,
+                        136
+                    ],
+                    [
+                        2,
+                        1,
+                        18
+                    ],
+                    [
+                        0,
+                        2,
+                        545
+                    ],
+                    [
+                        0,
+                        2,
+                        585
+                    ],
+                    [
+                        2,
+                        0,
+                        715
+                    ],
+                    [
+                        2,
+                        1,
+                        354
+                    ],
+                    [
+                        1,
+                        2,
+                        395
+                    ],
+                    [
+                        1,
+                        2,
+                        411
+                    ],
+                    [
+                        0,
+                        1,
+                        924
+                    ],
+                    [
+                        2,
+                        1,
+                        675
+                    ],
+                    [
+                        1,
+                        0,
+                        170
+                    ],
+                    [
+                        2,
+                        0,
+                        367
+                    ],
+                    [
+                        0,
+                        2,
+                        101
+                    ],
+                    [
+                        2,
+                        1,
+                        263
+                    ],
+                    [
+                        1,
+                        0,
+                        574
+                    ],
+                    [
+                        0,
+                        2,
+                        163
+                    ],
+                    [
+                        2,
+                        1,
+                        136
+                    ],
+                    [
+                        0,
+                        2,
+                        357
+                    ],
+                    [
+                        1,
+                        2,
+                        265
+                    ],
+                    [
+                        0,
+                        2,
+                        311
+                    ],
+                    [
+                        2,
+                        0,
+                        594
+                    ],
+                    [
+                        2,
+                        1,
+                        938
+                    ],
+                    [
+                        1,
+                        2,
+                        39
+                    ],
+                    [
+                        0,
+                        2,
+                        138
+                    ],
+                    [
+                        1,
+                        0,
+                        217
+                    ],
+                    [
+                        0,
+                        2,
+                        98
+                    ],
+                    [
+                        0,
+                        2,
+                        328
+                    ],
+                    [
+                        0,
+                        2,
+                        316
+                    ],
+                    [
+                        0,
+                        2,
+                        866
+                    ],
+                    [
+                        0,
+                        1,
+                        329
+                    ],
+                    [
+                        0,
+                        1,
+                        275
+                    ],
+                    [
+                        2,
+                        1,
+                        332
+                    ],
+                    [
+                        0,
+                        1,
+                        729
+                    ],
+                    [
+                        0,
+                        2,
+                        820
+                    ],
+                    [
+                        0,
+                        1,
+                        162
+                    ],
+                    [
+                        0,
+                        2,
+                        332
+                    ],
+                    [
+                        2,
+                        1,
+                        302
+                    ],
+                    [
+                        0,
+                        1,
+                        94
+                    ],
+                    [
+                        1,
+                        0,
+                        744
+                    ],
+                    [
+                        2,
+                        0,
+                        582
+                    ],
+                    [
+                        0,
+                        1,
+                        502
+                    ],
+                    [
+                        2,
+                        0,
+                        388
+                    ],
+                    [
+                        1,
+                        0,
+                        580
+                    ],
+                    [
+                        0,
+                        1,
+                        654
+                    ],
+                    [
+                        2,
+                        1,
+                        717
+                    ],
+                    [
+                        1,
+                        2,
+                        402
+                    ],
+                    [
+                        0,
+                        2,
+                        593
+                    ],
+                    [
+                        1,
+                        2,
+                        68
+                    ],
+                    [
+                        0,
+                        2,
+                        783
+                    ],
+                    [
+                        2,
+                        0,
+                        85
+                    ],
+                    [
+                        0,
+                        2,
+                        265
+                    ],
+                    [
+                        2,
+                        0,
+                        101
+                    ],
+                    [
+                        2,
+                        0,
+                        738
+                    ],
+                    [
+                        1,
+                        0,
+                        528
+                    ],
+                    [
+                        1,
+                        2,
+                        50
+                    ],
+                    [
+                        2,
+                        0,
+                        307
+                    ],
+                    [
+                        0,
+                        1,
+                        241
+                    ],
+                    [
+                        2,
+                        0,
+                        524
+                    ],
+                    [
+                        0,
+                        1,
+                        153
+                    ],
+                    [
+                        0,
+                        1,
+                        596
+                    ],
+                    [
+                        1,
+                        0,
+                        540
+                    ],
+                    [
+                        0,
+                        1,
+                        645
+                    ],
+                    [
+                        2,
+                        1,
+                        958
+                    ],
+                    [
+                        1,
+                        2,
+                        748
+                    ],
+                    [
+                        0,
+                        1,
+                        572
+                    ],
+                    [
+                        0,
+                        2,
+                        283
+                    ],
+                    [
+                        0,
+                        1,
+                        619
+                    ],
+                    [
+                        1,
+                        2,
+                        419
+                    ],
+                    [
+                        2,
+                        0,
+                        560
+                    ],
+                    [
+                        0,
+                        2,
+                        825
+                    ],
+                    [
+                        2,
+                        1,
+                        458
+                    ],
+                    [
+                        2,
+                        0,
+                        997
+                    ],
+                    [
+                        2,
+                        1,
+                        502
+                    ],
+                    [
+                        0,
+                        1,
+                        718
+                    ],
+                    [
+                        1,
+                        2,
+                        410
+                    ],
+                    [
+                        1,
+                        2,
+                        384
+                    ],
+                    [
+                        2,
+                        0,
+                        656
+                    ],
+                    [
+                        1,
+                        2,
+                        626
+                    ],
+                    [
+                        2,
+                        0,
+                        679
+                    ],
+                    [
+                        2,
+                        0,
+                        796
+                    ],
+                    [
+                        0,
+                        1,
+                        73
+                    ],
+                    [
+                        1,
+                        2,
+                        568
+                    ],
+                    [
+                        0,
+                        2,
+                        101
+                    ],
+                    [
+                        2,
+                        1,
+                        736
+                    ],
+                    [
+                        0,
+                        1,
+                        950
+                    ],
+                    [
+                        2,
+                        1,
+                        732
+                    ],
+                    [
+                        2,
+                        1,
+                        339
+                    ],
+                    [
+                        0,
+                        1,
+                        580
+                    ],
+                    [
+                        1,
+                        2,
+                        772
+                    ],
+                    [
+                        1,
+                        2,
+                        160
+                    ],
+                    [
+                        1,
+                        0,
+                        427
+                    ],
+                    [
+                        2,
+                        1,
+                        711
+                    ],
+                    [
+                        1,
+                        2,
+                        31
+                    ],
+                    [
+                        0,
+                        1,
+                        213
+                    ],
+                    [
+                        2,
+                        0,
+                        104
+                    ],
+                    [
+                        2,
+                        0,
+                        430
+                    ],
+                    [
+                        2,
+                        1,
+                        213
+                    ],
+                    [
+                        2,
+                        0,
+                        719
+                    ],
+                    [
+                        1,
+                        0,
+                        516
+                    ],
+                    [
+                        2,
+                        0,
+                        792
+                    ],
+                    [
+                        0,
+                        1,
+                        91
+                    ],
+                    [
+                        0,
+                        1,
+                        431
+                    ],
+                    [
+                        1,
+                        2,
+                        369
+                    ],
+                    [
+                        1,
+                        2,
+                        963
+                    ],
+                    [
+                        1,
+                        0,
+                        624
+                    ],
+                    [
+                        2,
+                        1,
+                        553
+                    ],
+                    [
+                        0,
+                        1,
+                        935
+                    ],
+                    [
+                        0,
+                        2,
+                        432
+                    ],
+                    [
+                        1,
+                        0,
+                        452
+                    ],
+                    [
+                        1,
+                        0,
+                        863
+                    ],
+                    [
+                        0,
+                        1,
+                        700
+                    ],
+                    [
+                        1,
+                        0,
+                        900
+                    ],
+                    [
+                        2,
+                        0,
+                        701
+                    ],
+                    [
+                        0,
+                        1,
+                        131
+                    ],
+                    [
+                        1,
+                        2,
+                        823
+                    ],
+                    [
+                        2,
+                        1,
+                        679
+                    ],
+                    [
+                        2,
+                        1,
+                        977
+                    ],
+                    [
+                        1,
+                        2,
+                        561
+                    ],
+                    [
+                        0,
+                        2,
+                        47
+                    ],
+                    [
+                        0,
+                        1,
+                        230
+                    ],
+                    [
+                        2,
+                        1,
+                        147
+                    ],
+                    [
+                        2,
+                        1,
+                        396
+                    ],
+                    [
+                        2,
+                        0,
+                        655
+                    ],
+                    [
+                        1,
+                        2,
+                        898
+                    ],
+                    [
+                        0,
+                        2,
+                        739
+                    ],
+                    [
+                        0,
+                        2,
+                        61
+                    ],
+                    [
+                        2,
+                        0,
+                        906
+                    ],
+                    [
+                        1,
+                        2,
+                        6
+                    ],
+                    [
+                        1,
+                        2,
+                        145
+                    ],
+                    [
+                        1,
+                        2,
+                        250
+                    ],
+                    [
+                        0,
+                        1,
+                        462
+                    ],
+                    [
+                        0,
+                        1,
+                        38
+                    ],
+                    [
+                        2,
+                        0,
+                        266
+                    ],
+                    [
+                        0,
+                        2,
+                        883
+                    ],
+                    [
+                        0,
+                        2,
+                        157
+                    ],
+                    [
+                        0,
+                        2,
+                        38
+                    ],
+                    [
+                        2,
+                        1,
+                        615
+                    ],
+                    [
+                        1,
+                        2,
+                        691
+                    ],
+                    [
+                        1,
+                        0,
+                        306
+                    ],
+                    [
+                        1,
+                        0,
+                        72
+                    ],
+                    [
+                        2,
+                        1,
+                        524
+                    ],
+                    [
+                        2,
+                        0,
+                        952
+                    ],
+                    [
+                        2,
+                        0,
+                        504
+                    ],
+                    [
+                        2,
+                        1,
+                        974
+                    ],
+                    [
+                        2,
+                        1,
+                        844
+                    ],
+                    [
+                        0,
+                        2,
+                        334
+                    ],
+                    [
+                        1,
+                        0,
+                        331
+                    ],
+                    [
+                        0,
+                        1,
+                        840
+                    ],
+                    [
+                        0,
+                        1,
+                        143
+                    ],
+                    [
+                        1,
+                        2,
+                        580
+                    ],
+                    [
+                        2,
+                        1,
+                        270
+                    ],
+                    [
+                        0,
+                        2,
+                        214
+                    ],
+                    [
+                        1,
+                        2,
+                        626
+                    ],
+                    [
+                        0,
+                        1,
+                        560
+                    ],
+                    [
+                        1,
+                        0,
+                        770
+                    ],
+                    [
+                        0,
+                        1,
+                        833
+                    ],
+                    [
+                        2,
+                        0,
+                        787
+                    ],
+                    [
+                        1,
+                        2,
+                        811
+                    ],
+                    [
+                        2,
+                        1,
+                        445
+                    ],
+                    [
+                        0,
+                        2,
+                        189
+                    ],
+                    [
+                        1,
+                        0,
+                        80
+                    ],
+                    [
+                        1,
+                        0,
+                        102
+                    ],
+                    [
+                        2,
+                        1,
+                        875
+                    ],
+                    [
+                        2,
+                        1,
+                        19
+                    ],
+                    [
+                        0,
+                        2,
+                        451
+                    ],
+                    [
+                        0,
+                        2,
+                        205
+                    ],
+                    [
+                        0,
+                        2,
+                        290
+                    ],
+                    [
+                        1,
+                        0,
+                        470
+                    ],
+                    [
+                        1,
+                        0,
+                        317
+                    ],
+                    [
+                        0,
+                        1,
+                        226
+                    ],
+                    [
+                        2,
+                        0,
+                        587
+                    ],
+                    [
+                        2,
+                        0,
+                        130
+                    ],
+                    [
+                        1,
+                        0,
+                        501
+                    ],
+                    [
+                        0,
+                        2,
+                        168
+                    ],
+                    [
+                        0,
+                        1,
+                        822
+                    ],
+                    [
+                        0,
+                        2,
+                        22
+                    ],
+                    [
+                        0,
+                        2,
+                        846
+                    ],
+                    [
+                        2,
+                        0,
+                        287
+                    ],
+                    [
+                        1,
+                        0,
+                        8
+                    ],
+                    [
+                        0,
+                        2,
+                        308
+                    ],
+                    [
+                        2,
+                        1,
+                        294
+                    ],
+                    [
+                        1,
+                        2,
+                        303
+                    ],
+                    [
+                        2,
+                        1,
+                        75
+                    ],
+                    [
+                        0,
+                        1,
+                        705
+                    ],
+                    [
+                        2,
+                        1,
+                        589
+                    ],
+                    [
+                        1,
+                        0,
+                        760
+                    ],
+                    [
+                        0,
+                        2,
+                        127
+                    ],
+                    [
+                        0,
+                        2,
+                        160
+                    ],
+                    [
+                        0,
+                        2,
+                        834
+                    ],
+                    [
+                        2,
+                        1,
+                        822
+                    ],
+                    [
+                        1,
+                        0,
+                        443
+                    ],
+                    [
+                        2,
+                        1,
+                        255
+                    ],
+                    [
+                        2,
+                        0,
+                        42
+                    ],
+                    [
+                        1,
+                        2,
+                        403
+                    ],
+                    [
+                        2,
+                        1,
+                        457
+                    ],
+                    [
+                        2,
+                        0,
+                        589
+                    ],
+                    [
+                        0,
+                        1,
+                        349
+                    ],
+                    [
+                        1,
+                        2,
+                        260
+                    ],
+                    [
+                        0,
+                        2,
+                        92
+                    ],
+                    [
+                        1,
+                        2,
+                        281
+                    ],
+                    [
+                        0,
+                        2,
+                        484
+                    ],
+                    [
+                        2,
+                        0,
+                        85
+                    ],
+                    [
+                        0,
+                        2,
+                        644
+                    ],
+                    [
+                        2,
+                        0,
+                        166
+                    ],
+                    [
+                        1,
+                        2,
+                        626
+                    ],
+                    [
+                        0,
+                        2,
+                        906
+                    ],
+                    [
+                        1,
+                        0,
+                        134
+                    ],
+                    [
+                        1,
+                        2,
+                        670
+                    ],
+                    [
+                        1,
+                        2,
+                        98
+                    ],
+                    [
+                        1,
+                        0,
+                        951
+                    ],
+                    [
+                        2,
+                        0,
+                        20
+                    ],
+                    [
+                        1,
+                        2,
+                        195
+                    ],
+                    [
+                        2,
+                        0,
+                        12
+                    ],
+                    [
+                        0,
+                        1,
+                        907
+                    ],
+                    [
+                        0,
+                        2,
+                        382
+                    ],
+                    [
+                        1,
+                        2,
+                        351
+                    ],
+                    [
+                        0,
+                        2,
+                        904
+                    ],
+                    [
+                        0,
+                        1,
+                        729
+                    ],
+                    [
+                        0,
+                        2,
+                        951
+                    ],
+                    [
+                        1,
+                        0,
+                        93
+                    ],
+                    [
+                        2,
+                        1,
+                        520
+                    ],
+                    [
+                        2,
+                        0,
+                        883
+                    ],
+                    [
+                        1,
+                        2,
+                        259
+                    ],
+                    [
+                        1,
+                        2,
+                        668
+                    ],
+                    [
+                        0,
+                        2,
+                        584
+                    ],
+                    [
+                        0,
+                        1,
+                        980
+                    ],
+                    [
+                        0,
+                        1,
+                        86
+                    ],
+                    [
+                        1,
+                        2,
+                        916
+                    ],
+                    [
+                        1,
+                        0,
+                        983
+                    ],
+                    [
+                        2,
+                        1,
+                        725
+                    ],
+                    [
+                        0,
+                        2,
+                        201
+                    ],
+                    [
+                        1,
+                        2,
+                        807
+                    ],
+                    [
+                        1,
+                        0,
+                        133
+                    ],
+                    [
+                        0,
+                        1,
+                        55
+                    ],
+                    [
+                        2,
+                        0,
+                        690
+                    ],
+                    [
+                        2,
+                        0,
+                        842
+                    ],
+                    [
+                        1,
+                        2,
+                        847
+                    ],
+                    [
+                        1,
+                        0,
+                        922
+                    ],
+                    [
+                        1,
+                        0,
+                        637
+                    ],
+                    [
+                        1,
+                        2,
+                        953
+                    ],
+                    [
+                        0,
+                        1,
+                        276
+                    ],
+                    [
+                        1,
+                        0,
+                        661
+                    ],
+                    [
+                        1,
+                        0,
+                        373
+                    ],
+                    [
+                        2,
+                        1,
+                        819
+                    ],
+                    [
+                        1,
+                        2,
+                        207
+                    ],
+                    [
+                        2,
+                        0,
+                        127
+                    ],
+                    [
+                        1,
+                        2,
+                        334
+                    ],
+                    [
+                        2,
+                        1,
+                        111
+                    ],
+                    [
+                        1,
+                        0,
+                        27
+                    ],
+                    [
+                        0,
+                        2,
+                        489
+                    ],
+                    [
+                        0,
+                        2,
+                        953
+                    ],
+                    [
+                        1,
+                        0,
+                        129
+                    ],
+                    [
+                        0,
+                        1,
+                        153
+                    ],
+                    [
+                        0,
+                        2,
+                        593
+                    ],
+                    [
+                        1,
+                        0,
+                        718
+                    ],
+                    [
+                        2,
+                        1,
+                        660
+                    ],
+                    [
+                        1,
+                        2,
+                        173
+                    ],
+                    [
+                        2,
+                        1,
+                        317
+                    ],
+                    [
+                        1,
+                        0,
+                        29
+                    ],
+                    [
+                        1,
+                        2,
+                        212
+                    ],
+                    [
+                        1,
+                        0,
+                        13
+                    ],
+                    [
+                        2,
+                        0,
+                        931
+                    ],
+                    [
+                        0,
+                        2,
+                        533
+                    ],
+                    [
+                        1,
+                        0,
+                        602
+                    ],
+                    [
+                        0,
+                        1,
+                        78
+                    ],
+                    [
+                        1,
+                        2,
+                        367
+                    ],
+                    [
+                        0,
+                        2,
+                        696
+                    ],
+                    [
+                        2,
+                        0,
+                        12
+                    ],
+                    [
+                        1,
+                        0,
+                        808
+                    ],
+                    [
+                        0,
+                        1,
+                        699
+                    ],
+                    [
+                        0,
+                        2,
+                        99
+                    ],
+                    [
+                        1,
+                        0,
+                        945
+                    ],
+                    [
+                        0,
+                        2,
+                        914
+                    ],
+                    [
+                        2,
+                        0,
+                        472
+                    ],
+                    [
+                        0,
+                        1,
+                        1000
+                    ],
+                    [
+                        2,
+                        1,
+                        438
+                    ],
+                    [
+                        2,
+                        0,
+                        543
+                    ],
+                    [
+                        0,
+                        2,
+                        589
+                    ],
+                    [
+                        0,
+                        1,
+                        336
+                    ],
+                    [
+                        2,
+                        1,
+                        591
+                    ],
+                    [
+                        1,
+                        2,
+                        850
+                    ],
+                    [
+                        0,
+                        2,
+                        872
+                    ],
+                    [
+                        1,
+                        2,
+                        920
+                    ],
+                    [
+                        0,
+                        2,
+                        924
+                    ],
+                    [
+                        1,
+                        0,
+                        706
+                    ],
+                    [
+                        1,
+                        0,
+                        705
+                    ],
+                    [
+                        1,
+                        0,
+                        314
+                    ],
+                    [
+                        2,
+                        0,
+                        513
+                    ],
+                    [
+                        0,
+                        1,
+                        450
+                    ],
+                    [
+                        2,
+                        0,
+                        747
+                    ],
+                    [
+                        1,
+                        2,
+                        867
+                    ],
+                    [
+                        0,
+                        2,
+                        811
+                    ],
+                    [
+                        1,
+                        2,
+                        851
+                    ],
+                    [
+                        0,
+                        2,
+                        387
+                    ],
+                    [
+                        0,
+                        2,
+                        115
+                    ],
+                    [
+                        0,
+                        2,
+                        933
+                    ],
+                    [
+                        2,
+                        0,
+                        315
+                    ],
+                    [
+                        1,
+                        0,
+                        289
+                    ],
+                    [
+                        1,
+                        0,
+                        556
+                    ],
+                    [
+                        0,
+                        2,
+                        855
+                    ],
+                    [
+                        2,
+                        0,
+                        943
+                    ],
+                    [
+                        1,
+                        0,
+                        595
+                    ],
+                    [
+                        0,
+                        1,
+                        791
+                    ],
+                    [
+                        2,
+                        0,
+                        896
+                    ],
+                    [
+                        0,
+                        1,
+                        296
+                    ],
+                    [
+                        0,
+                        1,
+                        115
+                    ],
+                    [
+                        0,
+                        2,
+                        171
+                    ],
+                    [
+                        2,
+                        0,
+                        579
+                    ],
+                    [
+                        1,
+                        2,
+                        700
+                    ],
+                    [
+                        0,
+                        1,
+                        445
+                    ],
+                    [
+                        2,
+                        1,
+                        239
+                    ],
+                    [
+                        2,
+                        0,
+                        487
+                    ],
+                    [
+                        0,
+                        1,
+                        79
+                    ],
+                    [
+                        2,
+                        1,
+                        991
+                    ],
+                    [
+                        1,
+                        0,
+                        432
+                    ],
+                    [
+                        2,
+                        0,
+                        215
+                    ],
+                    [
+                        2,
+                        0,
+                        95
+                    ],
+                    [
+                        1,
+                        0,
+                        253
+                    ],
+                    [
+                        0,
+                        2,
+                        627
+                    ],
+                    [
+                        1,
+                        2,
+                        52
+                    ],
+                    [
+                        2,
+                        0,
+                        102
+                    ],
+                    [
+                        0,
+                        2,
+                        574
+                    ],
+                    [
+                        1,
+                        2,
+                        131
+                    ],
+                    [
+                        1,
+                        2,
+                        107
+                    ],
+                    [
+                        1,
+                        0,
+                        660
+                    ],
+                    [
+                        1,
+                        0,
+                        167
+                    ],
+                    [
+                        0,
+                        1,
+                        799
+                    ],
+                    [
+                        0,
+                        2,
+                        455
+                    ],
+                    [
+                        1,
+                        2,
+                        350
+                    ],
+                    [
+                        0,
+                        1,
+                        206
+                    ],
+                    [
+                        1,
+                        2,
+                        286
+                    ],
+                    [
+                        2,
+                        0,
+                        291
+                    ],
+                    [
+                        1,
+                        0,
+                        760
+                    ],
+                    [
+                        2,
+                        1,
+                        611
+                    ],
+                    [
+                        0,
+                        1,
+                        48
+                    ],
+                    [
+                        1,
+                        0,
+                        983
+                    ],
+                    [
+                        0,
+                        1,
+                        857
+                    ],
+                    [
+                        0,
+                        2,
+                        776
+                    ],
+                    [
+                        0,
+                        2,
+                        807
+                    ],
+                    [
+                        0,
+                        2,
+                        145
+                    ],
+                    [
+                        0,
+                        1,
+                        236
+                    ],
+                    [
+                        2,
+                        1,
+                        760
+                    ],
+                    [
+                        2,
+                        1,
+                        684
+                    ],
+                    [
+                        0,
+                        2,
+                        35
+                    ],
+                    [
+                        1,
+                        2,
+                        189
+                    ],
+                    [
+                        1,
+                        2,
+                        989
+                    ],
+                    [
+                        0,
+                        2,
+                        317
+                    ],
+                    [
+                        0,
+                        2,
+                        669
+                    ],
+                    [
+                        1,
+                        2,
+                        863
+                    ],
+                    [
+                        1,
+                        0,
+                        338
+                    ],
+                    [
+                        2,
+                        1,
+                        527
+                    ],
+                    [
+                        1,
+                        0,
+                        358
+                    ],
+                    [
+                        0,
+                        2,
+                        28
+                    ],
+                    [
+                        0,
+                        2,
+                        83
+                    ],
+                    [
+                        2,
+                        1,
+                        540
+                    ],
+                    [
+                        2,
+                        1,
+                        278
+                    ],
+                    [
+                        0,
+                        2,
+                        91
+                    ],
+                    [
+                        2,
+                        0,
+                        747
+                    ],
+                    [
+                        2,
+                        1,
+                        999
+                    ],
+                    [
+                        1,
+                        2,
+                        677
+                    ],
+                    [
+                        1,
+                        0,
+                        58
+                    ],
+                    [
+                        1,
+                        0,
+                        511
+                    ],
+                    [
+                        1,
+                        0,
+                        939
+                    ],
+                    [
+                        2,
+                        1,
+                        319
+                    ],
+                    [
+                        2,
+                        1,
+                        600
+                    ],
+                    [
+                        2,
+                        1,
+                        531
+                    ],
+                    [
+                        2,
+                        1,
+                        589
+                    ],
+                    [
+                        2,
+                        1,
+                        189
+                    ],
+                    [
+                        1,
+                        0,
+                        937
+                    ],
+                    [
+                        2,
+                        0,
+                        828
+                    ],
+                    [
+                        0,
+                        2,
+                        407
+                    ],
+                    [
+                        2,
+                        0,
+                        32
+                    ],
+                    [
+                        0,
+                        1,
+                        99
+                    ],
+                    [
+                        2,
+                        1,
+                        54
+                    ],
+                    [
+                        1,
+                        0,
+                        919
+                    ],
+                    [
+                        2,
+                        1,
+                        397
+                    ],
+                    [
+                        0,
+                        2,
+                        10
+                    ],
+                    [
+                        0,
+                        2,
+                        791
+                    ],
+                    [
+                        2,
+                        0,
+                        724
+                    ],
+                    [
+                        1,
+                        2,
+                        273
+                    ],
+                    [
+                        0,
+                        2,
+                        520
+                    ],
+                    [
+                        1,
+                        2,
+                        73
+                    ],
+                    [
+                        2,
+                        0,
+                        168
+                    ],
+                    [
+                        0,
+                        2,
+                        979
+                    ],
+                    [
+                        1,
+                        2,
+                        931
+                    ],
+                    [
+                        1,
+                        2,
+                        208
+                    ],
+                    [
+                        0,
+                        1,
+                        908
+                    ],
+                    [
+                        2,
+                        0,
+                        337
+                    ],
+                    [
+                        2,
+                        1,
+                        20
+                    ],
+                    [
+                        0,
+                        1,
+                        615
+                    ],
+                    [
+                        2,
+                        1,
+                        524
+                    ],
+                    [
+                        1,
+                        0,
+                        961
+                    ],
+                    [
+                        2,
+                        1,
+                        200
+                    ],
+                    [
+                        1,
+                        2,
+                        547
+                    ],
+                    [
+                        1,
+                        2,
+                        897
+                    ],
+                    [
+                        1,
+                        0,
+                        787
+                    ],
+                    [
+                        2,
+                        1,
+                        907
+                    ],
+                    [
+                        2,
+                        1,
+                        950
+                    ],
+                    [
+                        0,
+                        2,
+                        27
+                    ],
+                    [
+                        2,
+                        1,
+                        464
+                    ],
+                    [
+                        1,
+                        0,
+                        998
+                    ],
+                    [
+                        0,
+                        1,
+                        789
+                    ],
+                    [
+                        0,
+                        2,
+                        529
+                    ],
+                    [
+                        1,
+                        0,
+                        66
+                    ],
+                    [
+                        0,
+                        1,
+                        773
+                    ],
+                    [
+                        2,
+                        1,
+                        230
+                    ],
+                    [
+                        2,
+                        1,
+                        667
+                    ],
+                    [
+                        2,
+                        0,
+                        204
+                    ],
+                    [
+                        2,
+                        0,
+                        701
+                    ],
+                    [
+                        2,
+                        1,
+                        705
+                    ],
+                    [
+                        2,
+                        1,
+                        381
+                    ],
+                    [
+                        0,
+                        1,
+                        82
+                    ],
+                    [
+                        1,
+                        2,
+                        857
+                    ],
+                    [
+                        2,
+                        0,
+                        662
+                    ],
+                    [
+                        1,
+                        2,
+                        205
+                    ],
+                    [
+                        2,
+                        1,
+                        477
+                    ],
+                    [
+                        1,
+                        2,
+                        566
+                    ],
+                    [
+                        2,
+                        0,
+                        511
+                    ],
+                    [
+                        0,
+                        1,
+                        564
+                    ],
+                    [
+                        1,
+                        2,
+                        761
+                    ],
+                    [
+                        1,
+                        2,
+                        292
+                    ],
+                    [
+                        0,
+                        2,
+                        424
+                    ],
+                    [
+                        2,
+                        1,
+                        544
+                    ],
+                    [
+                        0,
+                        1,
+                        756
+                    ],
+                    [
+                        2,
+                        0,
+                        327
+                    ],
+                    [
+                        2,
+                        1,
+                        580
+                    ],
+                    [
+                        0,
+                        2,
+                        808
+                    ],
+                    [
+                        1,
+                        2,
+                        54
+                    ],
+                    [
+                        1,
+                        0,
+                        409
+                    ],
+                    [
+                        1,
+                        0,
+                        837
+                    ],
+                    [
+                        0,
+                        2,
+                        663
+                    ],
+                    [
+                        1,
+                        2,
+                        731
+                    ],
+                    [
+                        1,
+                        2,
+                        888
+                    ],
+                    [
+                        1,
+                        0,
+                        578
+                    ],
+                    [
+                        2,
+                        0,
+                        625
+                    ],
+                    [
+                        2,
+                        1,
+                        856
+                    ],
+                    [
+                        1,
+                        2,
+                        824
+                    ],
+                    [
+                        1,
+                        0,
+                        400
+                    ],
+                    [
+                        1,
+                        0,
+                        110
+                    ],
+                    [
+                        2,
+                        0,
+                        543
+                    ],
+                    [
+                        1,
+                        2,
+                        531
+                    ],
+                    [
+                        1,
+                        0,
+                        24
+                    ],
+                    [
+                        1,
+                        0,
+                        720
+                    ],
+                    [
+                        2,
+                        0,
+                        341
+                    ],
+                    [
+                        2,
+                        0,
+                        822
+                    ],
+                    [
+                        2,
+                        0,
+                        526
+                    ],
+                    [
+                        0,
+                        2,
+                        10
+                    ],
+                    [
+                        1,
+                        0,
+                        733
+                    ],
+                    [
+                        0,
+                        2,
+                        872
+                    ],
+                    [
+                        0,
+                        1,
+                        857
+                    ],
+                    [
+                        1,
+                        2,
+                        696
+                    ],
+                    [
+                        2,
+                        1,
+                        835
+                    ],
+                    [
+                        2,
+                        0,
+                        13
+                    ],
+                    [
+                        1,
+                        2,
+                        540
+                    ],
+                    [
+                        2,
+                        0,
+                        701
+                    ],
+                    [
+                        2,
+                        0,
+                        89
+                    ],
+                    [
+                        0,
+                        1,
+                        615
+                    ],
+                    [
+                        2,
+                        1,
+                        751
+                    ],
+                    [
+                        1,
+                        0,
+                        679
+                    ],
+                    [
+                        1,
+                        2,
+                        484
+                    ],
+                    [
+                        2,
+                        1,
+                        494
+                    ],
+                    [
+                        1,
+                        2,
+                        297
+                    ],
+                    [
+                        2,
+                        0,
+                        931
+                    ],
+                    [
+                        0,
+                        1,
+                        462
+                    ],
+                    [
+                        1,
+                        2,
+                        742
+                    ],
+                    [
+                        1,
+                        0,
+                        437
+                    ],
+                    [
+                        1,
+                        0,
+                        385
+                    ],
+                    [
+                        0,
+                        1,
+                        431
+                    ],
+                    [
+                        2,
+                        0,
+                        383
+                    ],
+                    [
+                        2,
+                        1,
+                        710
+                    ],
+                    [
+                        1,
+                        2,
+                        954
+                    ],
+                    [
+                        1,
+                        2,
+                        517
+                    ],
+                    [
+                        1,
+                        2,
+                        584
+                    ],
+                    [
+                        2,
+                        1,
+                        462
+                    ],
+                    [
+                        2,
+                        1,
+                        667
+                    ],
+                    [
+                        2,
+                        0,
+                        184
+                    ],
+                    [
+                        0,
+                        1,
+                        922
+                    ],
+                    [
+                        0,
+                        1,
+                        987
+                    ],
+                    [
+                        2,
+                        1,
+                        221
+                    ],
+                    [
+                        0,
+                        2,
+                        640
+                    ],
+                    [
+                        0,
+                        1,
+                        715
+                    ],
+                    [
+                        2,
+                        1,
+                        559
+                    ],
+                    [
+                        0,
+                        2,
+                        919
+                    ],
+                    [
+                        0,
+                        1,
+                        408
+                    ],
+                    [
+                        2,
+                        1,
+                        931
+                    ],
+                    [
+                        1,
+                        0,
+                        804
+                    ],
+                    [
+                        2,
+                        1,
+                        79
+                    ],
+                    [
+                        0,
+                        1,
+                        620
+                    ],
+                    [
+                        0,
+                        1,
+                        179
+                    ],
+                    [
+                        0,
+                        2,
+                        594
+                    ],
+                    [
+                        0,
+                        1,
+                        532
+                    ],
+                    [
+                        2,
+                        1,
+                        381
+                    ],
+                    [
+                        2,
+                        1,
+                        932
+                    ],
+                    [
+                        1,
+                        2,
+                        708
+                    ],
+                    [
+                        1,
+                        0,
+                        662
+                    ],
+                    [
+                        2,
+                        0,
+                        372
+                    ],
+                    [
+                        0,
+                        1,
+                        921
+                    ],
+                    [
+                        0,
+                        2,
+                        778
+                    ],
+                    [
+                        2,
+                        0,
+                        840
+                    ],
+                    [
+                        1,
+                        0,
+                        730
+                    ],
+                    [
+                        2,
+                        1,
+                        876
+                    ],
+                    [
+                        0,
+                        2,
+                        106
+                    ],
+                    [
+                        0,
+                        1,
+                        268
+                    ],
+                    [
+                        2,
+                        0,
+                        503
+                    ],
+                    [
+                        0,
+                        1,
+                        587
+                    ],
+                    [
+                        0,
+                        1,
+                        213
+                    ],
+                    [
+                        2,
+                        0,
+                        724
+                    ],
+                    [
+                        1,
+                        0,
+                        258
+                    ],
+                    [
+                        2,
+                        0,
+                        673
+                    ],
+                    [
+                        1,
+                        2,
+                        773
+                    ],
+                    [
+                        1,
+                        0,
+                        199
+                    ],
+                    [
+                        0,
+                        2,
+                        446
+                    ],
+                    [
+                        0,
+                        2,
+                        961
+                    ],
+                    [
+                        1,
+                        2,
+                        771
+                    ],
+                    [
+                        1,
+                        0,
+                        991
+                    ],
+                    [
+                        1,
+                        2,
+                        463
+                    ],
+                    [
+                        0,
+                        2,
+                        272
+                    ],
+                    [
+                        2,
+                        1,
+                        645
+                    ],
+                    [
+                        0,
+                        2,
+                        896
+                    ],
+                    [
+                        1,
+                        2,
+                        39
+                    ],
+                    [
+                        1,
+                        2,
+                        231
+                    ],
+                    [
+                        2,
+                        0,
+                        717
+                    ],
+                    [
+                        2,
+                        1,
+                        586
+                    ],
+                    [
+                        1,
+                        0,
+                        45
+                    ],
+                    [
+                        0,
+                        1,
+                        569
+                    ],
+                    [
+                        2,
+                        0,
+                        378
+                    ],
+                    [
+                        2,
+                        1,
+                        887
+                    ],
+                    [
+                        1,
+                        0,
+                        721
+                    ],
+                    [
+                        2,
+                        0,
+                        784
+                    ],
+                    [
+                        2,
+                        0,
+                        807
+                    ],
+                    [
+                        1,
+                        2,
+                        860
+                    ],
+                    [
+                        1,
+                        0,
+                        236
+                    ],
+                    [
+                        2,
+                        0,
+                        492
+                    ],
+                    [
+                        0,
+                        1,
+                        215
+                    ],
+                    [
+                        0,
+                        1,
+                        526
+                    ],
+                    [
+                        1,
+                        0,
+                        758
+                    ],
+                    [
+                        0,
+                        1,
+                        17
+                    ],
+                    [
+                        1,
+                        0,
+                        566
+                    ],
+                    [
+                        1,
+                        2,
+                        640
+                    ],
+                    [
+                        0,
+                        1,
+                        96
+                    ],
+                    [
+                        0,
+                        1,
+                        591
+                    ],
+                    [
+                        0,
+                        2,
+                        94
+                    ],
+                    [
+                        1,
+                        2,
+                        336
+                    ],
+                    [
+                        0,
+                        2,
+                        150
+                    ],
+                    [
+                        0,
+                        2,
+                        13
+                    ],
+                    [
+                        1,
+                        0,
+                        924
+                    ],
+                    [
+                        2,
+                        0,
+                        450
+                    ],
+                    [
+                        0,
+                        2,
+                        402
+                    ],
+                    [
+                        2,
+                        0,
+                        132
+                    ],
+                    [
+                        0,
+                        2,
+                        968
+                    ],
+                    [
+                        1,
+                        2,
+                        842
+                    ],
+                    [
+                        0,
+                        2,
+                        775
+                    ],
+                    [
+                        2,
+                        1,
+                        16
+                    ],
+                    [
+                        2,
+                        0,
+                        81
+                    ],
+                    [
+                        1,
+                        0,
+                        393
+                    ],
+                    [
+                        2,
+                        0,
+                        805
+                    ],
+                    [
+                        0,
+                        1,
+                        72
+                    ],
+                    [
+                        1,
+                        2,
+                        229
+                    ],
+                    [
+                        2,
+                        1,
+                        166
+                    ],
+                    [
+                        0,
+                        1,
+                        958
+                    ],
+                    [
+                        0,
+                        1,
+                        705
+                    ],
+                    [
+                        0,
+                        2,
+                        869
+                    ],
+                    [
+                        0,
+                        2,
+                        95
+                    ],
+                    [
+                        0,
+                        2,
+                        246
+                    ],
+                    [
+                        0,
+                        1,
+                        686
+                    ],
+                    [
+                        2,
+                        0,
+                        577
+                    ],
+                    [
+                        1,
+                        2,
+                        342
+                    ],
+                    [
+                        0,
+                        2,
+                        254
+                    ],
+                    [
+                        2,
+                        1,
+                        694
+                    ],
+                    [
+                        1,
+                        2,
+                        824
+                    ],
+                    [
+                        1,
+                        2,
+                        12
+                    ],
+                    [
+                        0,
+                        1,
+                        312
+                    ],
+                    [
+                        1,
+                        0,
+                        122
+                    ],
+                    [
+                        1,
+                        0,
+                        16
+                    ],
+                    [
+                        1,
+                        0,
+                        424
+                    ],
+                    [
+                        2,
+                        1,
+                        334
+                    ],
+                    [
+                        0,
+                        2,
+                        866
+                    ],
+                    [
+                        1,
+                        0,
+                        842
+                    ],
+                    [
+                        2,
+                        0,
+                        57
+                    ],
+                    [
+                        0,
+                        2,
+                        5
+                    ],
+                    [
+                        2,
+                        1,
+                        507
+                    ],
+                    [
+                        1,
+                        2,
+                        166
+                    ],
+                    [
+                        0,
+                        1,
+                        272
+                    ],
+                    [
+                        0,
+                        2,
+                        212
+                    ],
+                    [
+                        2,
+                        1,
+                        554
+                    ],
+                    [
+                        1,
+                        0,
+                        557
+                    ],
+                    [
+                        0,
+                        2,
+                        870
+                    ],
+                    [
+                        0,
+                        2,
+                        495
+                    ],
+                    [
+                        1,
+                        2,
+                        115
+                    ],
+                    [
+                        1,
+                        0,
+                        670
+                    ],
+                    [
+                        0,
+                        1,
+                        202
+                    ],
+                    [
+                        2,
+                        0,
+                        476
+                    ],
+                    [
+                        2,
+                        0,
+                        293
+                    ],
+                    [
+                        0,
+                        2,
+                        111
+                    ],
+                    [
+                        2,
+                        1,
+                        258
+                    ],
+                    [
+                        0,
+                        2,
+                        135
+                    ],
+                    [
+                        0,
+                        2,
+                        141
+                    ],
+                    [
+                        0,
+                        2,
+                        43
+                    ],
+                    [
+                        2,
+                        0,
+                        272
+                    ],
+                    [
+                        1,
+                        0,
+                        732
+                    ],
+                    [
+                        1,
+                        0,
+                        130
+                    ],
+                    [
+                        2,
+                        0,
+                        771
+                    ],
+                    [
+                        1,
+                        2,
+                        498
+                    ],
+                    [
+                        0,
+                        1,
+                        86
+                    ],
+                    [
+                        0,
+                        1,
+                        642
+                    ],
+                    [
+                        0,
+                        1,
+                        184
+                    ],
+                    [
+                        1,
+                        0,
+                        856
+                    ],
+                    [
+                        1,
+                        2,
+                        53
+                    ],
+                    [
+                        0,
+                        1,
+                        284
+                    ],
+                    [
+                        0,
+                        2,
+                        100
+                    ],
+                    [
+                        0,
+                        1,
+                        207
+                    ],
+                    [
+                        2,
+                        1,
+                        409
+                    ],
+                    [
+                        1,
+                        0,
+                        602
+                    ],
+                    [
+                        1,
+                        2,
+                        474
+                    ],
+                    [
+                        1,
+                        0,
+                        637
+                    ],
+                    [
+                        0,
+                        1,
+                        519
+                    ],
+                    [
+                        1,
+                        2,
+                        678
+                    ],
+                    [
+                        0,
+                        1,
+                        503
+                    ],
+                    [
+                        1,
+                        2,
+                        518
+                    ],
+                    [
+                        1,
+                        2,
+                        819
+                    ],
+                    [
+                        0,
+                        2,
+                        551
+                    ],
+                    [
+                        1,
+                        2,
+                        871
+                    ],
+                    [
+                        2,
+                        0,
+                        999
+                    ],
+                    [
+                        0,
+                        2,
+                        692
+                    ],
+                    [
+                        1,
+                        0,
+                        467
+                    ],
+                    [
+                        0,
+                        2,
+                        945
+                    ],
+                    [
+                        1,
+                        0,
+                        555
+                    ],
+                    [
+                        2,
+                        0,
+                        542
+                    ]
+                ]
+            ],
+            "output": 8
+        }
+    ],
+    "haskell_template": "numberOfSets :: Int -> Int -> [[Int]] -> Int\nnumberOfSets n maxDistance roads ",
+    "ocaml_template": "let numberOfSets (n: int) (maxDistance: int) (roads: int list list) : int =  ",
+    "scala_template": "def numberOfSets(n: Int,maxDistance: Int,roads: List[List[Int]]): Int = { \n    \n}",
+    "java_template": "class Solution {\n    public int numberOfSets(int n, int maxDistance, int[][] roads) {\n        \n    }\n}",
+    "python_template": "class Solution(object):\n    def numberOfSets(self, n, maxDistance, roads):\n        \"\"\"\n        :type n: int\n        :type maxDistance: int\n        :type roads: List[List[int]]\n        :rtype: int\n        \"\"\"\n        "
+}
\ No newline at end of file