diff --git "a/earliest_second_to_mark_indices_i/meta.json" "b/earliest_second_to_mark_indices_i/meta.json"
new file mode 100644--- /dev/null
+++ "b/earliest_second_to_mark_indices_i/meta.json"
@@ -0,0 +1,19077 @@
+{
+    "id": 3292,
+    "name": "earliest_second_to_mark_indices_i",
+    "difficulty": "Medium",
+    "link": "https://leetcode.com/problems/earliest-second-to-mark-indices-i/",
+    "date": "2024-02-18 00:00:00",
+    "task_description": "You are given two **1-indexed** integer arrays, `nums` and, `changeIndices`, having lengths `n` and `m`, respectively. Initially, all indices in `nums` are unmarked. Your task is to mark **all** indices in `nums`. In each second, `s`, in order from `1` to `m` (**inclusive**), you can perform **one** of the following operations: Choose an index `i` in the range `[1, n]` and **decrement** `nums[i]` by `1`. If `nums[changeIndices[s]]` is **equal** to `0`, **mark** the index `changeIndices[s]`. Do nothing. Return _an integer denoting the **earliest second** in the range _`[1, m]`_ when **all** indices in _`nums`_ can be marked by choosing operations optimally, or _`-1`_ if it is impossible._ **Example 1:** ``` **Input:** nums = [2,2,0], changeIndices = [2,2,2,2,3,2,2,1] **Output:** 8 **Explanation:** In this example, we have 8 seconds. The following operations can be performed to mark all indices: Second 1: Choose index 1 and decrement nums[1] by one. nums becomes [1,2,0]. Second 2: Choose index 1 and decrement nums[1] by one. nums becomes [0,2,0]. Second 3: Choose index 2 and decrement nums[2] by one. nums becomes [0,1,0]. Second 4: Choose index 2 and decrement nums[2] by one. nums becomes [0,0,0]. Second 5: Mark the index changeIndices[5], which is marking index 3, since nums[3] is equal to 0. Second 6: Mark the index changeIndices[6], which is marking index 2, since nums[2] is equal to 0. Second 7: Do nothing. Second 8: Mark the index changeIndices[8], which is marking index 1, since nums[1] is equal to 0. Now all indices have been marked. It can be shown that it is not possible to mark all indices earlier than the 8th second. Hence, the answer is 8. ``` **Example 2:** ``` **Input:** nums = [1,3], changeIndices = [1,1,1,2,1,1,1] **Output:** 6 **Explanation:** In this example, we have 7 seconds. The following operations can be performed to mark all indices: Second 1: Choose index 2 and decrement nums[2] by one. nums becomes [1,2]. Second 2: Choose index 2 and decrement nums[2] by one. nums becomes [1,1]. Second 3: Choose index 2 and decrement nums[2] by one. nums becomes [1,0]. Second 4: Mark the index changeIndices[4], which is marking index 2, since nums[2] is equal to 0. Second 5: Choose index 1 and decrement nums[1] by one. nums becomes [0,0]. Second 6: Mark the index changeIndices[6], which is marking index 1, since nums[1] is equal to 0. Now all indices have been marked. It can be shown that it is not possible to mark all indices earlier than the 6th second. Hence, the answer is 6. ``` **Example 3:** ``` **Input:** nums = [0,1], changeIndices = [2,2,2] **Output:** -1 **Explanation:** In this example, it is impossible to mark all indices because index 1 isn't in changeIndices. Hence, the answer is -1. ``` **Constraints:** `1 <= n == nums.length <= 2000` `0 <= nums[i] <= 109` `1 <= m == changeIndices.length <= 2000` `1 <= changeIndices[i] <= n`",
+    "public_test_cases": [
+        {
+            "label": "Example 1",
+            "input": "nums = [2,2,0], changeIndices = [2,2,2,2,3,2,2,1]",
+            "output": "8 "
+        },
+        {
+            "label": "Example 2",
+            "input": "nums = [1,3], changeIndices = [1,1,1,2,1,1,1]",
+            "output": "6 "
+        },
+        {
+            "label": "Example 3",
+            "input": "nums = [0,1], changeIndices = [2,2,2]",
+            "output": "-1 "
+        }
+    ],
+    "private_test_cases": [
+        {
+            "input": [
+                [
+                    106614183,
+                    370338257,
+                    565846003,
+                    201543124,
+                    5367284,
+                    481639037,
+                    512447649,
+                    604001,
+                    484230553,
+                    331721161,
+                    146648412,
+                    915540568,
+                    374577465,
+                    618995447,
+                    9029519,
+                    114268410,
+                    529253811,
+                    426269515,
+                    478462829,
+                    478260305,
+                    366445906,
+                    98099063,
+                    972131003,
+                    799915478,
+                    175868243,
+                    145753603,
+                    723900030,
+                    32811065,
+                    71181985,
+                    121437790,
+                    530290908,
+                    335425161,
+                    438545751,
+                    100611255,
+                    700486951,
+                    569900896,
+                    58808670,
+                    399089075,
+                    853053299,
+                    569122305,
+                    858527626,
+                    555898758,
+                    522105833,
+                    324320067,
+                    599787804,
+                    991700791,
+                    344225785,
+                    426532697,
+                    758727111,
+                    577863671,
+                    460866659,
+                    87378989,
+                    392276650,
+                    511994290,
+                    256626128,
+                    682988315,
+                    262049195,
+                    438307911,
+                    372205550,
+                    683859813,
+                    909857711,
+                    22770982,
+                    415416509,
+                    171803387,
+                    750955955,
+                    16018424,
+                    93529544,
+                    896895111,
+                    385730877,
+                    185824843,
+                    343102397,
+                    302813363,
+                    569850169,
+                    504448334,
+                    23637178,
+                    795656324,
+                    455157768,
+                    443537034,
+                    707271993,
+                    166956886,
+                    78486477,
+                    509370422,
+                    701279826,
+                    27174715,
+                    834865954,
+                    613642558,
+                    118576749,
+                    443500970,
+                    340454535,
+                    699088159,
+                    921958850,
+                    595200885,
+                    47846212,
+                    676106894,
+                    252849169,
+                    39720162,
+                    50862765,
+                    120883734,
+                    405735425,
+                    673961683,
+                    537203373,
+                    428535729,
+                    480320894,
+                    610274780,
+                    641107184,
+                    93885235,
+                    423805548,
+                    841776552,
+                    58465922,
+                    23725927,
+                    528875199,
+                    212590194,
+                    526162561,
+                    887636520,
+                    843777589,
+                    172505445,
+                    420123556,
+                    137813799,
+                    500884676,
+                    772952819,
+                    194378963,
+                    271937048,
+                    837527180,
+                    647953634,
+                    942245931,
+                    522397623,
+                    297405238,
+                    34494843,
+                    678245108,
+                    41027121,
+                    564663169,
+                    170855858,
+                    743817225,
+                    917128896,
+                    965231358,
+                    636081108,
+                    479931199,
+                    998923519,
+                    374438546,
+                    100714786,
+                    503601499,
+                    879009958,
+                    245299705,
+                    446301870,
+                    562046954,
+                    355760253,
+                    743738179,
+                    193057780,
+                    559197063,
+                    59636137,
+                    530852167,
+                    640156110,
+                    609828556,
+                    471949607,
+                    325162217,
+                    872622206,
+                    464854561,
+                    98988799,
+                    715709599,
+                    282823955,
+                    727468434,
+                    896947883,
+                    439895152,
+                    663861304,
+                    91442234,
+                    525278801,
+                    340411283,
+                    238302856,
+                    220187480,
+                    764014089,
+                    268843725,
+                    717244668,
+                    842503042,
+                    654943204,
+                    65154164,
+                    908932118,
+                    300656725,
+                    142140971,
+                    837770396,
+                    389124787,
+                    276833044,
+                    406335127,
+                    152895948,
+                    901010527,
+                    250125522,
+                    741638303,
+                    197732249,
+                    125211664,
+                    895849704,
+                    440452109,
+                    852639747,
+                    268076095,
+                    454463312,
+                    124832881,
+                    685932636,
+                    871088625,
+                    144155028,
+                    994393021,
+                    695602042,
+                    552361724,
+                    144805723,
+                    136891826,
+                    50298675,
+                    997246944,
+                    812351503,
+                    467425705,
+                    207677272,
+                    642959114,
+                    472042520,
+                    68081035,
+                    748643237,
+                    699138828,
+                    384405223,
+                    399035107,
+                    648620893,
+                    338346060,
+                    726774172,
+                    146855863,
+                    927202851,
+                    810742762,
+                    876958714,
+                    730945238,
+                    714864362,
+                    698854726,
+                    477192211,
+                    47613305,
+                    970912210,
+                    572049115,
+                    255584422,
+                    770456714,
+                    410375207,
+                    527496782,
+                    986686666,
+                    756895176,
+                    794873509,
+                    88982940,
+                    983741206,
+                    825697772,
+                    947088659,
+                    147497764,
+                    465140969,
+                    776880966,
+                    260308788,
+                    144627913,
+                    399625776,
+                    201628515,
+                    704603775,
+                    382248363,
+                    132240216,
+                    840411298,
+                    832632074,
+                    161595340,
+                    650685834,
+                    391521327,
+                    510449449,
+                    686428992,
+                    883454716,
+                    475892285,
+                    517299996,
+                    480513702,
+                    195358879,
+                    499466404,
+                    825392384,
+                    644012165,
+                    564647705,
+                    12046790,
+                    578301486,
+                    848634527,
+                    212253512,
+                    565935093,
+                    679175694,
+                    35892424,
+                    912880381,
+                    218745445,
+                    377697991,
+                    213759968,
+                    35485576,
+                    28373550,
+                    516712497,
+                    857773543,
+                    976281999,
+                    145173670,
+                    403715623,
+                    169863785,
+                    247414015,
+                    359634258,
+                    422186414,
+                    899127760,
+                    708663292,
+                    4399115,
+                    587613829,
+                    742063943,
+                    54552052,
+                    780950359,
+                    281852596,
+                    520846793,
+                    642262999,
+                    882539393,
+                    681945044,
+                    684109359,
+                    436391070,
+                    351278247,
+                    350362634,
+                    78114691,
+                    139379415,
+                    784801240,
+                    641086144,
+                    834556903,
+                    317507707,
+                    269418111,
+                    769023992,
+                    168849426,
+                    598274003,
+                    973356404,
+                    314617590,
+                    148865717,
+                    756640373,
+                    267272362,
+                    983155118,
+                    888902550,
+                    457271397,
+                    328372524,
+                    450080212,
+                    271785416,
+                    842653325,
+                    587495950,
+                    720237712,
+                    143421007,
+                    320861537,
+                    639013742,
+                    319026241,
+                    600776692,
+                    901103844,
+                    267875747,
+                    307894760,
+                    90408293,
+                    789356765,
+                    628214431,
+                    381560017,
+                    166867330,
+                    162183376,
+                    984143092,
+                    343649744,
+                    712551372,
+                    929504640,
+                    455075718,
+                    309142653,
+                    182137524,
+                    34758474,
+                    486407631,
+                    985471460,
+                    472785205,
+                    825567138,
+                    709333595,
+                    632826072,
+                    486898130,
+                    973885432,
+                    936321713,
+                    830904841,
+                    134085231,
+                    376934764,
+                    820887642,
+                    912511780,
+                    656422251,
+                    643058411,
+                    11610810,
+                    753879296,
+                    451914301,
+                    539592656,
+                    920284696,
+                    207403071,
+                    327541958,
+                    24523161,
+                    941230918,
+                    274650435,
+                    878023926,
+                    8975976,
+                    807415536,
+                    969861838,
+                    605307816,
+                    618123398,
+                    296695720,
+                    241574769,
+                    854682934,
+                    600699465,
+                    740452185,
+                    404635397,
+                    729644313,
+                    87908903,
+                    769528679,
+                    417748957,
+                    676530112,
+                    682249683,
+                    1625347,
+                    526717661,
+                    397167834,
+                    595815167,
+                    747331903,
+                    863981361,
+                    866040332,
+                    249318966,
+                    836081859,
+                    602443414,
+                    961018105,
+                    967657881,
+                    122125259,
+                    830858566,
+                    665584383,
+                    109672989,
+                    760754468,
+                    854172876,
+                    41268301,
+                    479919610,
+                    375806127,
+                    540531135,
+                    744435550,
+                    786064302,
+                    152134458,
+                    829215196,
+                    678498613,
+                    658216685,
+                    294905731,
+                    443079538,
+                    608053447,
+                    763882464,
+                    441287558,
+                    814082486,
+                    164839217,
+                    709682626,
+                    875300791,
+                    852165276,
+                    775373705,
+                    451909356,
+                    461979628,
+                    302423704,
+                    666034802,
+                    534472123,
+                    326095189,
+                    957954332,
+                    249307758,
+                    528628488,
+                    521645626,
+                    89662505,
+                    625855910,
+                    43924579,
+                    218038198,
+                    565911551,
+                    835826668,
+                    96294554,
+                    53776173,
+                    381849606,
+                    63138921,
+                    893865158,
+                    147583642,
+                    295525649,
+                    921409645,
+                    517672291,
+                    510002719,
+                    538465126,
+                    913532919,
+                    697089380,
+                    529524989,
+                    266009499,
+                    274017534,
+                    310040935,
+                    284645947,
+                    159754396,
+                    301750821,
+                    455789500,
+                    863533182,
+                    305991906,
+                    271702276,
+                    45747090,
+                    414314572,
+                    63702239,
+                    432443982,
+                    742771855,
+                    3346559,
+                    816002113,
+                    221788282,
+                    654908012,
+                    147688766,
+                    136908348,
+                    126661060,
+                    881361295,
+                    945117121,
+                    417334944,
+                    875107969,
+                    797896128,
+                    959564065,
+                    648900088,
+                    799789030,
+                    448059415,
+                    595708370,
+                    984155890,
+                    574175018,
+                    394773950,
+                    393205886,
+                    543411454,
+                    589227559,
+                    596068757,
+                    497967752,
+                    4066287,
+                    675345839,
+                    863046931,
+                    267663012,
+                    220563864,
+                    813234186,
+                    179134278,
+                    905397768,
+                    910472203,
+                    839671057,
+                    799318789,
+                    705349649,
+                    574673133,
+                    985319910,
+                    152486079,
+                    702190029,
+                    972588869,
+                    393023018,
+                    733856993,
+                    914024656,
+                    927232990,
+                    624441456,
+                    274518080,
+                    520385447,
+                    17962692,
+                    591277764,
+                    339372420,
+                    273606774,
+                    880830000,
+                    547718000,
+                    536468994,
+                    248635609,
+                    596135426,
+                    572772007,
+                    717876695,
+                    313788157,
+                    458118494,
+                    649848151,
+                    38519475,
+                    159791702,
+                    730961047,
+                    247907962,
+                    673275008,
+                    494976453,
+                    685852279,
+                    369560577,
+                    35945738,
+                    704977989,
+                    281027809,
+                    794941348,
+                    509485379,
+                    144458210,
+                    698510387,
+                    18220393,
+                    138264875,
+                    740705327,
+                    199675057,
+                    738011666,
+                    166799028,
+                    408953833,
+                    522714533,
+                    25996573,
+                    754025231,
+                    270748520,
+                    555209111,
+                    952362980,
+                    490366174,
+                    69176866,
+                    877591446,
+                    906024720,
+                    371166299,
+                    110562798,
+                    143265915,
+                    29882704,
+                    560519279,
+                    85156964,
+                    393468961,
+                    464129432,
+                    112813478,
+                    258389074,
+                    742937107,
+                    949514687,
+                    395084736,
+                    350362515,
+                    467160512,
+                    681461278,
+                    106433857,
+                    604364583,
+                    127951601,
+                    821877611,
+                    253440078,
+                    740488119,
+                    811047561,
+                    62621522,
+                    191862952,
+                    29772719,
+                    528252009,
+                    37130611,
+                    543256324,
+                    949743911,
+                    359511576,
+                    343784459,
+                    31213393,
+                    163720464,
+                    676692246,
+                    682003440,
+                    939001703,
+                    160621286,
+                    294323409,
+                    331939971,
+                    768035094,
+                    139576781,
+                    201887429,
+                    335647153,
+                    533510724,
+                    837490812,
+                    293321931,
+                    746953404,
+                    702071554,
+                    402137484,
+                    432510162,
+                    295865486,
+                    554078278,
+                    688947800,
+                    150883758,
+                    368605158,
+                    100062242,
+                    501988111,
+                    577390202,
+                    36357050,
+                    349651611,
+                    943867453,
+                    918357585,
+                    168533243,
+                    163797367,
+                    539394999,
+                    484699864,
+                    512591843,
+                    98552400,
+                    997577973,
+                    421695611,
+                    770569086,
+                    6227667,
+                    384248943,
+                    605403087,
+                    539539325,
+                    444839293,
+                    381343350,
+                    771731137,
+                    876250478,
+                    411094286,
+                    795788155,
+                    302558724,
+                    643218196,
+                    940283937,
+                    588874811,
+                    353954225,
+                    765804150,
+                    31234737,
+                    917712959,
+                    869894904,
+                    646052327,
+                    688221206,
+                    258161586,
+                    202291896,
+                    86038814,
+                    29041551,
+                    381059435,
+                    634699922,
+                    763291713,
+                    520537102,
+                    909594908,
+                    873294993,
+                    188573089,
+                    671597859,
+                    222356573,
+                    860874985,
+                    147875632,
+                    695230862,
+                    890961970,
+                    401809753,
+                    83130491,
+                    662101281,
+                    973539084,
+                    159950433,
+                    701197334,
+                    496202212,
+                    250817190,
+                    984167503,
+                    895571664,
+                    254506987,
+                    646064565,
+                    832479782,
+                    802798564,
+                    300330569,
+                    897845911,
+                    209109455,
+                    424202307,
+                    106974227,
+                    974552310,
+                    554285806,
+                    319130821,
+                    210369909,
+                    702137792,
+                    319696204,
+                    931847450,
+                    983203821,
+                    848275015,
+                    558678965,
+                    320744653,
+                    602423529,
+                    844015142,
+                    693402818,
+                    829466595,
+                    240544948,
+                    781153104,
+                    506560693,
+                    107230282,
+                    749081272,
+                    996679844,
+                    765606202,
+                    760363850,
+                    180903357,
+                    695295517,
+                    51993363,
+                    611225800,
+                    642661065,
+                    712300404,
+                    546081912,
+                    292721203,
+                    474495969,
+                    982229666,
+                    365624700,
+                    196308097,
+                    706102938,
+                    839239249,
+                    459171648,
+                    55338595,
+                    369178130,
+                    912105318,
+                    660745579,
+                    180157436,
+                    185747466,
+                    789183221,
+                    346379435,
+                    667356257,
+                    140067446,
+                    552689843,
+                    780039080,
+                    207342244,
+                    534824376,
+                    742185858,
+                    661292284,
+                    576071543,
+                    961028281,
+                    957987626,
+                    593501591,
+                    203546641,
+                    60247101,
+                    294545207,
+                    239075863,
+                    233901438,
+                    873951851,
+                    804605985,
+                    730603129,
+                    475181530,
+                    499260170,
+                    640231405,
+                    717371797,
+                    878443791,
+                    743313067,
+                    304579997,
+                    164425111,
+                    190372716,
+                    688245665,
+                    474266210,
+                    955204864,
+                    682297858,
+                    552315438,
+                    161146621,
+                    499685391,
+                    372511507,
+                    524031625,
+                    125827614,
+                    929471676,
+                    940538196,
+                    972262592,
+                    493057373,
+                    389628551,
+                    989783158,
+                    7534611,
+                    744323509,
+                    415980594,
+                    711208369,
+                    155520005,
+                    185811732,
+                    82620187,
+                    109684750,
+                    230260574,
+                    812310171,
+                    934162564,
+                    739470398,
+                    739615307,
+                    278310,
+                    176421681,
+                    202616408,
+                    129888069,
+                    563562727,
+                    741544125,
+                    992848603,
+                    349646444,
+                    78489573,
+                    254831647,
+                    480234708,
+                    667949913,
+                    694199321,
+                    375652241,
+                    596140625,
+                    768319282,
+                    431817418,
+                    591104794,
+                    715826115,
+                    926058878,
+                    828579245,
+                    588053091,
+                    47918306,
+                    973027577,
+                    338553266,
+                    584673972,
+                    344104989,
+                    449001583,
+                    825999700,
+                    840021397,
+                    102204148,
+                    68275903,
+                    395161161,
+                    270540805,
+                    531779915,
+                    323642995,
+                    401368309,
+                    718518844,
+                    414642966,
+                    84747076,
+                    246749534,
+                    939302886,
+                    977414714,
+                    826752471,
+                    664282662,
+                    558437251,
+                    557501737,
+                    620465047,
+                    361967302,
+                    766218042,
+                    832713213,
+                    553880368,
+                    518698679,
+                    177736208,
+                    573446691,
+                    56052252,
+                    486429803,
+                    988482718,
+                    368816096,
+                    770685315,
+                    177101564,
+                    735875961,
+                    592388290,
+                    52252972,
+                    548001663,
+                    292293678,
+                    721419263,
+                    418295195,
+                    884408628,
+                    384301014,
+                    693829682,
+                    548728788,
+                    948257691,
+                    494282826,
+                    90160830,
+                    54092615,
+                    614850307,
+                    319028563,
+                    929122367,
+                    201415804,
+                    578483950,
+                    930431783,
+                    576798805,
+                    130269055,
+                    491059863,
+                    229300335,
+                    18255865,
+                    194060659,
+                    563224653,
+                    151629623,
+                    770219089,
+                    405337734,
+                    37534956,
+                    663011489,
+                    516008310,
+                    444489670,
+                    776202803,
+                    177467698,
+                    367614651,
+                    45475860,
+                    972362258,
+                    785246514,
+                    953132136,
+                    302837639,
+                    705370994,
+                    499443381,
+                    66288545,
+                    793895167,
+                    431899091,
+                    340820560,
+                    404823258,
+                    962310432,
+                    248185452,
+                    459250276,
+                    112905676,
+                    847876013,
+                    670694941,
+                    385449366,
+                    774896547,
+                    701091269,
+                    903972667,
+                    945021600,
+                    83741399,
+                    338610297,
+                    174552931,
+                    240087401,
+                    366763354,
+                    79290140,
+                    593364033,
+                    695127419,
+                    305934664,
+                    924428082,
+                    685878898,
+                    449609933,
+                    527680975,
+                    663158499,
+                    345707806,
+                    285052327,
+                    432449300,
+                    454816014,
+                    106897779,
+                    446439951,
+                    494986263,
+                    117054685,
+                    746255074,
+                    715685463,
+                    671626119,
+                    154340288,
+                    30070485,
+                    877852221,
+                    992549476,
+                    769068489,
+                    118256916,
+                    235043560,
+                    134392147,
+                    29292146,
+                    157268353,
+                    636048657,
+                    769920173,
+                    722210100,
+                    239527201,
+                    117792535,
+                    216225184,
+                    512570212,
+                    48874630,
+                    445227335,
+                    670824666,
+                    830922704,
+                    331642173,
+                    608139992,
+                    280062310,
+                    940490599,
+                    648496431,
+                    168195558,
+                    591357477,
+                    654903507,
+                    674180009,
+                    894031437,
+                    943272421,
+                    328960878,
+                    210985228,
+                    345181751,
+                    945860907,
+                    166736126,
+                    733297768,
+                    870827372,
+                    880711459,
+                    385766360,
+                    498942241,
+                    944621323,
+                    752365604,
+                    417903362,
+                    594855917,
+                    707500956,
+                    143173737,
+                    199676697,
+                    252723327,
+                    387788007,
+                    174268763,
+                    201038873,
+                    100969271,
+                    804910470,
+                    230786787,
+                    530648515,
+                    973643491,
+                    168381734,
+                    752632613,
+                    899220409,
+                    129797407,
+                    387875277,
+                    623461549,
+                    705819892,
+                    618216945,
+                    701568129,
+                    875594884,
+                    932164688,
+                    13957163,
+                    563431628,
+                    427280821,
+                    845265845,
+                    133520775,
+                    237018111,
+                    106820008,
+                    821862564,
+                    300656408,
+                    246669699,
+                    163911253,
+                    139839816,
+                    559856942,
+                    33481173,
+                    390729687,
+                    92893976,
+                    129692182,
+                    120445298,
+                    208508949,
+                    309916038,
+                    585791471,
+                    727311229,
+                    955781259,
+                    815697697,
+                    856128444,
+                    86308617,
+                    835583950,
+                    663825224,
+                    973054371,
+                    10319451,
+                    227920614,
+                    778076909,
+                    484323567,
+                    622510110,
+                    423492484,
+                    843609710,
+                    637088933,
+                    523555780,
+                    220241410,
+                    721177146,
+                    584084498,
+                    70060567,
+                    588325169,
+                    706149748,
+                    658428624,
+                    932458645,
+                    914727274,
+                    965943496,
+                    320592098,
+                    916813668,
+                    560632354,
+                    222968516,
+                    324239920,
+                    338867866,
+                    104224489,
+                    204270267,
+                    367723517,
+                    403202338,
+                    935449877,
+                    719800111,
+                    875185411,
+                    533743017,
+                    878059825,
+                    513167556,
+                    814235496,
+                    634240676,
+                    904770961,
+                    777134403,
+                    874308187,
+                    305729876,
+                    938613737,
+                    38567405,
+                    546238270,
+                    618055975,
+                    740000670,
+                    991927783,
+                    467149369,
+                    480608600,
+                    454870042,
+                    678249274,
+                    469979731,
+                    201886621,
+                    59235932,
+                    24766313,
+                    551054517,
+                    893993602,
+                    43943438,
+                    284151153,
+                    494855503,
+                    533496229,
+                    42262920,
+                    758983302,
+                    21836263,
+                    350489934,
+                    138775477,
+                    649458674,
+                    381155495,
+                    873565505,
+                    54184340,
+                    916375028,
+                    248986822,
+                    902560162,
+                    18102929,
+                    11581920,
+                    654195785,
+                    108340107,
+                    701892469,
+                    389903062,
+                    719409642,
+                    463697258,
+                    564687780,
+                    288944375,
+                    204334618,
+                    95159761,
+                    555363092,
+                    838060923,
+                    144968932,
+                    387971973,
+                    396494178,
+                    421908961,
+                    91587240,
+                    708892178,
+                    930001598,
+                    609993384,
+                    614317313,
+                    49592689,
+                    950692850,
+                    969775505,
+                    988312951,
+                    450446922,
+                    1348961,
+                    511422031,
+                    276143851,
+                    159746296,
+                    949158534,
+                    172335259,
+                    798974759,
+                    523140432,
+                    694541446,
+                    585826880,
+                    429628942,
+                    244043199,
+                    444240996,
+                    538228267,
+                    217760893,
+                    133192834,
+                    26234014,
+                    224573704,
+                    610311889,
+                    103541928,
+                    660685957,
+                    398919477,
+                    962219881,
+                    718039440,
+                    909438304,
+                    941870386,
+                    217774902,
+                    674733916,
+                    65856899,
+                    545672499,
+                    185954130,
+                    456164135,
+                    532445791,
+                    694632871,
+                    782188668,
+                    447704561,
+                    203695386,
+                    690075715,
+                    533747070,
+                    532854597,
+                    46227662,
+                    451007324,
+                    389749206,
+                    339935680,
+                    419286131,
+                    81192036,
+                    688803289,
+                    862304826,
+                    196064907,
+                    733210764,
+                    583978995,
+                    206305630,
+                    678680184,
+                    346734581,
+                    720210732,
+                    983487459,
+                    717889700,
+                    114014822,
+                    217200183,
+                    635551057,
+                    443507082,
+                    310142376,
+                    942010204,
+                    74108432,
+                    142803861,
+                    540338608,
+                    761504721,
+                    93462739,
+                    776778207,
+                    175645027,
+                    415766949,
+                    571862275,
+                    151420446,
+                    968435001,
+                    113344063,
+                    732503447,
+                    691623877,
+                    523052296,
+                    616067111,
+                    712212091,
+                    879559084,
+                    150599487,
+                    67670979,
+                    369850917,
+                    121800311,
+                    863849160,
+                    961429079,
+                    956864978,
+                    261358144,
+                    2111789,
+                    43246414,
+                    351504239,
+                    208042006,
+                    706338961,
+                    781558916,
+                    201613345,
+                    592244019,
+                    889507306,
+                    738841534,
+                    641058450,
+                    485795227,
+                    952139754,
+                    202443539,
+                    843107808,
+                    33295437,
+                    596182694,
+                    675057907,
+                    415483030,
+                    185127854,
+                    578829841,
+                    498100742,
+                    859557451,
+                    390635971,
+                    152712143,
+                    919348776,
+                    685624041,
+                    253815285,
+                    662155028,
+                    13875307,
+                    207588806,
+                    898370314,
+                    663124993,
+                    553032198,
+                    699248977,
+                    592408037,
+                    524293640,
+                    625752203,
+                    373243451,
+                    752167860,
+                    149545541,
+                    172083620,
+                    776233231,
+                    23363828,
+                    529741236,
+                    637275139,
+                    658446626,
+                    239361133,
+                    283978102,
+                    999162893,
+                    555504890,
+                    142213563,
+                    88880351,
+                    458365236,
+                    256610009,
+                    379331296,
+                    635447816,
+                    77468925,
+                    454994381,
+                    338742746,
+                    670594790,
+                    734282197,
+                    362766074,
+                    4569037,
+                    134188027,
+                    882829046,
+                    241796864,
+                    119901047,
+                    777847939,
+                    681137857,
+                    937676913,
+                    381457546,
+                    226757903,
+                    844581713,
+                    62825395,
+                    803650173,
+                    516128829,
+                    608129658,
+                    10508945,
+                    449336965,
+                    551333608,
+                    386538252,
+                    430733386,
+                    54736096,
+                    64289156,
+                    855471282,
+                    601013536,
+                    984596193,
+                    191073941,
+                    739639896,
+                    369121849,
+                    610016211,
+                    61202667,
+                    15914576,
+                    489195832,
+                    136477973,
+                    62879095,
+                    277975990,
+                    182160844,
+                    209093113,
+                    694464960,
+                    76563881,
+                    283561686,
+                    799253157,
+                    547028069,
+                    319337017,
+                    272970046,
+                    22723744,
+                    536884038,
+                    866413221,
+                    500863369,
+                    551860789,
+                    656797834,
+                    206426748,
+                    131656880,
+                    670533189,
+                    870835550,
+                    273603239,
+                    327056655,
+                    12543195,
+                    872480754,
+                    845555022,
+                    476666410,
+                    771723021,
+                    716051387,
+                    36941968,
+                    668112505,
+                    910217116,
+                    266069606,
+                    612115166,
+                    446707255,
+                    40187510,
+                    697496154,
+                    940574098,
+                    522764422,
+                    451420608,
+                    721914699,
+                    24547315,
+                    907478214,
+                    928037605,
+                    865462043,
+                    513837711,
+                    906666762,
+                    951461798,
+                    634514664,
+                    320207106,
+                    16241909,
+                    826951157,
+                    87577499,
+                    904163187,
+                    176829581,
+                    146266811,
+                    908451196,
+                    369259111,
+                    134658405,
+                    606914826,
+                    365474140,
+                    701183209,
+                    895554480,
+                    137896156,
+                    844692621,
+                    240185939,
+                    734719309,
+                    980656322,
+                    90591374,
+                    474224883,
+                    427136277,
+                    138949046,
+                    849265328,
+                    177897418,
+                    580752701,
+                    787773004,
+                    942541427,
+                    622706669,
+                    950652846,
+                    901691770,
+                    999100205,
+                    452833362,
+                    972880304,
+                    958215202,
+                    616338229,
+                    223114436,
+                    598348780,
+                    845907148,
+                    685397634,
+                    481037728,
+                    719158888,
+                    888549511,
+                    402352195,
+                    538466549,
+                    727712102,
+                    546105169,
+                    710763183,
+                    795926942,
+                    354598862,
+                    128073733,
+                    514656730,
+                    268158382,
+                    980412631,
+                    934124918,
+                    848297129,
+                    786993280,
+                    47963187,
+                    51548494,
+                    140860820,
+                    382996722,
+                    186011948,
+                    613825342,
+                    499213105,
+                    225472706,
+                    496058181,
+                    843366193,
+                    689051538,
+                    604981582,
+                    385468875,
+                    210219652,
+                    472287374,
+                    869402762,
+                    720057954,
+                    902285900,
+                    488810430,
+                    124892502,
+                    142811675,
+                    127534218,
+                    118225859,
+                    299334086,
+                    913729605,
+                    696801947,
+                    79273457,
+                    449763402,
+                    824308458,
+                    469345613,
+                    657809416,
+                    876333084,
+                    228238320,
+                    526528117,
+                    974743224,
+                    845924917,
+                    940613945,
+                    513034570,
+                    931490758,
+                    476255918,
+                    260100933,
+                    584740951,
+                    535498413,
+                    662445504,
+                    927183035,
+                    464328573,
+                    174021916,
+                    516995538,
+                    186479792,
+                    626174044,
+                    305950210,
+                    262406882,
+                    932441829,
+                    135025037,
+                    438498821,
+                    445479580,
+                    161629232,
+                    170236733,
+                    785745912,
+                    143772276,
+                    186049839,
+                    807996137,
+                    40248727,
+                    535672701,
+                    405819138,
+                    413836361,
+                    761686978,
+                    892231934,
+                    263150237,
+                    326291481,
+                    892718676,
+                    403825272,
+                    484493480,
+                    465742353,
+                    189944961,
+                    429425627,
+                    748373888,
+                    277349504,
+                    586387940,
+                    243127978,
+                    887315897,
+                    470389282,
+                    277401230,
+                    161204541,
+                    402380616,
+                    800671178,
+                    789548066,
+                    276265854,
+                    918526306,
+                    673873430,
+                    405330755,
+                    327903717,
+                    747006569,
+                    518602345,
+                    983834916,
+                    98826912,
+                    432657576,
+                    14131126,
+                    425237753,
+                    536482538,
+                    911265610,
+                    344905279,
+                    22656719,
+                    186373176,
+                    11277953,
+                    778994866,
+                    324272479,
+                    545591210,
+                    982699511,
+                    551471110,
+                    668508003,
+                    954196693,
+                    677161738,
+                    153175689,
+                    458321954,
+                    538306486,
+                    755577937,
+                    943473228,
+                    786308564,
+                    968226526,
+                    931193793,
+                    723249517,
+                    134926943,
+                    911514214,
+                    421909733,
+                    756562650,
+                    331721036,
+                    591061003,
+                    660567152,
+                    647190913,
+                    548252681,
+                    10297289,
+                    637920305,
+                    306495978,
+                    42863308,
+                    283406250,
+                    151162103,
+                    352057732,
+                    760014848,
+                    513637118,
+                    722761668,
+                    588971664,
+                    906530041,
+                    187463046,
+                    876684133,
+                    107509489,
+                    89092645,
+                    899403973,
+                    572699490,
+                    669565409,
+                    80178686
+                ],
+                [
+                    1473,
+                    872,
+                    405,
+                    301,
+                    804,
+                    655,
+                    1115,
+                    1062,
+                    256,
+                    692,
+                    442,
+                    222,
+                    544,
+                    348,
+                    275,
+                    1333,
+                    1045,
+                    1382,
+                    1223,
+                    986,
+                    1160,
+                    234,
+                    202,
+                    1051,
+                    592,
+                    1360,
+                    375,
+                    1312,
+                    1078,
+                    338,
+                    817,
+                    1087,
+                    515,
+                    1128,
+                    311,
+                    1571,
+                    72,
+                    767,
+                    302,
+                    1317,
+                    1114,
+                    614,
+                    1113,
+                    389,
+                    802,
+                    587,
+                    244,
+                    382,
+                    368,
+                    229,
+                    641,
+                    490,
+                    305,
+                    512,
+                    1433,
+                    115,
+                    217,
+                    1119,
+                    1480,
+                    1319,
+                    654,
+                    499,
+                    1190,
+                    663,
+                    65,
+                    919,
+                    491,
+                    247,
+                    1191,
+                    290,
+                    460,
+                    1504,
+                    1477,
+                    681,
+                    412,
+                    413,
+                    830,
+                    960,
+                    743,
+                    1141,
+                    558,
+                    286,
+                    1009,
+                    519,
+                    725,
+                    695,
+                    336,
+                    1225,
+                    948,
+                    1239,
+                    1163,
+                    701,
+                    1042,
+                    1463,
+                    1329,
+                    783,
+                    310,
+                    135,
+                    1111,
+                    307,
+                    932,
+                    1576,
+                    949,
+                    1357,
+                    1310,
+                    1392,
+                    3,
+                    1570,
+                    483,
+                    1483,
+                    1547,
+                    956,
+                    1115,
+                    800,
+                    740,
+                    1215,
+                    765,
+                    705,
+                    1254,
+                    450,
+                    1050,
+                    643,
+                    713,
+                    1340,
+                    445,
+                    1386,
+                    1136,
+                    801,
+                    1013,
+                    946,
+                    1309,
+                    478,
+                    161,
+                    464,
+                    1104,
+                    321,
+                    124,
+                    1308,
+                    648,
+                    194,
+                    1378,
+                    756,
+                    1343,
+                    1533,
+                    793,
+                    58,
+                    507,
+                    536,
+                    488,
+                    860,
+                    436,
+                    142,
+                    861,
+                    395,
+                    611,
+                    70,
+                    711,
+                    779,
+                    1279,
+                    1553,
+                    832,
+                    757,
+                    936,
+                    1031,
+                    815,
+                    1266,
+                    1215,
+                    1434,
+                    1244,
+                    305,
+                    928,
+                    1401,
+                    1316,
+                    572,
+                    129,
+                    1042,
+                    1364,
+                    762,
+                    1115,
+                    670,
+                    683,
+                    170,
+                    1284,
+                    1302,
+                    1358,
+                    344,
+                    965,
+                    698,
+                    209,
+                    514,
+                    350,
+                    236,
+                    171,
+                    365,
+                    1005,
+                    1122,
+                    454,
+                    683,
+                    223,
+                    425,
+                    1466,
+                    1012,
+                    40,
+                    1342,
+                    1284,
+                    944,
+                    1205,
+                    297,
+                    85,
+                    1115,
+                    253,
+                    1031,
+                    721,
+                    264,
+                    213,
+                    773,
+                    1342,
+                    928,
+                    392,
+                    1189,
+                    1299,
+                    347,
+                    160,
+                    992,
+                    1359,
+                    643,
+                    1257,
+                    327,
+                    816,
+                    802,
+                    1164,
+                    697,
+                    647,
+                    1127,
+                    397,
+                    1476,
+                    1581,
+                    908,
+                    945,
+                    834,
+                    489,
+                    809,
+                    755,
+                    577,
+                    234,
+                    848,
+                    216,
+                    1430,
+                    468,
+                    334,
+                    1560,
+                    398,
+                    419,
+                    1033,
+                    17,
+                    580,
+                    382,
+                    1241,
+                    287,
+                    137,
+                    729,
+                    1010,
+                    876,
+                    985,
+                    122,
+                    929,
+                    764,
+                    820,
+                    333,
+                    40,
+                    341,
+                    394,
+                    1515,
+                    1311,
+                    656,
+                    700,
+                    87,
+                    499,
+                    1191,
+                    1522,
+                    1308,
+                    138,
+                    601,
+                    610,
+                    653,
+                    938,
+                    1199,
+                    659,
+                    1461,
+                    885,
+                    901,
+                    35,
+                    1207,
+                    164,
+                    839,
+                    47,
+                    471,
+                    50,
+                    1507,
+                    514,
+                    170,
+                    272,
+                    684,
+                    35,
+                    836,
+                    1395,
+                    417,
+                    517,
+                    925,
+                    706,
+                    102,
+                    667,
+                    1121,
+                    133,
+                    502,
+                    1113,
+                    673,
+                    675,
+                    1388,
+                    95,
+                    628,
+                    832,
+                    1211,
+                    326,
+                    1548,
+                    1486,
+                    268,
+                    221,
+                    1562,
+                    1298,
+                    551,
+                    959,
+                    164,
+                    1156,
+                    250,
+                    720,
+                    1470,
+                    1218,
+                    1167,
+                    1501,
+                    860,
+                    722,
+                    97,
+                    232,
+                    681,
+                    289,
+                    1164,
+                    149,
+                    1064,
+                    1556,
+                    813,
+                    754,
+                    751,
+                    230,
+                    36,
+                    604,
+                    1302,
+                    728,
+                    1355,
+                    560,
+                    452,
+                    772,
+                    684,
+                    57,
+                    237,
+                    1591,
+                    172,
+                    117,
+                    589,
+                    1274,
+                    438,
+                    1369,
+                    1381,
+                    724,
+                    264,
+                    172,
+                    858,
+                    813,
+                    1523,
+                    570,
+                    374,
+                    1552,
+                    1393,
+                    870,
+                    475,
+                    512,
+                    645,
+                    770,
+                    247,
+                    1593,
+                    53,
+                    1497,
+                    574,
+                    1470,
+                    1263,
+                    1191,
+                    367,
+                    1141,
+                    1290,
+                    129,
+                    766,
+                    621,
+                    506,
+                    388,
+                    1079,
+                    1342,
+                    294,
+                    94,
+                    694,
+                    494,
+                    873,
+                    1042,
+                    843,
+                    728,
+                    1406,
+                    596,
+                    800,
+                    514,
+                    1452,
+                    763,
+                    197,
+                    1183,
+                    1019,
+                    1155,
+                    666,
+                    1077,
+                    1550,
+                    486,
+                    580,
+                    1119,
+                    1101,
+                    581,
+                    227,
+                    714,
+                    356,
+                    475,
+                    1247,
+                    160,
+                    764,
+                    1062,
+                    982,
+                    230,
+                    1046,
+                    920,
+                    798,
+                    854,
+                    1122,
+                    270,
+                    1107,
+                    1464,
+                    294,
+                    656,
+                    1078,
+                    1146,
+                    138,
+                    303,
+                    1497,
+                    1424,
+                    913,
+                    786,
+                    477,
+                    1065,
+                    1173,
+                    1021,
+                    59,
+                    1510,
+                    67,
+                    1190,
+                    1427,
+                    1192,
+                    173,
+                    720,
+                    1081,
+                    1352,
+                    848,
+                    407,
+                    128,
+                    832,
+                    841,
+                    1269,
+                    716,
+                    728,
+                    1332,
+                    1326,
+                    59,
+                    86,
+                    326,
+                    1144,
+                    730,
+                    527,
+                    988,
+                    658,
+                    1453,
+                    93,
+                    224,
+                    954,
+                    1263,
+                    1484,
+                    1322,
+                    882,
+                    341,
+                    1092,
+                    494,
+                    189,
+                    1389,
+                    1587,
+                    717,
+                    998,
+                    476,
+                    1055,
+                    1163,
+                    1466,
+                    527,
+                    170,
+                    250,
+                    1477,
+                    822,
+                    268,
+                    652,
+                    886,
+                    339,
+                    25,
+                    37,
+                    27,
+                    700,
+                    815,
+                    1242,
+                    1109,
+                    9,
+                    1223,
+                    716,
+                    1314,
+                    1397,
+                    686,
+                    573,
+                    1155,
+                    1087,
+                    1245,
+                    16,
+                    61,
+                    1225,
+                    1088,
+                    746,
+                    1368,
+                    188,
+                    853,
+                    129,
+                    1578,
+                    470,
+                    947,
+                    1073,
+                    36,
+                    1327,
+                    362,
+                    14,
+                    1561,
+                    39,
+                    734,
+                    52,
+                    1129,
+                    786,
+                    1113,
+                    1446,
+                    785,
+                    450,
+                    1563,
+                    11,
+                    1185,
+                    424,
+                    667,
+                    1332,
+                    660,
+                    278,
+                    1513,
+                    250,
+                    1402,
+                    703,
+                    867,
+                    447,
+                    509,
+                    1206,
+                    1482,
+                    1468,
+                    114,
+                    173,
+                    1237,
+                    841,
+                    751,
+                    1509,
+                    657,
+                    487,
+                    36,
+                    1543,
+                    1333,
+                    386,
+                    536,
+                    210,
+                    707,
+                    734,
+                    1091,
+                    1198,
+                    1428,
+                    728,
+                    799,
+                    919,
+                    757,
+                    439,
+                    206,
+                    1114,
+                    1041,
+                    1309,
+                    1536,
+                    1385,
+                    1324,
+                    603,
+                    339,
+                    1085,
+                    608,
+                    1467,
+                    314,
+                    306,
+                    45,
+                    575,
+                    353,
+                    1576,
+                    40,
+                    1304,
+                    519,
+                    39,
+                    781,
+                    1491,
+                    1347,
+                    1030,
+                    1147,
+                    1442,
+                    1082,
+                    799,
+                    1335,
+                    1404,
+                    1415,
+                    42,
+                    1577,
+                    1101,
+                    189,
+                    158,
+                    1521,
+                    317,
+                    200,
+                    359,
+                    1374,
+                    604,
+                    1555,
+                    226,
+                    1161,
+                    293,
+                    651,
+                    1423,
+                    1444,
+                    530,
+                    1238,
+                    1138,
+                    257,
+                    1153,
+                    1353,
+                    1292,
+                    1219,
+                    1220,
+                    46,
+                    849,
+                    260,
+                    1208,
+                    34,
+                    1180,
+                    1457,
+                    1374,
+                    1154,
+                    383,
+                    699,
+                    1389,
+                    1240,
+                    981,
+                    856,
+                    278,
+                    1067,
+                    163,
+                    867,
+                    1187,
+                    1516,
+                    97,
+                    519,
+                    1127,
+                    1110,
+                    1097,
+                    525,
+                    1419,
+                    1490,
+                    1233,
+                    1562,
+                    409,
+                    742,
+                    91,
+                    650,
+                    1387,
+                    393,
+                    1335,
+                    337,
+                    1175,
+                    773,
+                    866,
+                    1032,
+                    18,
+                    310,
+                    642,
+                    418,
+                    1361,
+                    842,
+                    719,
+                    137,
+                    1393,
+                    1446,
+                    569,
+                    925,
+                    457,
+                    879,
+                    1144,
+                    584,
+                    930,
+                    493,
+                    815,
+                    957,
+                    1082,
+                    1300,
+                    1529,
+                    1032,
+                    640,
+                    672,
+                    427,
+                    1516,
+                    572,
+                    52,
+                    1383,
+                    357,
+                    739,
+                    1442,
+                    1149,
+                    1321,
+                    1066,
+                    1300
+                ]
+            ],
+            "output": -1
+        },
+        {
+            "input": [
+                [
+                    592801403,
+                    717117287,
+                    771178369,
+                    406074287,
+                    44597686,
+                    235886504,
+                    255415318,
+                    405881070,
+                    155270658,
+                    794736482,
+                    709740605,
+                    360004969,
+                    258089056,
+                    886852835,
+                    85524437,
+                    401820917,
+                    580432771,
+                    151542982,
+                    19582576,
+                    93040522,
+                    606373351,
+                    362049205,
+                    205610348,
+                    624376280,
+                    513587693,
+                    450847809,
+                    300855796,
+                    866088957,
+                    901113077,
+                    765316865,
+                    28919979,
+                    673020288,
+                    320129257,
+                    399519661,
+                    823645991,
+                    138301410,
+                    441158705,
+                    700055911,
+                    794291057,
+                    347939707,
+                    162839160,
+                    269936551,
+                    204578792,
+                    592833086,
+                    596996183,
+                    805759572,
+                    53552889,
+                    406296645,
+                    624614297,
+                    909484167,
+                    368597697,
+                    616389057,
+                    44956311,
+                    228354890,
+                    699227908,
+                    928213778,
+                    809770450,
+                    253811407,
+                    117524296,
+                    222901669,
+                    290513472,
+                    94445585,
+                    60472345,
+                    779051912,
+                    356122444,
+                    608831499,
+                    311588697,
+                    548462953,
+                    378473524,
+                    804617532,
+                    788431418,
+                    738249089,
+                    938719040,
+                    879682982,
+                    741888946,
+                    166609480,
+                    426112220,
+                    113348533,
+                    918696306,
+                    400784401,
+                    28496395,
+                    202913747,
+                    498855593,
+                    399439240,
+                    384934790,
+                    762905640,
+                    3666339,
+                    537465074,
+                    18530708,
+                    980257649,
+                    473943489,
+                    706858499,
+                    90074668,
+                    33487439,
+                    397744827,
+                    602812617,
+                    860392568,
+                    998573987,
+                    461253473,
+                    674365680,
+                    876183349,
+                    954676936,
+                    54525960,
+                    845922266,
+                    486984123,
+                    823874074,
+                    120954391,
+                    646810746,
+                    828735828,
+                    983941725,
+                    689810589,
+                    671863310,
+                    599129105,
+                    986790616,
+                    424535455,
+                    596449353,
+                    161653051,
+                    495324068,
+                    91581279,
+                    40157599,
+                    845373455,
+                    366294589,
+                    718523528,
+                    189183053,
+                    678886675,
+                    174874548,
+                    423678971,
+                    632531863,
+                    896560226,
+                    700238131,
+                    753110341,
+                    218744680,
+                    296859583,
+                    21799467,
+                    973027807,
+                    807848636,
+                    79918671,
+                    648980076,
+                    91824705,
+                    719992058,
+                    902853575,
+                    825726712,
+                    488262592,
+                    590531532,
+                    540286501,
+                    204765241,
+                    284714901,
+                    135313184,
+                    214837291,
+                    884642450,
+                    854984955,
+                    231994185,
+                    623486415,
+                    673789134,
+                    222121531,
+                    631034950,
+                    163865138,
+                    603233397,
+                    174678038,
+                    234860267,
+                    352520067,
+                    186428356,
+                    712895341,
+                    69204308,
+                    870142821,
+                    547479833,
+                    705515679,
+                    410435123,
+                    843033140,
+                    170051794,
+                    273755342,
+                    785107327,
+                    986623071,
+                    409440022,
+                    672508461,
+                    163795561,
+                    952291188,
+                    921489464,
+                    433976333,
+                    141024260,
+                    250090558,
+                    360783709,
+                    635117180,
+                    224630259,
+                    51749141,
+                    306099373,
+                    550492007,
+                    539658,
+                    548830761,
+                    649750394,
+                    698959024,
+                    128798507,
+                    338975358,
+                    198337643,
+                    564962404,
+                    921349034,
+                    111915978,
+                    605470402,
+                    548821214,
+                    763502055,
+                    100437908,
+                    648443245,
+                    279988286,
+                    797366555,
+                    118352776,
+                    341550868,
+                    350522146,
+                    260002513,
+                    532524681,
+                    879630721,
+                    134756606,
+                    95992269,
+                    521044523,
+                    629849604,
+                    778142941,
+                    103562119,
+                    343984178,
+                    971184291,
+                    557565529,
+                    885939761,
+                    854586261,
+                    510274853,
+                    119588010,
+                    877221485,
+                    442003464,
+                    229488740,
+                    928187246,
+                    180644206,
+                    804884648,
+                    565645972,
+                    61400266,
+                    827717148,
+                    666876372,
+                    238428372,
+                    245525704,
+                    512176611,
+                    55371928,
+                    850216680,
+                    134993447,
+                    731279647,
+                    952504914,
+                    386343584,
+                    642321161,
+                    912552335,
+                    198979472,
+                    696927504,
+                    344546036,
+                    815584197,
+                    824242993,
+                    605304207,
+                    262468490,
+                    170853207,
+                    534328899,
+                    180611957,
+                    356823463,
+                    110675384,
+                    226504755,
+                    487167933,
+                    930024086,
+                    947723632,
+                    537715326,
+                    622967208,
+                    221821961,
+                    354334231,
+                    749560057,
+                    236653873,
+                    419896045,
+                    474556127,
+                    46626339,
+                    468751187,
+                    196232736,
+                    190222565,
+                    681326202,
+                    181505133,
+                    794947352,
+                    388637161,
+                    832146121,
+                    734121531,
+                    728026343,
+                    306505253,
+                    58479812,
+                    905181324,
+                    353495138,
+                    965047436,
+                    306660025,
+                    841876224,
+                    173156289,
+                    407377179,
+                    413266573,
+                    901084595,
+                    340427194,
+                    985156193,
+                    845244895,
+                    735387491,
+                    860387073,
+                    782407171,
+                    481536573,
+                    128268754,
+                    380374364,
+                    796092348,
+                    276158809,
+                    463809244,
+                    173961791,
+                    88685654,
+                    924130303,
+                    355410029,
+                    388511720,
+                    950124397,
+                    623965010,
+                    850158869,
+                    386231115,
+                    965438693,
+                    233112238,
+                    22738928,
+                    429250525,
+                    751542238,
+                    374053372,
+                    665364267,
+                    455337960,
+                    443299231,
+                    458743648,
+                    405506690,
+                    73491476,
+                    41192367,
+                    854886578,
+                    468563136,
+                    867837722,
+                    197810005,
+                    174090964,
+                    173225329,
+                    613211446,
+                    375746310,
+                    461082399,
+                    157333026,
+                    740621181,
+                    899050863,
+                    424881652,
+                    759694560,
+                    299834627,
+                    108678744,
+                    137155060,
+                    276772851,
+                    921819425,
+                    766939241,
+                    348035541,
+                    92162361,
+                    900502035,
+                    204092916,
+                    984436685,
+                    30628560,
+                    998740634,
+                    441411455,
+                    713976708,
+                    907052827,
+                    235754439,
+                    899117584,
+                    962731623,
+                    228432498,
+                    508223101,
+                    490420103,
+                    21179553,
+                    589546779,
+                    70806209,
+                    998397002,
+                    895730225,
+                    991913741,
+                    750384953,
+                    342089371,
+                    127272614,
+                    676621588,
+                    975752842,
+                    760540248,
+                    887005085,
+                    874365460,
+                    885024738,
+                    697622991,
+                    812902610,
+                    413291910,
+                    447595669,
+                    254693471,
+                    647790492,
+                    64304947,
+                    208839157,
+                    128229780,
+                    44060632,
+                    301834873,
+                    1615643,
+                    784092514,
+                    51868207,
+                    41202613,
+                    327804678,
+                    640812081,
+                    662177198,
+                    455856828,
+                    110728561,
+                    329570421,
+                    978973250,
+                    616303387,
+                    50403040,
+                    190633832,
+                    613801501,
+                    304530913,
+                    596726928,
+                    627568663,
+                    915976180,
+                    394273683,
+                    462346197,
+                    165278556,
+                    964052565,
+                    331973999,
+                    943036376,
+                    84696692,
+                    913635999,
+                    578024298,
+                    715867034,
+                    267765868,
+                    901199695,
+                    32747092,
+                    223953016,
+                    605162562,
+                    369509932,
+                    844537635,
+                    523867050,
+                    267797063,
+                    288669369,
+                    60247781,
+                    603095075,
+                    571870829,
+                    909680589,
+                    638373634,
+                    495236115,
+                    534497382,
+                    409716925,
+                    706272717,
+                    533024104,
+                    669584786,
+                    105285399,
+                    117791894,
+                    459187607,
+                    11693041,
+                    38252974,
+                    880633438,
+                    899303154,
+                    934684290,
+                    592052883,
+                    348817429,
+                    33159048,
+                    150503177,
+                    107808544,
+                    264052263,
+                    482247028,
+                    5652786,
+                    641672085,
+                    830445159,
+                    981511313,
+                    935410113,
+                    255437309,
+                    110484607,
+                    776125221,
+                    735498609,
+                    466096874,
+                    96270698,
+                    382923037,
+                    615458524,
+                    329689445,
+                    127894675,
+                    256481290,
+                    431905558,
+                    166922785,
+                    498616091,
+                    466632649,
+                    388329174,
+                    457169996,
+                    167654927,
+                    984658988,
+                    415540801,
+                    575356224,
+                    228817734,
+                    387167584,
+                    584028806,
+                    201914155,
+                    820811804,
+                    749289400,
+                    982137818,
+                    286142321,
+                    179430173,
+                    716264348,
+                    220898021,
+                    226758130,
+                    792809294,
+                    25723913,
+                    911176212,
+                    349906466,
+                    992238311,
+                    529873870,
+                    466116878,
+                    362820759,
+                    758739623,
+                    484818888,
+                    318675550,
+                    818775337,
+                    61147680,
+                    237274595,
+                    524079325,
+                    427456997,
+                    968936864,
+                    485046940,
+                    921484755,
+                    869252263,
+                    319406871,
+                    788614588,
+                    339262138,
+                    74195813,
+                    768114109,
+                    168094376,
+                    457076622,
+                    465781949,
+                    653463908,
+                    658990383,
+                    846034864,
+                    244828829,
+                    621966565,
+                    626433649,
+                    438539428,
+                    632442933,
+                    317437193,
+                    745534895,
+                    230287726,
+                    192369740,
+                    301615970,
+                    213477218,
+                    339534998,
+                    223681578,
+                    603104911,
+                    305928266,
+                    778700737,
+                    721009749,
+                    154374803,
+                    446660909,
+                    813914529,
+                    905890735,
+                    157642085,
+                    309237883,
+                    233490118,
+                    893692716,
+                    77463874,
+                    499151123,
+                    114299572,
+                    479852632,
+                    981635514,
+                    381357807,
+                    756053378,
+                    765275788,
+                    668313463,
+                    720761129,
+                    211607402,
+                    653044999,
+                    239946923,
+                    340961417,
+                    514899200,
+                    616959730,
+                    784006182,
+                    812006982,
+                    78484125,
+                    518894951,
+                    839068867,
+                    7241840,
+                    55729898,
+                    722649451,
+                    596217191,
+                    263077807,
+                    363734710,
+                    369862507,
+                    745682005,
+                    846423249,
+                    546965665,
+                    543531089,
+                    116531464,
+                    217646024,
+                    884591217,
+                    895443721,
+                    863550347,
+                    561860260,
+                    872038168,
+                    70436622,
+                    729656656,
+                    291048053,
+                    610821150,
+                    409172682,
+                    340172917,
+                    715780418,
+                    410219082,
+                    613994514,
+                    177269283,
+                    655369518,
+                    657734649,
+                    451423153,
+                    921621344,
+                    16904189,
+                    758874049,
+                    488339496,
+                    261918105,
+                    343437094,
+                    909349480,
+                    529493134,
+                    452300312,
+                    649528238,
+                    120065003,
+                    100434964,
+                    563143737,
+                    696368106,
+                    64668172,
+                    208306669,
+                    866163228,
+                    429382406,
+                    683874379,
+                    771283030,
+                    415382544,
+                    392703198,
+                    800399035,
+                    791763039,
+                    787610301,
+                    63238882,
+                    982182128,
+                    827513731,
+                    809055645,
+                    229957745,
+                    351523785,
+                    395182110,
+                    711546439,
+                    610353811,
+                    626097507,
+                    9755699,
+                    411056760,
+                    670697533,
+                    276063731,
+                    909166235,
+                    793555572,
+                    868325756,
+                    792522757,
+                    518146443,
+                    554300151,
+                    791057537,
+                    520010815,
+                    498332402,
+                    116841921,
+                    674174012,
+                    21763763,
+                    151058136,
+                    2240414,
+                    879134817,
+                    546811284,
+                    803431675,
+                    165933106,
+                    35685964,
+                    141064305,
+                    508852657,
+                    535684075,
+                    180304537,
+                    996822875,
+                    526366604,
+                    742236985,
+                    938468499,
+                    930727949,
+                    443978256,
+                    601371279,
+                    386641992,
+                    506822011,
+                    673355194,
+                    806303667,
+                    803631224,
+                    283505100,
+                    28639552,
+                    72216337,
+                    976208919,
+                    467039905,
+                    293786155,
+                    987842663,
+                    481567698,
+                    551369901,
+                    196668942,
+                    276485669,
+                    656035734,
+                    42116023,
+                    287295656,
+                    852526102,
+                    429737370,
+                    512366477,
+                    868286732,
+                    956224190,
+                    545575243,
+                    735123922,
+                    870737286,
+                    653048063,
+                    750751084,
+                    596695304,
+                    629293164,
+                    992260687,
+                    358257632,
+                    905969642,
+                    54996135,
+                    164912100,
+                    932975587,
+                    401843988,
+                    227016848,
+                    164174481,
+                    378304911,
+                    210656522,
+                    84275815,
+                    581981265,
+                    79688073,
+                    919319655,
+                    816673519,
+                    600277476,
+                    283387096,
+                    895135895,
+                    92755863,
+                    501706390,
+                    964743585,
+                    215101971,
+                    961938152,
+                    360191582,
+                    959025731,
+                    59338236,
+                    221841268,
+                    228596720,
+                    789656871,
+                    932681530,
+                    592411573,
+                    612224425,
+                    850131032,
+                    622945693,
+                    434524571,
+                    583449625,
+                    223772279,
+                    294129030,
+                    164577487,
+                    160727965,
+                    590129826,
+                    920230323,
+                    529350078,
+                    867297708,
+                    842785126,
+                    189834660,
+                    60174403,
+                    313895150,
+                    452992747,
+                    637267376,
+                    487375370,
+                    411144173,
+                    836580086,
+                    821174300,
+                    100648558,
+                    491961185,
+                    675454679,
+                    398777849,
+                    673545055,
+                    870938169,
+                    253865677,
+                    3454857,
+                    668436233,
+                    701526802,
+                    105226146,
+                    191255202,
+                    151276620,
+                    605394210,
+                    234624160,
+                    916555155,
+                    370217802,
+                    14714949,
+                    976830290,
+                    293189877,
+                    917471271,
+                    455483393,
+                    311324871,
+                    516731272,
+                    229304991,
+                    946653838,
+                    874167233,
+                    187520271,
+                    719886082,
+                    967629169,
+                    280761380,
+                    558675781,
+                    293292041,
+                    764171350,
+                    539622057,
+                    211791762,
+                    559856439,
+                    87042666,
+                    89527735,
+                    404704749,
+                    54507291,
+                    286017721,
+                    815586836,
+                    944830847,
+                    77345013,
+                    920552195,
+                    596582213,
+                    787795056,
+                    697869491,
+                    202200350,
+                    997029470,
+                    506947327,
+                    855705463,
+                    694045410,
+                    909553435,
+                    692938951,
+                    296680737,
+                    434867930,
+                    277123488,
+                    264596290,
+                    505687070,
+                    906805717,
+                    844489041,
+                    842577381,
+                    297527284,
+                    444899024,
+                    800108159,
+                    176223986,
+                    536958572,
+                    864198092,
+                    127944414,
+                    519954618,
+                    367499714,
+                    468570108,
+                    945362204,
+                    701082296,
+                    891512313,
+                    828701120,
+                    506014765,
+                    568738193,
+                    503538574,
+                    268442678,
+                    47261572,
+                    16676551,
+                    934182538,
+                    37198463,
+                    124450963,
+                    889330700,
+                    691196933,
+                    728899210,
+                    622967763,
+                    647742925,
+                    568179970,
+                    57915037,
+                    740103149,
+                    943797852,
+                    853536746,
+                    841158463,
+                    944815346,
+                    432391570,
+                    868262898,
+                    321650196,
+                    905570764,
+                    950808631,
+                    401230252,
+                    765962309,
+                    854875548,
+                    160477878,
+                    939860368,
+                    924304890,
+                    907876502,
+                    524312091,
+                    599719667,
+                    315354466,
+                    193821620,
+                    532224915,
+                    538040417,
+                    366458596,
+                    89893532,
+                    55311120,
+                    956172798,
+                    304999149,
+                    329313466,
+                    164982632,
+                    435281198,
+                    591324891,
+                    432480467,
+                    84386347,
+                    193492113,
+                    570756555,
+                    861531435,
+                    964240628,
+                    866757197,
+                    65861220,
+                    578668693,
+                    95487174,
+                    278664883,
+                    853879485,
+                    99996705,
+                    679559820,
+                    517162926,
+                    398388834,
+                    601756769,
+                    291865150,
+                    564866604,
+                    63956213,
+                    937066391,
+                    470572864,
+                    745154179,
+                    298080192,
+                    972367767,
+                    54297435,
+                    613445918,
+                    254546709,
+                    771470363,
+                    275342448,
+                    612532613,
+                    398176319,
+                    100630006,
+                    627276583,
+                    164542660,
+                    401570636,
+                    212780404,
+                    404766829,
+                    233924423,
+                    836769375,
+                    632960790,
+                    295719426,
+                    809329367,
+                    419289515,
+                    951543777,
+                    268905651,
+                    296838864,
+                    252635613,
+                    714230941,
+                    326219759,
+                    136632819,
+                    953857763,
+                    966425815,
+                    933621081,
+                    692558702,
+                    720392191,
+                    656549411,
+                    489348902,
+                    834994864,
+                    952084325,
+                    516828550,
+                    406879054,
+                    172069823,
+                    475651935,
+                    442825775,
+                    844449728,
+                    624848239,
+                    627635580,
+                    413008057,
+                    453525689,
+                    395801301,
+                    143396822,
+                    130648206,
+                    276179592,
+                    431757461,
+                    335074761,
+                    907320568,
+                    936739471,
+                    548091681,
+                    361374081,
+                    30208363,
+                    854341456,
+                    136390299,
+                    567212965,
+                    20674170,
+                    339559739,
+                    139737649,
+                    2392871,
+                    20267146,
+                    234539819,
+                    940494460,
+                    903334833,
+                    807485646,
+                    850038266,
+                    277326021,
+                    877561584,
+                    878170723,
+                    901892626,
+                    871395202,
+                    249339885,
+                    311325309,
+                    560714092,
+                    398527963,
+                    386534405,
+                    104205756,
+                    101389436,
+                    829221836,
+                    158078520,
+                    874503200,
+                    204931431,
+                    420769493,
+                    808675981,
+                    604604242,
+                    166470903,
+                    383036555,
+                    830412361,
+                    586462047,
+                    36827740,
+                    90945711,
+                    221718481,
+                    756151545,
+                    853794739,
+                    255020826,
+                    856156837,
+                    224720794,
+                    355071865,
+                    381789420,
+                    580554491,
+                    207249820,
+                    875295204,
+                    337747578,
+                    239208298,
+                    529599357,
+                    926243684,
+                    335794166,
+                    267386614,
+                    808340597,
+                    190577966,
+                    393796920,
+                    73726057,
+                    675464122,
+                    943718850,
+                    859455479,
+                    684557370,
+                    778216187,
+                    217347170,
+                    320032254,
+                    211507154,
+                    308851958,
+                    57835376,
+                    101359152,
+                    2870130,
+                    67927016,
+                    735765701,
+                    279968913,
+                    150744358,
+                    807960510,
+                    433944894,
+                    964053708,
+                    560844089,
+                    837314932,
+                    466686725,
+                    100940710,
+                    454443777,
+                    23647546,
+                    942640496,
+                    338039865,
+                    335660623,
+                    452469690,
+                    402196067,
+                    872924531,
+                    700911803,
+                    270554077,
+                    803168356,
+                    167382100,
+                    10424937,
+                    974610782,
+                    903578933,
+                    266745925,
+                    631390067,
+                    350038076,
+                    934201535,
+                    619565570,
+                    188353082,
+                    411576973,
+                    564607588,
+                    828557185,
+                    68634435,
+                    620449076,
+                    450505517,
+                    11306852,
+                    103283368,
+                    524830390,
+                    359580474,
+                    465617065,
+                    99294464,
+                    7748635,
+                    584057059,
+                    748179447,
+                    193269157,
+                    764017213,
+                    951618899,
+                    147263737,
+                    825236875,
+                    778533222,
+                    818079001,
+                    567670297,
+                    631970548,
+                    247559169,
+                    899995410,
+                    571805801,
+                    185982137,
+                    996415169,
+                    582707864,
+                    977428299,
+                    774144220,
+                    941887459,
+                    834324025,
+                    378177867,
+                    408310851,
+                    168011365,
+                    175663103,
+                    996228866,
+                    786388281,
+                    802523643,
+                    578489010,
+                    64251110,
+                    957189724,
+                    424808235,
+                    542071669,
+                    197227676,
+                    712300626,
+                    648018130,
+                    328273523,
+                    655326389,
+                    129903733,
+                    626625260,
+                    565877345,
+                    885315620,
+                    925111314,
+                    851649770,
+                    700722142,
+                    412574752,
+                    634932545,
+                    952753999,
+                    380708759,
+                    756614381,
+                    945777752,
+                    569462794,
+                    516811304,
+                    324630142,
+                    222952599,
+                    896339697,
+                    52116799,
+                    412544070,
+                    320128778,
+                    617634124,
+                    65907283,
+                    449558978,
+                    655072005,
+                    314402763,
+                    255559835,
+                    286073516,
+                    659235156,
+                    831873967,
+                    645881866,
+                    303096299,
+                    37347688,
+                    44760205,
+                    375354439,
+                    149421285,
+                    587831023,
+                    49474345,
+                    491255507,
+                    514371939,
+                    377114936,
+                    982023157,
+                    686821848,
+                    938071770,
+                    37372785,
+                    567007466,
+                    179042398,
+                    713378842,
+                    592995105,
+                    101734512,
+                    782140601,
+                    690055415,
+                    612273207,
+                    453437634,
+                    450724764,
+                    355012486,
+                    166033432,
+                    274782246,
+                    148476853,
+                    156290309,
+                    195266515,
+                    981350397,
+                    174090700,
+                    537142059,
+                    335801993,
+                    92013527,
+                    906940945,
+                    836095559,
+                    466288675,
+                    200713926,
+                    559581813,
+                    389589952,
+                    358515160,
+                    22717076,
+                    304588102,
+                    135146927,
+                    483260825,
+                    831480107,
+                    78693032,
+                    204255023,
+                    373638799,
+                    699190666,
+                    597073823,
+                    529172402,
+                    307824846,
+                    527833414,
+                    543122185,
+                    807145568,
+                    290700543,
+                    944268697,
+                    309436449,
+                    339841833,
+                    579865818,
+                    816679892,
+                    122326402,
+                    726790437,
+                    212091605,
+                    713601295,
+                    479166238,
+                    327877967,
+                    95508140,
+                    420311434,
+                    204678586,
+                    671708459,
+                    153892707,
+                    933266461,
+                    943174536,
+                    94288487,
+                    979178549,
+                    144939513,
+                    851570320,
+                    484301496,
+                    577716312,
+                    85692320,
+                    488071322,
+                    866884520,
+                    992147295,
+                    468481381,
+                    61122827,
+                    626508866,
+                    543694015,
+                    421383630,
+                    733069391,
+                    364810803,
+                    41379110,
+                    127197845,
+                    526853737,
+                    472332889,
+                    200479822,
+                    140276166,
+                    69763021,
+                    16124765,
+                    990668465,
+                    151768591,
+                    711362948,
+                    200241252,
+                    323575928,
+                    191912265,
+                    575016088,
+                    909099548,
+                    648027780,
+                    266443122,
+                    564175385,
+                    777187587,
+                    265135538,
+                    536107738,
+                    312785913,
+                    834967816,
+                    899521191,
+                    81549943,
+                    410341080,
+                    234742690,
+                    318901994,
+                    636176133,
+                    193551581,
+                    863234283,
+                    350370654,
+                    612130351,
+                    183308944,
+                    948366069,
+                    995874332,
+                    897933976,
+                    245687678,
+                    896225795,
+                    256174872,
+                    463311485,
+                    941065736,
+                    847940064,
+                    692672896,
+                    452402184,
+                    955646595,
+                    961432994,
+                    39105940,
+                    769957645,
+                    680765560,
+                    174727101,
+                    94988710,
+                    845321288,
+                    592722615,
+                    688266826,
+                    360319986,
+                    336881395,
+                    434969517,
+                    114034596,
+                    378522328,
+                    249987453,
+                    478473147,
+                    872466419,
+                    982658829,
+                    216212247,
+                    213784170,
+                    900009908,
+                    238693194,
+                    919204088,
+                    922182419,
+                    361778608,
+                    271814978,
+                    710429861,
+                    694471293,
+                    863318004,
+                    400971314,
+                    858138281,
+                    140454338,
+                    371948439,
+                    813145130,
+                    538502243,
+                    113146868,
+                    324389497,
+                    925278608,
+                    789025652,
+                    55699464,
+                    98950770,
+                    306490776,
+                    713028765,
+                    646367301,
+                    994020114,
+                    143443616,
+                    947703884,
+                    704302613,
+                    546527928,
+                    142267164,
+                    844585497,
+                    40793192,
+                    273399691,
+                    231964239,
+                    125177926,
+                    746606247,
+                    719929782,
+                    101316410,
+                    548202981,
+                    427141489,
+                    599879243,
+                    938649575,
+                    417412761,
+                    644179802,
+                    5802143,
+                    797204306,
+                    193281694,
+                    961815467,
+                    46212321,
+                    333846674,
+                    575104705,
+                    333958170,
+                    269265755,
+                    28968659,
+                    256487297,
+                    105868680,
+                    474624180,
+                    21861483,
+                    498816820,
+                    693186240,
+                    503901902,
+                    996530110,
+                    957200173,
+                    469608681,
+                    810936196,
+                    699414245,
+                    544268959,
+                    597975590,
+                    679747796,
+                    567312233,
+                    282214447,
+                    72935859,
+                    499152430,
+                    400285065,
+                    332164426,
+                    794678466,
+                    422563089,
+                    16603549,
+                    699749952,
+                    455054647,
+                    975064014,
+                    425040235,
+                    722191738,
+                    918731924,
+                    172669464,
+                    836239935,
+                    829682014,
+                    377906293,
+                    491200816,
+                    462304721,
+                    145395435,
+                    251317948,
+                    120309005,
+                    880704515,
+                    3752223,
+                    544117921,
+                    858075532,
+                    248886028,
+                    378999203,
+                    116920042,
+                    136415693,
+                    292237747,
+                    265359445,
+                    476535290,
+                    616068407,
+                    402600470,
+                    598302302,
+                    374987093,
+                    228604372,
+                    7122855,
+                    104046299
+                ],
+                [
+                    425,
+                    240,
+                    190,
+                    902,
+                    684,
+                    51,
+                    1294,
+                    673,
+                    1183,
+                    639,
+                    1321,
+                    1287,
+                    1239,
+                    521,
+                    1199,
+                    808,
+                    308,
+                    227,
+                    1351,
+                    103,
+                    201,
+                    682,
+                    456,
+                    313,
+                    358,
+                    45,
+                    743,
+                    1293,
+                    556,
+                    358,
+                    581,
+                    930,
+                    1101,
+                    50,
+                    835,
+                    228,
+                    1268,
+                    1366,
+                    925,
+                    1258,
+                    256,
+                    807,
+                    1380,
+                    1173,
+                    103,
+                    58,
+                    911,
+                    509,
+                    593,
+                    127,
+                    768,
+                    1008,
+                    658,
+                    1172,
+                    59,
+                    147,
+                    1269,
+                    726,
+                    756,
+                    643,
+                    1042,
+                    463,
+                    1,
+                    948,
+                    871,
+                    163,
+                    756,
+                    705,
+                    946,
+                    562,
+                    396,
+                    694,
+                    892,
+                    549,
+                    669,
+                    1244,
+                    127,
+                    106,
+                    1262,
+                    1204,
+                    115,
+                    1211,
+                    696,
+                    822,
+                    95,
+                    421,
+                    1005,
+                    1005,
+                    1129,
+                    145,
+                    282,
+                    495,
+                    1004,
+                    976,
+                    28,
+                    177,
+                    553,
+                    932,
+                    1395,
+                    859,
+                    590,
+                    1041,
+                    526,
+                    1409,
+                    486,
+                    569,
+                    97,
+                    1216,
+                    250,
+                    123,
+                    6,
+                    4,
+                    986,
+                    1022,
+                    650,
+                    108,
+                    1055,
+                    333,
+                    591,
+                    1047,
+                    18,
+                    1169,
+                    703,
+                    1190,
+                    408,
+                    544,
+                    1213,
+                    839,
+                    879,
+                    47,
+                    988,
+                    849,
+                    589,
+                    42,
+                    970,
+                    1145,
+                    1331,
+                    961,
+                    406,
+                    1062,
+                    556,
+                    577,
+                    95,
+                    1378,
+                    1033,
+                    304,
+                    264,
+                    1198,
+                    505,
+                    784,
+                    578,
+                    335,
+                    456,
+                    123,
+                    710,
+                    562,
+                    307,
+                    1415,
+                    1392,
+                    1240,
+                    906,
+                    628,
+                    233,
+                    555,
+                    911,
+                    256,
+                    796,
+                    442,
+                    135,
+                    781,
+                    1018,
+                    1166,
+                    113,
+                    226,
+                    900,
+                    60,
+                    577,
+                    158,
+                    342,
+                    233,
+                    1338,
+                    352,
+                    1224,
+                    318,
+                    866,
+                    911,
+                    462,
+                    945,
+                    1169,
+                    937,
+                    99,
+                    1165,
+                    234,
+                    695,
+                    497,
+                    553,
+                    778,
+                    591,
+                    315,
+                    568,
+                    964,
+                    1199,
+                    546,
+                    695,
+                    805,
+                    48,
+                    1142,
+                    1297,
+                    1099,
+                    675,
+                    1399,
+                    891,
+                    1199,
+                    1257,
+                    21,
+                    1392,
+                    1099,
+                    1305,
+                    654,
+                    713,
+                    720,
+                    50,
+                    1270,
+                    1358,
+                    413,
+                    1107,
+                    432,
+                    473,
+                    191,
+                    1137,
+                    627,
+                    647,
+                    1022,
+                    340,
+                    711,
+                    18,
+                    670,
+                    1390,
+                    676,
+                    1124,
+                    86,
+                    609,
+                    1081,
+                    178,
+                    560,
+                    1041,
+                    563,
+                    82,
+                    1141,
+                    489,
+                    81,
+                    1123,
+                    218,
+                    845,
+                    11,
+                    658,
+                    722,
+                    575,
+                    1070,
+                    208,
+                    481,
+                    938,
+                    587,
+                    673,
+                    801,
+                    854,
+                    371,
+                    697,
+                    943,
+                    85,
+                    1131,
+                    489,
+                    154,
+                    335,
+                    1321,
+                    125,
+                    1292,
+                    1106,
+                    367,
+                    519,
+                    1,
+                    817,
+                    596,
+                    202,
+                    244,
+                    466,
+                    1241,
+                    458,
+                    497,
+                    943,
+                    263,
+                    1288,
+                    1003,
+                    412,
+                    153,
+                    1046,
+                    1283,
+                    346,
+                    1118,
+                    636,
+                    1328,
+                    42,
+                    1127,
+                    726,
+                    466,
+                    392,
+                    1211,
+                    424,
+                    206,
+                    1214,
+                    1359,
+                    1161,
+                    1067,
+                    961,
+                    995,
+                    427,
+                    1314,
+                    1336,
+                    27,
+                    902,
+                    716,
+                    309,
+                    1081,
+                    841,
+                    216,
+                    1164,
+                    178,
+                    46,
+                    1269,
+                    47,
+                    1120,
+                    1219,
+                    439,
+                    1167,
+                    197,
+                    1394,
+                    809,
+                    650,
+                    724,
+                    89,
+                    1117,
+                    217,
+                    1105,
+                    130,
+                    798,
+                    644,
+                    1186,
+                    659,
+                    836,
+                    866,
+                    812,
+                    328,
+                    113,
+                    36,
+                    1044,
+                    1055,
+                    752,
+                    658,
+                    1100,
+                    462,
+                    148,
+                    552,
+                    370,
+                    1258,
+                    413,
+                    369,
+                    929,
+                    257,
+                    679,
+                    639,
+                    1262,
+                    109,
+                    439,
+                    502,
+                    112,
+                    1093,
+                    843,
+                    1022,
+                    106,
+                    870,
+                    660,
+                    87,
+                    1289,
+                    342,
+                    1398,
+                    394,
+                    1024,
+                    283,
+                    634,
+                    1357,
+                    748,
+                    402,
+                    946,
+                    298,
+                    399,
+                    296,
+                    982,
+                    292,
+                    1110,
+                    909,
+                    1407,
+                    43,
+                    926,
+                    1052,
+                    767,
+                    26,
+                    1044,
+                    885,
+                    1050,
+                    576,
+                    603,
+                    54,
+                    269,
+                    1363,
+                    1313,
+                    699,
+                    636,
+                    694,
+                    571,
+                    1045,
+                    222,
+                    474,
+                    993,
+                    392,
+                    1079,
+                    593,
+                    540,
+                    919,
+                    1171,
+                    119,
+                    1,
+                    776,
+                    807,
+                    1385,
+                    475,
+                    17,
+                    646,
+                    875,
+                    1373,
+                    648,
+                    212,
+                    230,
+                    824,
+                    392,
+                    679,
+                    397,
+                    1252,
+                    965,
+                    48,
+                    385,
+                    933,
+                    477,
+                    873,
+                    1245,
+                    958,
+                    840,
+                    1003,
+                    546,
+                    1172,
+                    1415,
+                    418,
+                    875,
+                    1380,
+                    935,
+                    400,
+                    382,
+                    374,
+                    737,
+                    913,
+                    813,
+                    113,
+                    329,
+                    340,
+                    1343,
+                    697,
+                    200,
+                    839,
+                    1268,
+                    1201,
+                    724,
+                    89,
+                    586,
+                    1398,
+                    1340,
+                    825,
+                    355,
+                    1050,
+                    857,
+                    340,
+                    281,
+                    1141,
+                    766,
+                    973,
+                    641,
+                    266,
+                    799,
+                    138,
+                    1176,
+                    427,
+                    148,
+                    117,
+                    61,
+                    452,
+                    1007,
+                    445,
+                    1024,
+                    1213,
+                    1115,
+                    243,
+                    511,
+                    80,
+                    502,
+                    1196,
+                    108,
+                    151,
+                    270,
+                    682,
+                    184,
+                    58,
+                    1355,
+                    45,
+                    616,
+                    234,
+                    270,
+                    776,
+                    184,
+                    460,
+                    622,
+                    1298,
+                    1103,
+                    219,
+                    422,
+                    362,
+                    1213,
+                    1237,
+                    599,
+                    1184,
+                    966,
+                    359,
+                    559,
+                    192,
+                    1303,
+                    161,
+                    294,
+                    318,
+                    656,
+                    372,
+                    1268,
+                    924,
+                    323,
+                    241,
+                    933,
+                    1033,
+                    674,
+                    897,
+                    453,
+                    1162,
+                    924,
+                    158,
+                    765,
+                    443,
+                    410,
+                    1006,
+                    208,
+                    1382,
+                    999,
+                    1237,
+                    76,
+                    1153,
+                    312,
+                    537,
+                    486,
+                    989,
+                    553,
+                    22,
+                    1107,
+                    1370,
+                    547,
+                    968,
+                    1344,
+                    737,
+                    364,
+                    1012,
+                    1214,
+                    1127,
+                    627,
+                    286,
+                    108,
+                    696,
+                    375,
+                    621,
+                    176,
+                    1188,
+                    1276,
+                    46,
+                    665,
+                    910,
+                    1266,
+                    790,
+                    1069,
+                    569,
+                    487,
+                    528,
+                    1292,
+                    198,
+                    629,
+                    483,
+                    1414,
+                    1326,
+                    390,
+                    664,
+                    334,
+                    8,
+                    534,
+                    883,
+                    856,
+                    320,
+                    326,
+                    1296,
+                    277,
+                    611,
+                    257,
+                    664,
+                    388,
+                    6,
+                    629,
+                    383,
+                    332,
+                    1342,
+                    239,
+                    495,
+                    1415,
+                    669,
+                    774,
+                    916,
+                    356,
+                    1049,
+                    571,
+                    559,
+                    950,
+                    1383,
+                    1392,
+                    587,
+                    1269,
+                    490,
+                    446,
+                    344,
+                    257,
+                    500,
+                    285,
+                    1161,
+                    1337,
+                    1154,
+                    273,
+                    747,
+                    31,
+                    859,
+                    317,
+                    530,
+                    162,
+                    354,
+                    999,
+                    1181,
+                    330,
+                    161,
+                    961,
+                    772,
+                    443,
+                    1079,
+                    425,
+                    842,
+                    583,
+                    324,
+                    892,
+                    1328,
+                    109,
+                    867,
+                    1301,
+                    754,
+                    76,
+                    448,
+                    851,
+                    840,
+                    336,
+                    412,
+                    623,
+                    1246,
+                    195,
+                    358,
+                    572,
+                    955,
+                    53,
+                    530,
+                    1093,
+                    1281,
+                    1203,
+                    1133,
+                    690,
+                    278,
+                    144,
+                    747,
+                    616,
+                    704,
+                    1341,
+                    44,
+                    465,
+                    580,
+                    1023,
+                    688,
+                    1262,
+                    1127,
+                    1406,
+                    1131,
+                    5,
+                    723,
+                    323,
+                    301,
+                    364,
+                    874,
+                    36,
+                    556,
+                    646,
+                    1389,
+                    1170,
+                    1099,
+                    1278,
+                    1291,
+                    272,
+                    877,
+                    1155,
+                    1245,
+                    697,
+                    133,
+                    323,
+                    658,
+                    593,
+                    965,
+                    99,
+                    449,
+                    137,
+                    1178,
+                    661,
+                    1087,
+                    1292,
+                    693,
+                    1247,
+                    907,
+                    1127,
+                    1036,
+                    260,
+                    751,
+                    205,
+                    1072,
+                    1259,
+                    274,
+                    621,
+                    1090,
+                    877,
+                    946,
+                    981,
+                    509,
+                    961,
+                    1265,
+                    1409,
+                    1243,
+                    747,
+                    741,
+                    473,
+                    287,
+                    2,
+                    1298,
+                    468,
+                    850,
+                    730,
+                    824,
+                    580,
+                    1338,
+                    1047,
+                    1127,
+                    644,
+                    511,
+                    596,
+                    447,
+                    629,
+                    1183,
+                    691,
+                    1399,
+                    1163,
+                    243,
+                    758,
+                    17,
+                    705,
+                    1323,
+                    31,
+                    548,
+                    991,
+                    1133,
+                    50,
+                    935,
+                    688,
+                    1356,
+                    629,
+                    360,
+                    93,
+                    1218,
+                    1361,
+                    122,
+                    72,
+                    1288,
+                    117,
+                    1143,
+                    317,
+                    603,
+                    5,
+                    436,
+                    307,
+                    1090,
+                    501,
+                    856,
+                    271,
+                    356,
+                    866,
+                    49,
+                    1148,
+                    454,
+                    985,
+                    514,
+                    1145,
+                    1180,
+                    357,
+                    819,
+                    338,
+                    318,
+                    604,
+                    1185,
+                    1105,
+                    85,
+                    1362,
+                    935,
+                    989,
+                    1093,
+                    1245,
+                    656,
+                    1370,
+                    1365,
+                    935,
+                    1123,
+                    727,
+                    200,
+                    493,
+                    632,
+                    39,
+                    1321,
+                    18,
+                    757,
+                    686,
+                    702,
+                    927,
+                    77,
+                    175,
+                    196,
+                    630,
+                    634,
+                    1308,
+                    1298,
+                    583,
+                    238,
+                    583,
+                    1049,
+                    510,
+                    922,
+                    336,
+                    1177,
+                    1163,
+                    1020,
+                    117,
+                    880,
+                    12,
+                    471,
+                    398,
+                    933,
+                    490,
+                    110,
+                    160,
+                    653,
+                    623,
+                    1121,
+                    552,
+                    953,
+                    1301,
+                    70,
+                    1203,
+                    469,
+                    244,
+                    735,
+                    887,
+                    1269,
+                    1187,
+                    1128,
+                    777,
+                    512,
+                    1390,
+                    870,
+                    269,
+                    1030,
+                    631,
+                    1120,
+                    323,
+                    936,
+                    193,
+                    1023,
+                    1126,
+                    1054,
+                    838,
+                    533,
+                    686,
+                    1171,
+                    1409,
+                    1030,
+                    248,
+                    268,
+                    195,
+                    1068,
+                    377,
+                    881,
+                    910,
+                    1194,
+                    1099,
+                    1270,
+                    1403,
+                    221,
+                    180,
+                    1125,
+                    1410,
+                    728,
+                    332,
+                    149,
+                    411,
+                    673,
+                    113,
+                    820,
+                    791,
+                    200,
+                    701,
+                    1238,
+                    507,
+                    436,
+                    152,
+                    1241,
+                    703,
+                    326,
+                    7,
+                    626,
+                    1106,
+                    927,
+                    43,
+                    1312,
+                    1020,
+                    1213,
+                    1397,
+                    875,
+                    1130,
+                    943,
+                    924,
+                    671,
+                    955,
+                    242,
+                    1041,
+                    388,
+                    137,
+                    1382,
+                    1211,
+                    156,
+                    101,
+                    826,
+                    1091,
+                    1146,
+                    883,
+                    1167,
+                    53,
+                    45,
+                    279,
+                    1153,
+                    305,
+                    624,
+                    209,
+                    1173,
+                    241,
+                    730,
+                    801,
+                    917,
+                    772,
+                    624,
+                    429,
+                    666,
+                    611,
+                    1061,
+                    578,
+                    228,
+                    879,
+                    433,
+                    930,
+                    1265,
+                    964,
+                    99,
+                    433,
+                    741,
+                    570,
+                    115,
+                    1086,
+                    1332,
+                    1145,
+                    188,
+                    1111,
+                    843,
+                    139,
+                    757,
+                    1094,
+                    1400,
+                    639,
+                    729,
+                    1393,
+                    558,
+                    199,
+                    292,
+                    969,
+                    943,
+                    1121,
+                    923,
+                    1415,
+                    377,
+                    1178,
+                    1223,
+                    127,
+                    1155,
+                    731,
+                    207,
+                    299,
+                    622,
+                    307,
+                    1340,
+                    1228,
+                    616,
+                    1317,
+                    413,
+                    338,
+                    1065,
+                    76,
+                    21,
+                    587,
+                    673,
+                    360,
+                    742,
+                    217,
+                    764,
+                    1023,
+                    635,
+                    893,
+                    362,
+                    999,
+                    230,
+                    500,
+                    858,
+                    236,
+                    433,
+                    857,
+                    797,
+                    1134,
+                    949,
+                    299,
+                    880,
+                    1147,
+                    312,
+                    966,
+                    1286,
+                    532,
+                    1263,
+                    1314,
+                    75,
+                    326,
+                    72,
+                    173,
+                    1269,
+                    1064,
+                    1071,
+                    1106,
+                    1254,
+                    1373,
+                    646,
+                    361,
+                    29,
+                    1229,
+                    1187,
+                    1053,
+                    1215,
+                    171,
+                    856,
+                    1171,
+                    376,
+                    885,
+                    867,
+                    642,
+                    894,
+                    575,
+                    995,
+                    993,
+                    587,
+                    1167,
+                    878,
+                    1041,
+                    812,
+                    1144,
+                    416,
+                    1292,
+                    509,
+                    377,
+                    715,
+                    490,
+                    952,
+                    195,
+                    346,
+                    1221,
+                    1115,
+                    112,
+                    1367,
+                    901,
+                    684,
+                    42,
+                    665,
+                    883,
+                    394,
+                    845,
+                    1350,
+                    369,
+                    484,
+                    244,
+                    160,
+                    326,
+                    231,
+                    1208,
+                    305,
+                    1123,
+                    973,
+                    419,
+                    12,
+                    150,
+                    374,
+                    103,
+                    116,
+                    1108,
+                    209,
+                    1235,
+                    1138,
+                    119,
+                    127,
+                    498,
+                    864,
+                    1006,
+                    127,
+                    1400,
+                    644,
+                    1181,
+                    1074,
+                    673,
+                    422,
+                    150,
+                    414,
+                    718,
+                    471,
+                    1191,
+                    1111,
+                    379,
+                    952,
+                    599,
+                    961,
+                    435,
+                    247,
+                    422,
+                    1207,
+                    817,
+                    1113,
+                    690,
+                    949,
+                    1092,
+                    1105,
+                    268,
+                    521,
+                    903,
+                    620,
+                    669,
+                    735,
+                    226,
+                    817,
+                    493,
+                    157,
+                    992,
+                    539,
+                    1008,
+                    732,
+                    1235,
+                    394,
+                    636,
+                    313,
+                    606,
+                    28,
+                    835,
+                    1224,
+                    410,
+                    48,
+                    1384,
+                    644,
+                    1289,
+                    81,
+                    201,
+                    1368,
+                    665,
+                    1195,
+                    83,
+                    783,
+                    116,
+                    224,
+                    429,
+                    695,
+                    1284,
+                    571,
+                    1231,
+                    824,
+                    217,
+                    15,
+                    1410,
+                    1037,
+                    867,
+                    1071,
+                    261,
+                    154,
+                    928,
+                    1147,
+                    1200,
+                    810,
+                    224,
+                    494,
+                    573,
+                    352,
+                    481,
+                    880,
+                    194,
+                    332,
+                    255,
+                    973,
+                    932,
+                    617,
+                    1126,
+                    535,
+                    228,
+                    945,
+                    1189,
+                    698,
+                    1251,
+                    1053,
+                    295,
+                    291,
+                    1131,
+                    124,
+                    950,
+                    919,
+                    482,
+                    627,
+                    768,
+                    753,
+                    1295,
+                    516,
+                    1134,
+                    919,
+                    45,
+                    949,
+                    692,
+                    1219,
+                    1328,
+                    421,
+                    1218,
+                    117,
+                    297,
+                    679,
+                    301,
+                    799,
+                    685,
+                    1199,
+                    1320,
+                    1002,
+                    818,
+                    64,
+                    1290,
+                    722,
+                    1344,
+                    317,
+                    225,
+                    851,
+                    233,
+                    1130,
+                    1192,
+                    1365,
+                    745,
+                    352,
+                    503,
+                    512,
+                    1341,
+                    933,
+                    881,
+                    86,
+                    136,
+                    692,
+                    190,
+                    199,
+                    714,
+                    137,
+                    1084,
+                    738,
+                    565,
+                    1303,
+                    275,
+                    283,
+                    252,
+                    112,
+                    989,
+                    359,
+                    832,
+                    988,
+                    315,
+                    186,
+                    825,
+                    1346,
+                    445,
+                    231,
+                    267,
+                    201,
+                    1235,
+                    664,
+                    759,
+                    188,
+                    1345,
+                    104,
+                    385,
+                    362,
+                    982,
+                    1389,
+                    882,
+                    1087,
+                    744,
+                    210,
+                    768,
+                    609,
+                    187,
+                    473,
+                    878,
+                    1246,
+                    1340,
+                    1103,
+                    301,
+                    406,
+                    915,
+                    311,
+                    1063,
+                    953,
+                    612,
+                    1112,
+                    209,
+                    1209,
+                    1269,
+                    1380,
+                    315,
+                    410,
+                    181,
+                    1399,
+                    1037,
+                    76,
+                    950,
+                    359,
+                    1170,
+                    1180,
+                    866,
+                    188,
+                    648,
+                    773,
+                    651,
+                    1249,
+                    637,
+                    57,
+                    998,
+                    1241,
+                    1240,
+                    384,
+                    91,
+                    147,
+                    595,
+                    863,
+                    617,
+                    1131,
+                    1230,
+                    130,
+                    1200,
+                    321,
+                    487,
+                    199,
+                    286,
+                    466,
+                    78,
+                    476,
+                    1356,
+                    798,
+                    265,
+                    1081,
+                    1217,
+                    1289,
+                    1240,
+                    661,
+                    762,
+                    1265,
+                    593,
+                    613,
+                    993,
+                    1039,
+                    711,
+                    1087,
+                    875,
+                    20,
+                    121,
+                    1008,
+                    453,
+                    397,
+                    1054,
+                    153,
+                    1324,
+                    1281,
+                    755,
+                    518,
+                    1395,
+                    261,
+                    100,
+                    1349,
+                    564,
+                    290,
+                    1370,
+                    1212,
+                    265,
+                    328,
+                    463,
+                    1272,
+                    1412,
+                    546,
+                    413,
+                    502,
+                    964,
+                    1027,
+                    848,
+                    909,
+                    40,
+                    1298,
+                    546,
+                    546,
+                    724,
+                    1195,
+                    841,
+                    110,
+                    1334,
+                    164,
+                    785,
+                    1177,
+                    631,
+                    384,
+                    54,
+                    607,
+                    891,
+                    290,
+                    729,
+                    120,
+                    1296,
+                    1166,
+                    102,
+                    180,
+                    816,
+                    881,
+                    742,
+                    852,
+                    1334,
+                    1348,
+                    998,
+                    752,
+                    832,
+                    1362,
+                    679,
+                    608,
+                    296,
+                    864,
+                    440,
+                    500,
+                    1081,
+                    576,
+                    433,
+                    25,
+                    1077,
+                    935,
+                    119,
+                    1330,
+                    327,
+                    696,
+                    530,
+                    228,
+                    211,
+                    591,
+                    182,
+                    388,
+                    739,
+                    1073,
+                    1166,
+                    332,
+                    919,
+                    1190,
+                    175,
+                    144,
+                    339,
+                    869,
+                    452,
+                    298,
+                    479,
+                    359,
+                    792,
+                    933,
+                    518,
+                    1396,
+                    613,
+                    627,
+                    728,
+                    1034,
+                    888,
+                    851,
+                    1019,
+                    995,
+                    229,
+                    760,
+                    102,
+                    1035,
+                    1385,
+                    207,
+                    1206,
+                    874,
+                    671,
+                    1280,
+                    172,
+                    1366,
+                    9,
+                    1175,
+                    151,
+                    1136,
+                    151,
+                    573,
+                    416,
+                    1170,
+                    1108,
+                    774,
+                    1351,
+                    481,
+                    110,
+                    1233,
+                    581,
+                    105,
+                    335,
+                    587,
+                    1376,
+                    1325,
+                    562,
+                    1282,
+                    110,
+                    697,
+                    1149,
+                    991,
+                    72,
+                    779,
+                    361,
+                    138,
+                    719,
+                    683,
+                    950,
+                    795,
+                    604,
+                    262,
+                    1033,
+                    1327,
+                    785,
+                    121,
+                    430,
+                    317,
+                    294,
+                    740,
+                    468,
+                    29,
+                    915,
+                    602,
+                    430,
+                    777,
+                    460,
+                    116,
+                    1244,
+                    612,
+                    1200,
+                    934,
+                    731,
+                    724,
+                    812,
+                    1316,
+                    735,
+                    357,
+                    152,
+                    40,
+                    1373,
+                    490,
+                    1113,
+                    1173,
+                    688,
+                    950,
+                    49,
+                    907,
+                    1171,
+                    716,
+                    394,
+                    106,
+                    11,
+                    1326,
+                    1150,
+                    1,
+                    760,
+                    1212,
+                    1273,
+                    693,
+                    753,
+                    223,
+                    503,
+                    941,
+                    164,
+                    453,
+                    246,
+                    583,
+                    236,
+                    646,
+                    1397,
+                    287,
+                    128,
+                    55,
+                    705,
+                    1413,
+                    840,
+                    1213,
+                    259,
+                    643,
+                    1007,
+                    933,
+                    268,
+                    602,
+                    221,
+                    683,
+                    60,
+                    1380,
+                    1271,
+                    574,
+                    1254,
+                    69,
+                    1295,
+                    1013,
+                    119,
+                    659,
+                    1034,
+                    974,
+                    546,
+                    352,
+                    1155,
+                    1023,
+                    754,
+                    901,
+                    443,
+                    609,
+                    194,
+                    640,
+                    1083,
+                    1377,
+                    1278,
+                    523,
+                    1344,
+                    1022,
+                    771,
+                    922,
+                    804,
+                    659,
+                    607,
+                    507,
+                    1076,
+                    93,
+                    344,
+                    1166,
+                    740,
+                    316,
+                    410,
+                    670,
+                    347,
+                    273,
+                    739,
+                    1042,
+                    1054,
+                    239,
+                    1245,
+                    1074,
+                    1021,
+                    243,
+                    789,
+                    764,
+                    1247,
+                    1358,
+                    856,
+                    737,
+                    577,
+                    985,
+                    1004,
+                    522,
+                    673,
+                    951,
+                    920,
+                    357,
+                    1361,
+                    1096,
+                    890,
+                    599,
+                    1230,
+                    971,
+                    860,
+                    181,
+                    186,
+                    647,
+                    280,
+                    1086,
+                    1087,
+                    209,
+                    930,
+                    437,
+                    273,
+                    518,
+                    364,
+                    885,
+                    1081,
+                    651,
+                    460,
+                    97,
+                    334,
+                    903,
+                    200,
+                    776,
+                    469,
+                    1325,
+                    535,
+                    37,
+                    833,
+                    1033,
+                    1066,
+                    904,
+                    288,
+                    205,
+                    1109,
+                    419,
+                    631,
+                    1007,
+                    1074,
+                    116,
+                    115,
+                    252,
+                    275,
+                    96,
+                    323,
+                    292,
+                    607,
+                    626,
+                    1178,
+                    1234,
+                    1029,
+                    662,
+                    101,
+                    1253,
+                    1356,
+                    841,
+                    453,
+                    322,
+                    309,
+                    1220,
+                    610,
+                    1086,
+                    600,
+                    748,
+                    943,
+                    132,
+                    341,
+                    228,
+                    288,
+                    703,
+                    1039,
+                    52,
+                    581,
+                    1174,
+                    1315,
+                    491,
+                    1080,
+                    1342,
+                    1408,
+                    113,
+                    283,
+                    833,
+                    462,
+                    1136,
+                    758,
+                    752,
+                    240,
+                    3,
+                    611,
+                    235,
+                    452,
+                    651,
+                    642,
+                    625,
+                    51,
+                    963,
+                    480,
+                    575,
+                    1158,
+                    271,
+                    365,
+                    1025,
+                    997,
+                    1387,
+                    1067,
+                    482,
+                    878,
+                    1054,
+                    242,
+                    893,
+                    517,
+                    406,
+                    125,
+                    1403,
+                    1092,
+                    1391,
+                    1336,
+                    148,
+                    1333,
+                    982,
+                    792,
+                    549,
+                    485,
+                    1184,
+                    459,
+                    216,
+                    823,
+                    888,
+                    1049,
+                    543,
+                    877,
+                    95
+                ]
+            ],
+            "output": -1
+        },
+        {
+            "input": [
+                [
+                    123688019,
+                    999330573,
+                    492142632,
+                    406773723,
+                    471511105,
+                    752258721,
+                    741285699,
+                    566098734,
+                    119260654,
+                    400328628,
+                    54135515,
+                    798562907,
+                    137203325,
+                    781112297,
+                    136825424,
+                    978078002,
+                    568284044,
+                    842966895,
+                    387303287,
+                    135181415,
+                    708757277,
+                    575317105,
+                    500914896,
+                    194734748,
+                    33580171,
+                    635720774,
+                    450284888,
+                    522954921,
+                    585317040,
+                    688606397,
+                    133261117,
+                    8565851,
+                    943068933,
+                    504767448,
+                    938359317,
+                    860559126,
+                    413585978,
+                    88310367,
+                    291798236,
+                    95108074,
+                    394599930,
+                    647653948,
+                    431490459,
+                    786689764,
+                    612122981,
+                    849459519,
+                    372570029,
+                    675420089,
+                    912536059,
+                    716280608,
+                    105487416,
+                    941832648,
+                    986722702,
+                    684983872,
+                    331254226,
+                    719044978,
+                    731155210,
+                    669380312,
+                    148867013,
+                    456280123,
+                    971398361,
+                    599347540,
+                    260816115,
+                    225009746,
+                    475143443,
+                    737617797,
+                    827117379,
+                    192138770,
+                    764582506,
+                    110192806,
+                    312417933,
+                    893753560,
+                    903849831,
+                    657578484,
+                    858682500,
+                    542498659,
+                    684909632,
+                    250423413,
+                    168737763,
+                    704878872,
+                    145709588,
+                    534424025,
+                    197883108,
+                    387288879,
+                    671255544,
+                    830248932,
+                    477569597,
+                    539096408,
+                    507288104,
+                    216648950,
+                    329238887,
+                    322122824,
+                    381331136,
+                    985325320,
+                    473703168,
+                    987378591,
+                    590765914,
+                    649528438,
+                    379015018,
+                    931437308,
+                    800254913,
+                    301804208,
+                    600935810,
+                    957336833,
+                    179780099,
+                    453951847,
+                    647531892,
+                    894852755,
+                    482578665,
+                    604433359,
+                    93029125,
+                    45524280,
+                    292231018,
+                    249785252,
+                    427840879,
+                    20697843,
+                    346785256,
+                    207054020,
+                    963277115,
+                    411345527,
+                    214357795,
+                    968056798,
+                    861643577,
+                    447414098,
+                    789217513,
+                    365260516,
+                    441196382,
+                    224328850,
+                    456521573,
+                    10161507,
+                    951931249,
+                    689099874,
+                    125347884,
+                    832327397,
+                    595124668,
+                    140624916,
+                    742471136,
+                    755529432,
+                    683853783,
+                    463183666,
+                    78378586,
+                    67448706,
+                    41114033,
+                    116810904,
+                    896110284,
+                    709912656,
+                    220194643,
+                    422841862,
+                    740540130,
+                    607936548,
+                    11810183,
+                    300694273,
+                    117186786,
+                    135403144,
+                    195896098,
+                    852575114,
+                    286855113,
+                    654987044,
+                    370256396,
+                    407514752,
+                    789267043,
+                    93403954,
+                    144062266,
+                    5152084,
+                    158788271,
+                    629804924,
+                    397012803,
+                    951897644,
+                    153808658,
+                    989579764,
+                    52757079,
+                    647938183,
+                    277625052,
+                    984786798,
+                    523715683,
+                    99776955,
+                    145467768,
+                    907091154,
+                    656908725,
+                    411367064,
+                    2943019,
+                    133933404,
+                    279016175,
+                    401582511,
+                    623108995,
+                    255360967,
+                    603481852,
+                    505190420,
+                    387245138,
+                    88981165,
+                    670167316,
+                    897760429,
+                    770403473,
+                    794966145,
+                    166748500,
+                    189014174,
+                    406461318,
+                    252683441,
+                    284669358,
+                    847342503,
+                    81164173,
+                    984086664,
+                    770887866,
+                    991271425,
+                    352610848,
+                    310161443,
+                    176821591,
+                    132491581,
+                    454715552,
+                    803333218,
+                    758607911,
+                    411002883,
+                    317310353,
+                    153127134,
+                    23826953,
+                    532356703,
+                    579564463,
+                    197539049,
+                    163374531,
+                    385979648,
+                    683835826,
+                    389591096,
+                    844916246,
+                    384795464,
+                    584552879,
+                    509771984,
+                    398982289,
+                    463233696,
+                    243750144,
+                    538002843,
+                    786220907,
+                    85135600,
+                    837294326,
+                    158540850,
+                    566753648,
+                    611173312,
+                    671683455,
+                    761259827,
+                    731713413,
+                    314447690,
+                    264369666,
+                    488073650,
+                    606326347,
+                    904925101,
+                    469718640,
+                    337869890,
+                    949766856,
+                    720796390,
+                    44927323,
+                    514022027,
+                    781640391,
+                    224777186,
+                    776567837,
+                    665346281,
+                    509419278,
+                    658166294,
+                    686121116,
+                    551274222,
+                    72098745,
+                    147147444,
+                    14956885,
+                    87074203,
+                    376590654,
+                    632049107,
+                    151657806,
+                    283002671,
+                    874537983,
+                    526977674,
+                    272937744,
+                    50261680,
+                    991640750,
+                    174688256,
+                    187061318,
+                    915965587,
+                    324820265,
+                    229499367,
+                    285255985,
+                    261184198,
+                    669675975,
+                    997754073,
+                    362379363,
+                    149280283,
+                    518234763,
+                    523765758,
+                    298965689,
+                    812008745,
+                    590058427,
+                    38218988,
+                    970320044,
+                    94152375,
+                    176935046,
+                    957636375,
+                    711086444,
+                    249531860,
+                    913255230,
+                    295583655,
+                    758374134,
+                    3318742,
+                    838863357,
+                    954444171,
+                    414085565,
+                    390806985,
+                    238435749,
+                    281639030,
+                    79078636,
+                    115309650,
+                    532507004,
+                    452931815,
+                    559596664,
+                    169531356,
+                    893718343,
+                    682720918,
+                    318945183,
+                    371154521,
+                    932878604,
+                    350921579,
+                    864632970,
+                    298640876,
+                    383698473,
+                    294240175,
+                    283311652,
+                    770535496,
+                    420799480,
+                    518574693,
+                    485123525,
+                    124850013,
+                    154436951,
+                    947285565,
+                    990777992,
+                    245337174,
+                    659394558,
+                    530828035,
+                    911114657,
+                    673350488,
+                    434326585,
+                    88042654,
+                    229131504,
+                    530637511,
+                    76075613,
+                    392384486,
+                    198290913,
+                    316025997,
+                    571474608,
+                    250954265,
+                    761585666,
+                    711757503,
+                    423443126,
+                    320539099,
+                    602332626,
+                    140526175,
+                    904190356,
+                    774393253,
+                    962715964,
+                    806673709,
+                    982074605,
+                    323792340,
+                    619765581,
+                    478012689,
+                    405798937,
+                    178136609,
+                    842684231,
+                    298946813,
+                    231292879,
+                    424544583,
+                    220895513,
+                    716502989,
+                    627102404,
+                    977000775,
+                    590847228,
+                    325748960,
+                    390448830,
+                    34433853,
+                    66696252,
+                    621540187,
+                    302784405,
+                    927033614,
+                    254368841,
+                    97540381,
+                    568755676,
+                    594480722,
+                    721611530,
+                    927544590,
+                    668557694,
+                    83280289,
+                    230912330,
+                    565028403,
+                    905213577,
+                    348697313,
+                    245340944,
+                    932829016,
+                    813664524,
+                    763250208,
+                    268703933,
+                    977577807,
+                    241500555,
+                    881783010,
+                    106272396,
+                    283447005,
+                    351865184,
+                    530283830,
+                    724655254,
+                    178045970,
+                    721081100,
+                    352535401,
+                    993588585,
+                    61092322,
+                    828841732,
+                    932058593,
+                    219840409,
+                    218269979,
+                    426791619,
+                    342684629,
+                    811880559,
+                    244075262,
+                    81257119,
+                    545768539,
+                    311137566,
+                    99226688,
+                    713818356,
+                    75946708,
+                    528079518,
+                    565161755,
+                    182656844,
+                    422813397,
+                    200438859,
+                    705626848,
+                    796754505,
+                    400216039,
+                    779815838,
+                    330900874,
+                    133714738,
+                    690940134,
+                    779769036,
+                    254291819,
+                    638859507,
+                    680247715,
+                    793409522,
+                    777854657,
+                    695894446,
+                    738264554,
+                    456430674,
+                    462762868,
+                    712342464,
+                    354940508,
+                    801086592,
+                    539146095,
+                    899942548,
+                    900431064,
+                    181271090,
+                    468424607,
+                    402420515,
+                    321167581,
+                    11966636,
+                    46348809,
+                    699253928,
+                    187855851,
+                    71677489,
+                    590688375,
+                    98950673,
+                    53788232,
+                    380191517,
+                    666124151,
+                    419853024,
+                    823848388,
+                    473372187,
+                    928586426,
+                    869380744,
+                    952443268,
+                    121872436,
+                    436896829,
+                    325497869,
+                    139307640,
+                    781898203,
+                    230382685,
+                    791917395,
+                    183978493,
+                    483223469,
+                    801034624,
+                    602534148,
+                    592703988,
+                    205989005,
+                    713452771,
+                    985968018,
+                    13952545,
+                    694651034,
+                    327865279,
+                    95958656,
+                    963006204,
+                    932917852,
+                    689446090,
+                    279357227,
+                    578303303,
+                    627363501,
+                    757220908,
+                    428907598,
+                    195454920,
+                    751225432,
+                    543283409,
+                    593784404,
+                    181547671,
+                    235129945,
+                    664795656,
+                    740574335,
+                    654203356,
+                    30878714,
+                    627643594,
+                    246895703,
+                    600834259,
+                    549595750,
+                    641782181,
+                    771931507,
+                    480520483,
+                    673937647,
+                    611472289,
+                    80386634,
+                    532921652,
+                    62064916,
+                    646454978,
+                    531961007,
+                    496650116,
+                    853043521,
+                    341357143,
+                    172474639,
+                    651741958,
+                    679295562,
+                    804130351,
+                    991635827,
+                    465160231,
+                    511074602,
+                    41992518,
+                    534054032,
+                    309556594,
+                    9759483,
+                    511214946,
+                    688783869,
+                    665781490,
+                    712885226,
+                    483644985,
+                    356105892,
+                    532112899,
+                    438410,
+                    565843689,
+                    146233808,
+                    877870608,
+                    467300238,
+                    937224035,
+                    965405332,
+                    410978178,
+                    296851677,
+                    239362234,
+                    87894157,
+                    615934366,
+                    712506088,
+                    969526738,
+                    74117798,
+                    705823928,
+                    350493218,
+                    553272481,
+                    332030243,
+                    368385745,
+                    758874434,
+                    250010841,
+                    578121796,
+                    588105091,
+                    35503320,
+                    839983146,
+                    219469686,
+                    942316957,
+                    543400641,
+                    300671135,
+                    80025016,
+                    423118153,
+                    258213885,
+                    47445714,
+                    969542632,
+                    557514600,
+                    68241788,
+                    363996308,
+                    846327929,
+                    501436843,
+                    910259453,
+                    553604096,
+                    661466169,
+                    145977466,
+                    989769268,
+                    516043422,
+                    799561470,
+                    17493685,
+                    697408970,
+                    803675040,
+                    252822441,
+                    397892842,
+                    287238906,
+                    847216982,
+                    686643279,
+                    57339439,
+                    978583529,
+                    284141520,
+                    948291513,
+                    580102533,
+                    479140187,
+                    465954029,
+                    429778493,
+                    775518593,
+                    275739230,
+                    196104305,
+                    100901953,
+                    305531518,
+                    236880964,
+                    667184224,
+                    134860372,
+                    610381297,
+                    787865148,
+                    780358479,
+                    175318933,
+                    278787053,
+                    302960254,
+                    23158395,
+                    809215273,
+                    536673271,
+                    84239018,
+                    860321287,
+                    412682077,
+                    552260652,
+                    341877879,
+                    444804967,
+                    459505709,
+                    440254171,
+                    105057382,
+                    812530769,
+                    626569322,
+                    537340993,
+                    987679478,
+                    223105571,
+                    416780461,
+                    325732601,
+                    974506499,
+                    267598077,
+                    655563231,
+                    622617966,
+                    875349510,
+                    905631910,
+                    34986985,
+                    882635804,
+                    942566025,
+                    199415359,
+                    155577854,
+                    842582118,
+                    991541613,
+                    998741737,
+                    421721328,
+                    277894557,
+                    397981923,
+                    252076646,
+                    800654732,
+                    925246547,
+                    880152267,
+                    890698463,
+                    617483591,
+                    511477365,
+                    784143666,
+                    33686496,
+                    414781017,
+                    806336383,
+                    858679295,
+                    868321195,
+                    616047242,
+                    934331989,
+                    10443848,
+                    251244355,
+                    667672705,
+                    610768140,
+                    153086510,
+                    337130878,
+                    433826396,
+                    367565651,
+                    93614656,
+                    499882502,
+                    580712289,
+                    781815224,
+                    792901844,
+                    304283993,
+                    552984182,
+                    785098895,
+                    663910706,
+                    364074100,
+                    775499041,
+                    140345854,
+                    862060285,
+                    655931075,
+                    735947049,
+                    781228111,
+                    789681280,
+                    87936033,
+                    143640410,
+                    650768176,
+                    17167305,
+                    762879624,
+                    43201256,
+                    55264719,
+                    271812760,
+                    282718317,
+                    127306985,
+                    522983217,
+                    73684719,
+                    554182689,
+                    873528142,
+                    647457813,
+                    755901039,
+                    117902720,
+                    97010662,
+                    450710678,
+                    615294274,
+                    287660988,
+                    16517376,
+                    508813289,
+                    129743954,
+                    868053658,
+                    321473836,
+                    444979300,
+                    983331633,
+                    33959411,
+                    551993124,
+                    470990624,
+                    341043994,
+                    986160993,
+                    116809220,
+                    421547285,
+                    771273862,
+                    277233571,
+                    514068812,
+                    81791587,
+                    413222671,
+                    28014945,
+                    969644923,
+                    530827351,
+                    594193609,
+                    613422383,
+                    208259239,
+                    497334355,
+                    639382671,
+                    636555947,
+                    155260555,
+                    986942054,
+                    736734931,
+                    223999907,
+                    550777985,
+                    862703627,
+                    815628203,
+                    813822346,
+                    211228642,
+                    351723650,
+                    195566435,
+                    490171214,
+                    912282483,
+                    111931949,
+                    19060214,
+                    754001126,
+                    366801680,
+                    62257167,
+                    369196247,
+                    104219749,
+                    938583685,
+                    997919086,
+                    71119325,
+                    596086687,
+                    723268815,
+                    458413338,
+                    29664938,
+                    851035477,
+                    923668185,
+                    119772363,
+                    578553485,
+                    259584805,
+                    938150968,
+                    618343393,
+                    121344425,
+                    187282500,
+                    399189582,
+                    135575732,
+                    691453106,
+                    648254997,
+                    992262593,
+                    678457620,
+                    399451562,
+                    126496341,
+                    414564142,
+                    645781742,
+                    566263703,
+                    281483731,
+                    806102292,
+                    600911040,
+                    163374502,
+                    915169433,
+                    500583239,
+                    839364150,
+                    263518377,
+                    368235965,
+                    124537346,
+                    440219606,
+                    192995801,
+                    76108971,
+                    467783389,
+                    756031179,
+                    240840178,
+                    833908027,
+                    793910264,
+                    758496142,
+                    470708744,
+                    842887393,
+                    582089771,
+                    173274279,
+                    616561296,
+                    158377189,
+                    468427580,
+                    403237342,
+                    287341774,
+                    997019495,
+                    714061020,
+                    876686964,
+                    673264720
+                ],
+                [
+                    598,
+                    711,
+                    42,
+                    69,
+                    364,
+                    556,
+                    590,
+                    436,
+                    487,
+                    423,
+                    576,
+                    749,
+                    391,
+                    440,
+                    801,
+                    451,
+                    650,
+                    712,
+                    116,
+                    67,
+                    450,
+                    509,
+                    122,
+                    177,
+                    308,
+                    708,
+                    712,
+                    359,
+                    356,
+                    404,
+                    54,
+                    785,
+                    160,
+                    709,
+                    459,
+                    93,
+                    285,
+                    656,
+                    118,
+                    136,
+                    629,
+                    318,
+                    797,
+                    600,
+                    96,
+                    236,
+                    139,
+                    146,
+                    58,
+                    792,
+                    656,
+                    560,
+                    33,
+                    510,
+                    681,
+                    193,
+                    300,
+                    793,
+                    804,
+                    206,
+                    649,
+                    458,
+                    267,
+                    631,
+                    363,
+                    127,
+                    693,
+                    97,
+                    647,
+                    467,
+                    553,
+                    143,
+                    755,
+                    291,
+                    619,
+                    758,
+                    773,
+                    462,
+                    491,
+                    755,
+                    132,
+                    211,
+                    675,
+                    461,
+                    384,
+                    670,
+                    105,
+                    495,
+                    316,
+                    22,
+                    242,
+                    288,
+                    772,
+                    90,
+                    652,
+                    575,
+                    373,
+                    751,
+                    259,
+                    514,
+                    267,
+                    672,
+                    732,
+                    461,
+                    456,
+                    317,
+                    46,
+                    440,
+                    415,
+                    550,
+                    366,
+                    206,
+                    82,
+                    672,
+                    287,
+                    464,
+                    440,
+                    262,
+                    682,
+                    617,
+                    433,
+                    288,
+                    260,
+                    142,
+                    674,
+                    623,
+                    496,
+                    38,
+                    178,
+                    812,
+                    590,
+                    234,
+                    47,
+                    54,
+                    38,
+                    196,
+                    184,
+                    213,
+                    89,
+                    619,
+                    43,
+                    359,
+                    640,
+                    176,
+                    744,
+                    94,
+                    46,
+                    242,
+                    422,
+                    693,
+                    589,
+                    336,
+                    724,
+                    618,
+                    555,
+                    492,
+                    644,
+                    325,
+                    578,
+                    642,
+                    817,
+                    462,
+                    166,
+                    414,
+                    499,
+                    607,
+                    699,
+                    568,
+                    227,
+                    641,
+                    447,
+                    209,
+                    38,
+                    251,
+                    233,
+                    266,
+                    108,
+                    138,
+                    646,
+                    797,
+                    122,
+                    340,
+                    85,
+                    424,
+                    655,
+                    638,
+                    382,
+                    258,
+                    406,
+                    34,
+                    698,
+                    492,
+                    52,
+                    677,
+                    567,
+                    412,
+                    77,
+                    555,
+                    606,
+                    74,
+                    468,
+                    685,
+                    624,
+                    644,
+                    312,
+                    782,
+                    605,
+                    717,
+                    527,
+                    819,
+                    24,
+                    357,
+                    392,
+                    567,
+                    118,
+                    123,
+                    399,
+                    451,
+                    330,
+                    376,
+                    322,
+                    123,
+                    497,
+                    261,
+                    236,
+                    425,
+                    659,
+                    107,
+                    82,
+                    165,
+                    462,
+                    669,
+                    32,
+                    769,
+                    331,
+                    79,
+                    467,
+                    570,
+                    297,
+                    9,
+                    104,
+                    351,
+                    557,
+                    43,
+                    611,
+                    640,
+                    143,
+                    343,
+                    665,
+                    329,
+                    124,
+                    528,
+                    341,
+                    342,
+                    159,
+                    355,
+                    493,
+                    229,
+                    283,
+                    166,
+                    783,
+                    45,
+                    336,
+                    734,
+                    419,
+                    434,
+                    593,
+                    308,
+                    435,
+                    236,
+                    84,
+                    680,
+                    494,
+                    543,
+                    380,
+                    112,
+                    268,
+                    131,
+                    747,
+                    218,
+                    559,
+                    736,
+                    43,
+                    307,
+                    13,
+                    72,
+                    218,
+                    381,
+                    199,
+                    351,
+                    322,
+                    58,
+                    671,
+                    146,
+                    220,
+                    290,
+                    751,
+                    9,
+                    46,
+                    259,
+                    93,
+                    105,
+                    28,
+                    144,
+                    443,
+                    509,
+                    189,
+                    254,
+                    534,
+                    613,
+                    809,
+                    313,
+                    329,
+                    782,
+                    556,
+                    99,
+                    670,
+                    520,
+                    210,
+                    298,
+                    383,
+                    158,
+                    388,
+                    638,
+                    388,
+                    445,
+                    151,
+                    633,
+                    425,
+                    477,
+                    813,
+                    314,
+                    319,
+                    547,
+                    661,
+                    811,
+                    717,
+                    821,
+                    475,
+                    767,
+                    465,
+                    594,
+                    783,
+                    292,
+                    663,
+                    575,
+                    730,
+                    45,
+                    290,
+                    519,
+                    278,
+                    9,
+                    731,
+                    209,
+                    90,
+                    598,
+                    665,
+                    112,
+                    443,
+                    709,
+                    443,
+                    74,
+                    797,
+                    278,
+                    577,
+                    812,
+                    88,
+                    631,
+                    455,
+                    414,
+                    104,
+                    325,
+                    213,
+                    664,
+                    789,
+                    310,
+                    151,
+                    309,
+                    416,
+                    427,
+                    71,
+                    180,
+                    505,
+                    340,
+                    794,
+                    409,
+                    42,
+                    18,
+                    166,
+                    216,
+                    496,
+                    403,
+                    428,
+                    628,
+                    125,
+                    686,
+                    17,
+                    31,
+                    677,
+                    639,
+                    57,
+                    247,
+                    718,
+                    314,
+                    333,
+                    58,
+                    707,
+                    476,
+                    44,
+                    716,
+                    539,
+                    444,
+                    401,
+                    628,
+                    108,
+                    537,
+                    376,
+                    683,
+                    329,
+                    180,
+                    313,
+                    668,
+                    345,
+                    98,
+                    84,
+                    476,
+                    657,
+                    103,
+                    29,
+                    803,
+                    99,
+                    814,
+                    429,
+                    316,
+                    775,
+                    802,
+                    231,
+                    809,
+                    416,
+                    327,
+                    776,
+                    633,
+                    40,
+                    153,
+                    690,
+                    538,
+                    492,
+                    479,
+                    382,
+                    55,
+                    135,
+                    39,
+                    497,
+                    451,
+                    764,
+                    695,
+                    389,
+                    690,
+                    72,
+                    451,
+                    618,
+                    226,
+                    416,
+                    612,
+                    607,
+                    503,
+                    231,
+                    694,
+                    793,
+                    425,
+                    529,
+                    743,
+                    212,
+                    112,
+                    459,
+                    187,
+                    164,
+                    271,
+                    318,
+                    705,
+                    37,
+                    287,
+                    278,
+                    157,
+                    245,
+                    10,
+                    716,
+                    557,
+                    104,
+                    240,
+                    802,
+                    381,
+                    61,
+                    809,
+                    109,
+                    688,
+                    769,
+                    259,
+                    571,
+                    504,
+                    101,
+                    262,
+                    490,
+                    253,
+                    547,
+                    21,
+                    42,
+                    90,
+                    756,
+                    318,
+                    734,
+                    77,
+                    219,
+                    603,
+                    460,
+                    221,
+                    556,
+                    633,
+                    490,
+                    383,
+                    293,
+                    293,
+                    156,
+                    794,
+                    505,
+                    652,
+                    573,
+                    550,
+                    806,
+                    461,
+                    538,
+                    435,
+                    377,
+                    42,
+                    455,
+                    807,
+                    586,
+                    701,
+                    641,
+                    378,
+                    120,
+                    685,
+                    534,
+                    24,
+                    209,
+                    422,
+                    690,
+                    138,
+                    712,
+                    239,
+                    583,
+                    122,
+                    49,
+                    218,
+                    161,
+                    32,
+                    30,
+                    163,
+                    52,
+                    488,
+                    374,
+                    118,
+                    436,
+                    209,
+                    209,
+                    24,
+                    590,
+                    448,
+                    60,
+                    689,
+                    235,
+                    663,
+                    69,
+                    186,
+                    790,
+                    428,
+                    2,
+                    352,
+                    401,
+                    532,
+                    225,
+                    56,
+                    28,
+                    204,
+                    626,
+                    210,
+                    662,
+                    689,
+                    105,
+                    508,
+                    749,
+                    74,
+                    590,
+                    529,
+                    112,
+                    29,
+                    573,
+                    276,
+                    541,
+                    344,
+                    263,
+                    705,
+                    382,
+                    147,
+                    782,
+                    124,
+                    350,
+                    43,
+                    211,
+                    74,
+                    45,
+                    153,
+                    327,
+                    489,
+                    515,
+                    327,
+                    382,
+                    30,
+                    405,
+                    728,
+                    186,
+                    700,
+                    512,
+                    643,
+                    354,
+                    123,
+                    238,
+                    470,
+                    718,
+                    637,
+                    506,
+                    652,
+                    565,
+                    89,
+                    201,
+                    24,
+                    416,
+                    431,
+                    185,
+                    731,
+                    243,
+                    352,
+                    229,
+                    677,
+                    390,
+                    642,
+                    501,
+                    637,
+                    664,
+                    436,
+                    524,
+                    790,
+                    714,
+                    14,
+                    70,
+                    806,
+                    313,
+                    203,
+                    332,
+                    69,
+                    145,
+                    10,
+                    426,
+                    303,
+                    114,
+                    687,
+                    10,
+                    723,
+                    274,
+                    153,
+                    245,
+                    719,
+                    61,
+                    342,
+                    293,
+                    158,
+                    56,
+                    99,
+                    88,
+                    811,
+                    792,
+                    640,
+                    639,
+                    289,
+                    23,
+                    374,
+                    99,
+                    725,
+                    637,
+                    192,
+                    132,
+                    740,
+                    156,
+                    75,
+                    341,
+                    367,
+                    396,
+                    126,
+                    479,
+                    535,
+                    384,
+                    32,
+                    414,
+                    815,
+                    95,
+                    639,
+                    45,
+                    689,
+                    359,
+                    706,
+                    368,
+                    80,
+                    148,
+                    505,
+                    420,
+                    219,
+                    816,
+                    346,
+                    703,
+                    458,
+                    151,
+                    738,
+                    486,
+                    179,
+                    368,
+                    661,
+                    711,
+                    722,
+                    122,
+                    297,
+                    353,
+                    171,
+                    275,
+                    491,
+                    166,
+                    692,
+                    300,
+                    611,
+                    665,
+                    8,
+                    158,
+                    408,
+                    45,
+                    616,
+                    350,
+                    281,
+                    310,
+                    111,
+                    105,
+                    95,
+                    668,
+                    368,
+                    7,
+                    601,
+                    667,
+                    167,
+                    661,
+                    279,
+                    564,
+                    706,
+                    557,
+                    337,
+                    305,
+                    464,
+                    648,
+                    599,
+                    306,
+                    308,
+                    600,
+                    504,
+                    164,
+                    592,
+                    140,
+                    608,
+                    543,
+                    282,
+                    252,
+                    44,
+                    641,
+                    728,
+                    27,
+                    740,
+                    152,
+                    422,
+                    592,
+                    657,
+                    670,
+                    324,
+                    500,
+                    508,
+                    623,
+                    102,
+                    442,
+                    613,
+                    709,
+                    681,
+                    468,
+                    260,
+                    380,
+                    409,
+                    67,
+                    408,
+                    32,
+                    264,
+                    581,
+                    430,
+                    285,
+                    46,
+                    787,
+                    600,
+                    591,
+                    359,
+                    127,
+                    188,
+                    56,
+                    532,
+                    709,
+                    681,
+                    208,
+                    171,
+                    370,
+                    787,
+                    555,
+                    696,
+                    311,
+                    557,
+                    330,
+                    321,
+                    721,
+                    51,
+                    2,
+                    347,
+                    742,
+                    502,
+                    634,
+                    259,
+                    169,
+                    430,
+                    604,
+                    17,
+                    11,
+                    773,
+                    301,
+                    608,
+                    776,
+                    603,
+                    379,
+                    675,
+                    165,
+                    214,
+                    147,
+                    553,
+                    637,
+                    718,
+                    606,
+                    150,
+                    347,
+                    659,
+                    376,
+                    631,
+                    40,
+                    368,
+                    418,
+                    702,
+                    29,
+                    368,
+                    515,
+                    215,
+                    537,
+                    24,
+                    601,
+                    116,
+                    577,
+                    429,
+                    521,
+                    707,
+                    245,
+                    641,
+                    557,
+                    669,
+                    740,
+                    161,
+                    728,
+                    652,
+                    211,
+                    238,
+                    724,
+                    804,
+                    56,
+                    819,
+                    643,
+                    174,
+                    359,
+                    190,
+                    505,
+                    300,
+                    252,
+                    777,
+                    169,
+                    667,
+                    738,
+                    443,
+                    242,
+                    130,
+                    90,
+                    762,
+                    132,
+                    76,
+                    456,
+                    674,
+                    34,
+                    218,
+                    20,
+                    321,
+                    495,
+                    497,
+                    618,
+                    290,
+                    512,
+                    300,
+                    799,
+                    27,
+                    743,
+                    366,
+                    402,
+                    237,
+                    254,
+                    127,
+                    610,
+                    343,
+                    263,
+                    465,
+                    632,
+                    87,
+                    538,
+                    329,
+                    662,
+                    810,
+                    584,
+                    814,
+                    277,
+                    510,
+                    711,
+                    669,
+                    153,
+                    750,
+                    492,
+                    499,
+                    422,
+                    419,
+                    175,
+                    137,
+                    385,
+                    157,
+                    78,
+                    557,
+                    592,
+                    583,
+                    151,
+                    271,
+                    170,
+                    20,
+                    525,
+                    79,
+                    423,
+                    118,
+                    64,
+                    337,
+                    87,
+                    287,
+                    40,
+                    776,
+                    813,
+                    385,
+                    361,
+                    106,
+                    608,
+                    535,
+                    387,
+                    642,
+                    608,
+                    549,
+                    228,
+                    509,
+                    287,
+                    393,
+                    237,
+                    406,
+                    233,
+                    646,
+                    413,
+                    200,
+                    476,
+                    2,
+                    478,
+                    148,
+                    645,
+                    787,
+                    152,
+                    100,
+                    363,
+                    85,
+                    132,
+                    763,
+                    201,
+                    598,
+                    808,
+                    784,
+                    556,
+                    713,
+                    783,
+                    332,
+                    441,
+                    387,
+                    432,
+                    673,
+                    52,
+                    510,
+                    621,
+                    281,
+                    448,
+                    610,
+                    69,
+                    561,
+                    305,
+                    222,
+                    228,
+                    127,
+                    261,
+                    404,
+                    495,
+                    771,
+                    275,
+                    804,
+                    344,
+                    52,
+                    746,
+                    439,
+                    531,
+                    777,
+                    495,
+                    453,
+                    145,
+                    689,
+                    46,
+                    579,
+                    683,
+                    617,
+                    179,
+                    53,
+                    208,
+                    686,
+                    523,
+                    259,
+                    448,
+                    672,
+                    535,
+                    435,
+                    73,
+                    310,
+                    478,
+                    348,
+                    161,
+                    805,
+                    640,
+                    780,
+                    736,
+                    278,
+                    150,
+                    564,
+                    718,
+                    513,
+                    181,
+                    818,
+                    80,
+                    454,
+                    54,
+                    312,
+                    227,
+                    18,
+                    250,
+                    187,
+                    438,
+                    390,
+                    494,
+                    389,
+                    83,
+                    719,
+                    640,
+                    89,
+                    686,
+                    524,
+                    674,
+                    667,
+                    467,
+                    222,
+                    468,
+                    594,
+                    571,
+                    747,
+                    663,
+                    475,
+                    500,
+                    2,
+                    608,
+                    310,
+                    507,
+                    806,
+                    380,
+                    502,
+                    553,
+                    711,
+                    292,
+                    125,
+                    349,
+                    538,
+                    470,
+                    632,
+                    739,
+                    543,
+                    662,
+                    745,
+                    611,
+                    30,
+                    143,
+                    694,
+                    129,
+                    32,
+                    748,
+                    278,
+                    559,
+                    358,
+                    43,
+                    326,
+                    818,
+                    88,
+                    246,
+                    331,
+                    615,
+                    541,
+                    254,
+                    616,
+                    422,
+                    273,
+                    289,
+                    328,
+                    230,
+                    21,
+                    771,
+                    435,
+                    310,
+                    30,
+                    92,
+                    188,
+                    195,
+                    115,
+                    614,
+                    256,
+                    309,
+                    775,
+                    193,
+                    398,
+                    253,
+                    498,
+                    526,
+                    288,
+                    776,
+                    621,
+                    188,
+                    544,
+                    75,
+                    373,
+                    102,
+                    344,
+                    641,
+                    725,
+                    536,
+                    172,
+                    734,
+                    328,
+                    501,
+                    434,
+                    640,
+                    505,
+                    213,
+                    235,
+                    532,
+                    49,
+                    641,
+                    239,
+                    267,
+                    723,
+                    11,
+                    322,
+                    328,
+                    719,
+                    513,
+                    513,
+                    785,
+                    446,
+                    347,
+                    442,
+                    600,
+                    617,
+                    166,
+                    445,
+                    300,
+                    61,
+                    31,
+                    536,
+                    530,
+                    98,
+                    309,
+                    576,
+                    68,
+                    260,
+                    641,
+                    411,
+                    226,
+                    509,
+                    541,
+                    225,
+                    17,
+                    94,
+                    622,
+                    742,
+                    748,
+                    316,
+                    351,
+                    223,
+                    182,
+                    283,
+                    362,
+                    8,
+                    314,
+                    594,
+                    768,
+                    323,
+                    231,
+                    116,
+                    224,
+                    195,
+                    10,
+                    724,
+                    177,
+                    747,
+                    18,
+                    614,
+                    434,
+                    788,
+                    26,
+                    568,
+                    693,
+                    685,
+                    496,
+                    174,
+                    384,
+                    539,
+                    524,
+                    156,
+                    90,
+                    641,
+                    326,
+                    486,
+                    318,
+                    254,
+                    352,
+                    722,
+                    749,
+                    428,
+                    167,
+                    504,
+                    421,
+                    751,
+                    511,
+                    636,
+                    718,
+                    205,
+                    465,
+                    782,
+                    106,
+                    96,
+                    552,
+                    187,
+                    460,
+                    305,
+                    368,
+                    643,
+                    742,
+                    170,
+                    123,
+                    188,
+                    155,
+                    55,
+                    169,
+                    260,
+                    58,
+                    250,
+                    550,
+                    423,
+                    564,
+                    651,
+                    815,
+                    719,
+                    428,
+                    725,
+                    794,
+                    48,
+                    544,
+                    619,
+                    580,
+                    168,
+                    84,
+                    444,
+                    113,
+                    242,
+                    113,
+                    546,
+                    267,
+                    452,
+                    153,
+                    144,
+                    330,
+                    291,
+                    75,
+                    489,
+                    326,
+                    791,
+                    199,
+                    609,
+                    286,
+                    464,
+                    355,
+                    416,
+                    392,
+                    724,
+                    292,
+                    46,
+                    80,
+                    288,
+                    170,
+                    568,
+                    340,
+                    286,
+                    189,
+                    56,
+                    721,
+                    98,
+                    691,
+                    623,
+                    682,
+                    678,
+                    190,
+                    53,
+                    294,
+                    798,
+                    155,
+                    675,
+                    703,
+                    602,
+                    402,
+                    633,
+                    173,
+                    566,
+                    355,
+                    426,
+                    640,
+                    641,
+                    203,
+                    740,
+                    793,
+                    174,
+                    318,
+                    68,
+                    65,
+                    456,
+                    123,
+                    192,
+                    262,
+                    194,
+                    265,
+                    132,
+                    475,
+                    720,
+                    188,
+                    467,
+                    130,
+                    91,
+                    380,
+                    100,
+                    239,
+                    255,
+                    184,
+                    690,
+                    821,
+                    325,
+                    357,
+                    14,
+                    227,
+                    795,
+                    372,
+                    767,
+                    468,
+                    54,
+                    363,
+                    290,
+                    83,
+                    715,
+                    345,
+                    326,
+                    702,
+                    117,
+                    780,
+                    505,
+                    445,
+                    466,
+                    667,
+                    103,
+                    686,
+                    155,
+                    647,
+                    805,
+                    48,
+                    590,
+                    16,
+                    104,
+                    816,
+                    41,
+                    340,
+                    218,
+                    467,
+                    352,
+                    315,
+                    377,
+                    299,
+                    31,
+                    312,
+                    298,
+                    743,
+                    381,
+                    188,
+                    220,
+                    700,
+                    507,
+                    732,
+                    514,
+                    305,
+                    136,
+                    317,
+                    283,
+                    358,
+                    729,
+                    620,
+                    722,
+                    681,
+                    460,
+                    70,
+                    9,
+                    127,
+                    765,
+                    409,
+                    689,
+                    30,
+                    468,
+                    432,
+                    576,
+                    672,
+                    355,
+                    605,
+                    176,
+                    740,
+                    226,
+                    434,
+                    374,
+                    156,
+                    155,
+                    157,
+                    481,
+                    265,
+                    150,
+                    110,
+                    483,
+                    500,
+                    398,
+                    810,
+                    149,
+                    415,
+                    351,
+                    176,
+                    656,
+                    192,
+                    755,
+                    403,
+                    577,
+                    279,
+                    563,
+                    706,
+                    171,
+                    144,
+                    282,
+                    600,
+                    58,
+                    428,
+                    182,
+                    439,
+                    564,
+                    540,
+                    398,
+                    516,
+                    547,
+                    249,
+                    243,
+                    535,
+                    729,
+                    408,
+                    485,
+                    581,
+                    347,
+                    521,
+                    283,
+                    196,
+                    545,
+                    395,
+                    397,
+                    720,
+                    572,
+                    701,
+                    591,
+                    275,
+                    711,
+                    35,
+                    484,
+                    445,
+                    540,
+                    813,
+                    306,
+                    81,
+                    219,
+                    583,
+                    805,
+                    248,
+                    663,
+                    328,
+                    238,
+                    591,
+                    764,
+                    752,
+                    485,
+                    97,
+                    56,
+                    689,
+                    710,
+                    22,
+                    360,
+                    339,
+                    189,
+                    355,
+                    441,
+                    102,
+                    543,
+                    60,
+                    699,
+                    384,
+                    748,
+                    615,
+                    454,
+                    285,
+                    747,
+                    131,
+                    475,
+                    220,
+                    353,
+                    220,
+                    421,
+                    775,
+                    219,
+                    478,
+                    207,
+                    411,
+                    200,
+                    468,
+                    156,
+                    559,
+                    309,
+                    9,
+                    544,
+                    277,
+                    761,
+                    715,
+                    496,
+                    423,
+                    272,
+                    767,
+                    371,
+                    526,
+                    113,
+                    728,
+                    684,
+                    105,
+                    256,
+                    744,
+                    762,
+                    637,
+                    566,
+                    10,
+                    442,
+                    317,
+                    29,
+                    320,
+                    56,
+                    761,
+                    642,
+                    419,
+                    748,
+                    497,
+                    690,
+                    81,
+                    648,
+                    455,
+                    508,
+                    178,
+                    606,
+                    87,
+                    700,
+                    722,
+                    440,
+                    726,
+                    798,
+                    596,
+                    189,
+                    223,
+                    503,
+                    64,
+                    323,
+                    271,
+                    628,
+                    246,
+                    65,
+                    584,
+                    147,
+                    27,
+                    164,
+                    186,
+                    282,
+                    411,
+                    325,
+                    690,
+                    116,
+                    528,
+                    125,
+                    111,
+                    502,
+                    541,
+                    517,
+                    401,
+                    819,
+                    95,
+                    582,
+                    306,
+                    412,
+                    373,
+                    165,
+                    595,
+                    722
+                ]
+            ],
+            "output": -1
+        },
+        {
+            "input": [
+                [
+                    112457345,
+                    865971795,
+                    869953699,
+                    353899892,
+                    952779552,
+                    161113313,
+                    986272094,
+                    960203192,
+                    710274203,
+                    310442806,
+                    586973173,
+                    763930781,
+                    168588136,
+                    45767671,
+                    561859093,
+                    406050085,
+                    168070146,
+                    199168517,
+                    828566639,
+                    336503038,
+                    553358139,
+                    637282517,
+                    282320575,
+                    316287558,
+                    651735176,
+                    323486490,
+                    130995863,
+                    960224150,
+                    218589291,
+                    299703431,
+                    27248815,
+                    260314449,
+                    137931405,
+                    325138190,
+                    268827999,
+                    696879529,
+                    299573440,
+                    760657538,
+                    327076332,
+                    413971818,
+                    739531641,
+                    259797612,
+                    306537475,
+                    3770897,
+                    165456984,
+                    646605190,
+                    546186672,
+                    470647229,
+                    708060817,
+                    915870111,
+                    958077310,
+                    230476918,
+                    187862651,
+                    757666201,
+                    871783883,
+                    114908906,
+                    921297652,
+                    277741432,
+                    516251049,
+                    624171379,
+                    546446216,
+                    286515941,
+                    437196137,
+                    621113609,
+                    703121002,
+                    961851986,
+                    763686710,
+                    427308316,
+                    133161635,
+                    724407456,
+                    10668078,
+                    610672065,
+                    879990700,
+                    162566591,
+                    250044535,
+                    788996545,
+                    892103108,
+                    260459120,
+                    482766100,
+                    603731024,
+                    770463413,
+                    238910843,
+                    721416722,
+                    426066,
+                    178083726,
+                    966916060,
+                    583661461,
+                    19676933,
+                    445417703,
+                    427364037,
+                    916821901,
+                    118770970,
+                    584903350,
+                    385507624,
+                    29211808,
+                    585821863,
+                    983200525,
+                    147985317,
+                    160440192,
+                    233009044,
+                    283422271,
+                    335471603,
+                    545898193,
+                    526193438,
+                    187040630,
+                    685205950,
+                    768199322,
+                    390504219,
+                    969086042,
+                    714350585,
+                    848467775,
+                    261504921,
+                    61381058,
+                    479662427,
+                    130385356,
+                    106294337,
+                    262046495,
+                    687209680,
+                    536471133,
+                    309734341,
+                    511485671,
+                    187115508,
+                    570310505,
+                    604770357,
+                    846031519,
+                    290791953,
+                    577971360,
+                    893405092,
+                    369830934,
+                    160175704,
+                    15558050,
+                    748057423,
+                    538451082,
+                    24798504,
+                    297880617,
+                    224882446,
+                    112555264,
+                    442466152,
+                    985303040,
+                    507302159,
+                    856459997,
+                    929322348,
+                    899333822,
+                    799607461,
+                    981856633,
+                    639179462,
+                    122200091,
+                    980793438,
+                    737131022,
+                    85503631,
+                    251518286,
+                    322036948,
+                    321264270,
+                    964833191,
+                    578996750,
+                    440891136,
+                    350233494,
+                    453520939,
+                    764197901,
+                    557040228,
+                    833168977,
+                    979740665,
+                    46075729,
+                    125996686,
+                    459783482,
+                    825432790,
+                    296550438,
+                    956531820,
+                    703958787,
+                    808424998,
+                    349524516,
+                    802610491,
+                    311525347,
+                    781709218,
+                    383327830,
+                    353755463,
+                    806161634,
+                    991903748,
+                    351060477,
+                    168474465,
+                    778529623,
+                    418055648,
+                    796508266,
+                    672178656,
+                    609598809,
+                    18595640,
+                    161625422,
+                    544916159,
+                    672826510,
+                    255009033,
+                    30531310,
+                    58162144,
+                    407365219,
+                    202811644,
+                    769849159,
+                    622698779,
+                    727230462,
+                    975027076,
+                    951602002,
+                    758388596,
+                    58022210,
+                    226109584,
+                    910875214,
+                    570335196,
+                    276839164,
+                    942205517,
+                    545580798,
+                    259706508,
+                    107801020,
+                    981428098,
+                    663925114,
+                    885000145,
+                    859969767,
+                    521678800,
+                    446253422,
+                    593582823,
+                    954773034,
+                    187607903,
+                    961165592,
+                    420954136,
+                    389663525,
+                    591774515,
+                    700210810,
+                    552267427,
+                    19119721,
+                    203784907,
+                    628443588,
+                    366072992,
+                    792132930,
+                    874841206,
+                    112103803,
+                    476459507,
+                    724651429,
+                    940181053,
+                    331670146,
+                    636910315,
+                    944741269,
+                    919764966,
+                    77519249,
+                    879491907,
+                    526869846,
+                    114100820,
+                    844099521,
+                    88328701,
+                    763210812,
+                    218202763,
+                    261501219,
+                    732811436,
+                    859885239,
+                    463851868,
+                    352687846,
+                    20976082,
+                    834242434,
+                    405487295,
+                    825588721,
+                    949565142,
+                    65676113,
+                    550803945,
+                    603560709,
+                    514615568,
+                    211991349,
+                    208675799,
+                    220405957,
+                    723072438,
+                    189821564,
+                    912509977,
+                    473025078,
+                    450658025,
+                    505370620,
+                    826118567,
+                    362144123,
+                    966183279,
+                    652325798,
+                    829755497,
+                    140799487,
+                    885228306,
+                    190007572,
+                    546780964,
+                    280583004,
+                    738941397,
+                    781770559,
+                    498394335,
+                    190456942,
+                    900213515,
+                    538520195,
+                    232774629,
+                    874898335,
+                    557294258,
+                    71020650,
+                    578458875,
+                    114496449,
+                    635596480,
+                    338265268,
+                    915047900,
+                    145036951,
+                    242144129,
+                    835018700,
+                    665094776,
+                    33850300,
+                    205239514,
+                    436151834,
+                    70938019,
+                    310206978,
+                    617047969,
+                    129804399,
+                    554391117,
+                    336494232,
+                    789246513,
+                    727459386,
+                    676367589,
+                    819614891,
+                    488327632,
+                    600016672,
+                    735710883,
+                    894992529,
+                    295978876,
+                    416534675,
+                    968942281,
+                    661282653,
+                    462514634,
+                    168415998,
+                    203513393,
+                    934257162,
+                    648312728,
+                    391695883,
+                    902204331,
+                    649722429,
+                    253662165,
+                    126819917,
+                    598605759,
+                    554316248,
+                    196997177,
+                    339530879,
+                    637711040,
+                    980287733,
+                    153226668,
+                    857373245,
+                    112823715,
+                    707805138,
+                    196463418,
+                    29998239,
+                    512413600,
+                    315746520,
+                    877350727,
+                    22240271,
+                    677570999,
+                    777152388,
+                    756133953,
+                    288547244,
+                    418282911,
+                    281417379,
+                    539491816,
+                    30349493,
+                    563836724,
+                    393637741,
+                    437626273,
+                    611914139,
+                    459843788,
+                    415926389,
+                    152440267,
+                    370539047,
+                    522819249,
+                    317795522,
+                    895639417,
+                    218563422,
+                    12680031,
+                    349506185,
+                    295236353,
+                    336279096,
+                    419359763,
+                    616749556,
+                    434110569,
+                    340116793,
+                    132342402,
+                    984829292,
+                    71613845,
+                    562390343,
+                    235012240,
+                    119147642,
+                    29611562,
+                    454111988,
+                    690953930,
+                    668617885,
+                    714026424,
+                    34766766,
+                    159563354,
+                    952843934,
+                    620748014,
+                    233577098,
+                    206309096,
+                    283394211,
+                    792008396,
+                    503763832,
+                    453871573,
+                    507703443,
+                    352898352,
+                    676915718,
+                    945274040,
+                    148197765,
+                    743532016,
+                    726539868,
+                    883140758,
+                    544195746,
+                    412754886,
+                    616663468,
+                    892350749,
+                    631037087,
+                    712182219,
+                    471208677,
+                    550807829,
+                    79009663,
+                    411070139,
+                    698033107,
+                    243478630,
+                    73660134,
+                    276439409,
+                    339030908,
+                    926393752,
+                    172364555,
+                    824389937,
+                    252671213,
+                    658316105,
+                    532236718,
+                    144627952,
+                    768620035,
+                    197766118,
+                    316993369,
+                    396687275,
+                    359566431,
+                    576434956,
+                    828023967,
+                    952288090,
+                    671383536,
+                    585750020,
+                    403860571,
+                    82375395,
+                    755119585,
+                    252332879,
+                    647895459,
+                    218703641,
+                    530334823,
+                    774712939,
+                    305429835,
+                    670434144,
+                    556493611,
+                    213370098,
+                    998043190,
+                    521195334,
+                    942045548,
+                    10434520,
+                    289281677,
+                    780617545,
+                    65194926,
+                    266039917,
+                    488890265,
+                    386481506,
+                    187866467,
+                    490016692,
+                    617008577,
+                    266296239,
+                    604624069,
+                    743238038,
+                    466110566,
+                    650028565,
+                    779392418,
+                    679413784,
+                    902528339,
+                    603433615,
+                    134537639,
+                    411796014,
+                    780973669,
+                    606766170,
+                    166687501,
+                    518289156,
+                    190162179,
+                    335622452,
+                    384959675,
+                    976262067,
+                    591473343,
+                    731209984,
+                    917239327,
+                    758080788,
+                    44214270,
+                    925551333,
+                    396887524,
+                    476269625,
+                    322394491,
+                    454040639,
+                    273248396,
+                    664956739,
+                    910021011,
+                    424298432,
+                    402102021,
+                    482158955,
+                    643416441,
+                    663353183,
+                    374051462,
+                    304659343,
+                    802356372,
+                    17186236,
+                    730758087,
+                    349734848,
+                    69873182,
+                    29862683,
+                    368199172,
+                    299116194,
+                    12504930,
+                    53401968,
+                    180512530,
+                    139382185,
+                    614623254,
+                    897145521,
+                    749254111,
+                    766908332,
+                    187759844,
+                    376332313,
+                    515013754,
+                    83097235,
+                    567626189,
+                    340066226,
+                    941604306,
+                    707773628,
+                    704674369,
+                    21781154,
+                    502904107,
+                    127180893,
+                    809322886,
+                    245265622,
+                    795881059,
+                    797483916,
+                    599242388,
+                    744702450,
+                    34227194,
+                    865118460,
+                    96363728,
+                    868514594,
+                    573152231,
+                    530853873,
+                    817025073,
+                    495984592,
+                    350649637,
+                    560560846,
+                    668994192,
+                    216700124,
+                    717051563,
+                    172000660,
+                    984015214,
+                    725740596,
+                    501450325,
+                    671493355,
+                    59975617,
+                    137500816,
+                    46853583,
+                    708229898,
+                    816589650,
+                    314661110,
+                    788040939,
+                    388085267,
+                    552716154,
+                    445111997,
+                    388691576,
+                    873282552,
+                    708119247,
+                    900722506,
+                    492421933,
+                    251999929,
+                    138776776,
+                    142120878,
+                    452349830,
+                    260014813,
+                    641982376,
+                    445850227,
+                    71150546,
+                    740553169,
+                    761368619,
+                    214337709,
+                    246764091,
+                    725946778,
+                    986956786,
+                    567330203,
+                    50018032,
+                    681376476,
+                    590029640,
+                    364103333,
+                    829882652,
+                    349053642,
+                    6583730,
+                    525854721,
+                    360049919,
+                    297535744,
+                    32321170,
+                    405124602,
+                    891181607,
+                    893822816,
+                    503809902,
+                    239177091,
+                    41295053,
+                    988236760,
+                    637410170,
+                    615198424,
+                    168898467,
+                    187322874,
+                    244632154,
+                    323808041,
+                    375683301,
+                    65933138,
+                    58891590,
+                    875879960,
+                    291675441,
+                    527555453,
+                    372571920,
+                    882650339,
+                    210124344,
+                    622054163,
+                    265202794,
+                    984370416,
+                    476862451,
+                    307590595,
+                    964251711,
+                    270179748,
+                    519019516,
+                    425463927,
+                    993373523,
+                    449318712,
+                    627092303,
+                    105327601,
+                    527171055,
+                    136780455,
+                    222662316,
+                    820724193,
+                    541980701,
+                    770619388,
+                    762013746,
+                    302562267,
+                    479084840,
+                    387750924,
+                    433953204,
+                    283983253,
+                    484392405,
+                    587427635,
+                    955621738,
+                    946092931,
+                    902567143,
+                    378391934,
+                    960622567,
+                    279369308,
+                    683839875,
+                    981398785,
+                    693406190,
+                    863014023,
+                    965893669,
+                    375074046,
+                    924992293,
+                    888625877,
+                    921136527,
+                    187524330,
+                    972935273,
+                    581905386,
+                    57568556,
+                    487025594,
+                    659968414,
+                    93107259,
+                    932832589,
+                    245085777,
+                    103662649,
+                    329046032,
+                    79842240,
+                    48853993,
+                    33978387,
+                    592043193,
+                    579608301,
+                    981230344,
+                    533748844,
+                    437375953,
+                    515399088,
+                    396784146,
+                    131771439,
+                    286535969,
+                    565903820,
+                    776150310,
+                    100726669,
+                    764907381,
+                    664393189,
+                    930981447,
+                    870309576,
+                    746121081,
+                    76401210,
+                    427654426,
+                    858599839,
+                    266677889,
+                    254480196,
+                    480760952,
+                    806151228,
+                    617130713,
+                    648713558,
+                    972343263,
+                    633744250,
+                    204717762,
+                    151839551,
+                    704390141,
+                    610529082,
+                    502392900,
+                    601792874,
+                    816796536,
+                    700196939,
+                    511968038,
+                    904376584,
+                    386421498,
+                    686507719,
+                    571255394,
+                    135721832,
+                    22102286,
+                    694190093,
+                    694305321,
+                    586800179,
+                    711078286,
+                    571126475,
+                    190163246,
+                    381719774,
+                    37163874,
+                    622335013,
+                    794059267,
+                    521969582,
+                    160773549,
+                    744361135,
+                    747910192,
+                    462292792,
+                    711349469,
+                    244696522,
+                    938714633,
+                    54222480,
+                    995978551,
+                    807287238,
+                    215551137,
+                    991030577,
+                    15619689,
+                    95775047,
+                    659226585,
+                    133474546,
+                    679432847,
+                    368707060,
+                    779339529,
+                    223236233,
+                    225639589,
+                    854594593,
+                    975567760,
+                    671657641,
+                    910719356,
+                    707032432,
+                    407120253,
+                    121449649,
+                    790684856,
+                    604328858,
+                    554361331,
+                    733798872,
+                    440329582,
+                    13045949,
+                    609315279,
+                    116472697,
+                    161816454,
+                    663106748,
+                    149537980,
+                    582704308,
+                    558902342,
+                    269527074,
+                    155537567,
+                    75242945,
+                    324586288,
+                    374769315,
+                    85249796,
+                    557683798,
+                    771292002,
+                    853007950,
+                    642189326,
+                    264777735,
+                    307076314,
+                    646685044,
+                    91200986,
+                    732671143,
+                    796327709,
+                    169194663,
+                    310700073,
+                    72156325,
+                    743751126,
+                    882258996,
+                    735963292,
+                    146884962,
+                    769906912,
+                    610629606,
+                    566840384,
+                    168937444,
+                    138218401,
+                    657816314,
+                    600197400,
+                    74694266,
+                    604881843,
+                    174818445,
+                    944161388,
+                    973664411,
+                    889725189,
+                    281933527,
+                    241014507,
+                    704740068,
+                    993026360,
+                    499497659,
+                    680172057,
+                    909685932,
+                    10885431,
+                    657459242,
+                    147748855,
+                    736837686,
+                    708360581,
+                    240357632,
+                    864509569,
+                    216066965,
+                    403465359,
+                    560094620,
+                    466314943,
+                    152529334,
+                    62942594,
+                    478566735,
+                    172197973,
+                    711053238,
+                    773245447,
+                    553961554,
+                    102619095,
+                    467319099,
+                    283599672,
+                    259846239,
+                    647665637,
+                    783507747,
+                    828784866,
+                    731483755,
+                    757998008,
+                    186342347,
+                    37703966,
+                    895995101,
+                    60009971,
+                    65597501,
+                    352883500,
+                    436511089,
+                    492656959,
+                    411722037,
+                    524639908,
+                    165278474,
+                    69134264,
+                    766215011,
+                    11890444,
+                    434482126,
+                    977180577,
+                    66704033,
+                    883395654,
+                    320116075,
+                    872531333,
+                    228981624,
+                    453220623,
+                    730953314,
+                    192686879,
+                    786708645,
+                    632432725,
+                    653308526,
+                    796250853,
+                    589628829,
+                    610881372,
+                    596167270,
+                    820488031,
+                    637711476,
+                    86203834,
+                    17023853,
+                    660843936,
+                    918660849,
+                    866213327,
+                    360971299,
+                    279514254,
+                    984883689,
+                    932451967,
+                    524399183,
+                    870301229,
+                    277402894,
+                    308148828,
+                    611975026,
+                    804884863,
+                    428287039,
+                    903209110,
+                    264556837,
+                    679273490,
+                    633425786,
+                    399361752,
+                    413893196,
+                    682200954,
+                    775910365,
+                    299395006,
+                    404524749,
+                    223139605,
+                    306346635,
+                    661375613,
+                    369017627,
+                    334234284,
+                    793481860,
+                    259622986,
+                    475448655,
+                    413909950,
+                    897315618,
+                    831836462,
+                    695381423,
+                    881685429,
+                    915975379,
+                    859470903,
+                    184277248,
+                    601674659,
+                    41158222,
+                    508950140,
+                    752375340,
+                    371841882,
+                    533296381,
+                    925091813,
+                    672482585,
+                    849763993,
+                    250019811,
+                    352696287,
+                    890159928,
+                    996585234,
+                    262078389,
+                    567800728,
+                    311264626,
+                    585524076,
+                    376363640,
+                    326932962,
+                    182406603,
+                    216611882,
+                    842010103,
+                    691144289,
+                    621136997,
+                    12734809,
+                    224315201,
+                    289449065,
+                    606004468,
+                    876571014,
+                    520928305,
+                    205174545,
+                    146520926,
+                    987989116,
+                    17678199,
+                    355793199,
+                    482396690,
+                    644459112,
+                    286732292,
+                    140058698,
+                    770052010,
+                    182740300,
+                    533241560,
+                    997033173,
+                    720229165,
+                    390044928,
+                    477233358,
+                    763904265,
+                    872919406,
+                    785273271,
+                    40077948,
+                    436134690,
+                    320984661,
+                    286689673
+                ],
+                [
+                    788,
+                    607,
+                    793,
+                    14,
+                    163,
+                    6,
+                    787,
+                    239,
+                    229,
+                    770,
+                    66,
+                    754,
+                    170,
+                    762,
+                    543,
+                    211,
+                    696,
+                    194,
+                    328,
+                    239,
+                    700,
+                    849,
+                    140,
+                    279,
+                    175,
+                    727,
+                    334,
+                    418,
+                    389,
+                    394,
+                    298,
+                    398,
+                    282,
+                    39,
+                    834,
+                    19,
+                    521,
+                    519,
+                    91,
+                    310,
+                    538,
+                    202,
+                    337,
+                    924,
+                    806,
+                    879,
+                    437,
+                    905,
+                    576,
+                    879,
+                    138,
+                    422,
+                    737,
+                    270,
+                    885,
+                    447,
+                    163,
+                    689,
+                    519,
+                    828,
+                    351,
+                    692,
+                    621,
+                    608,
+                    320,
+                    720,
+                    204,
+                    305,
+                    65,
+                    164,
+                    29,
+                    608,
+                    373,
+                    360,
+                    475,
+                    848,
+                    133,
+                    227,
+                    959,
+                    307,
+                    737,
+                    594,
+                    876,
+                    322,
+                    762,
+                    568,
+                    364,
+                    879,
+                    427,
+                    932,
+                    197,
+                    539,
+                    152,
+                    84,
+                    412,
+                    754,
+                    205,
+                    452,
+                    262,
+                    331,
+                    802,
+                    111,
+                    255,
+                    798,
+                    752,
+                    776,
+                    429,
+                    311,
+                    548,
+                    105,
+                    868,
+                    593,
+                    156,
+                    846,
+                    946,
+                    596,
+                    391,
+                    879,
+                    276,
+                    326,
+                    631,
+                    846,
+                    203,
+                    840,
+                    9,
+                    931,
+                    546,
+                    873,
+                    208,
+                    559,
+                    795,
+                    482,
+                    667,
+                    772,
+                    150,
+                    464,
+                    792,
+                    726,
+                    99,
+                    539,
+                    261,
+                    845,
+                    498,
+                    803,
+                    763,
+                    48,
+                    665,
+                    843,
+                    162,
+                    548,
+                    305,
+                    241,
+                    5,
+                    73,
+                    522,
+                    55,
+                    238,
+                    258,
+                    509
+                ]
+            ],
+            "output": -1
+        },
+        {
+            "input": [
+                [
+                    846536219,
+                    770722748,
+                    766173002,
+                    944396521,
+                    372010849,
+                    14118998,
+                    880248220,
+                    555177336,
+                    212611763,
+                    708039145,
+                    287135677,
+                    401045311,
+                    670066670,
+                    275569619,
+                    601201024,
+                    878275726,
+                    109275928,
+                    990646225,
+                    37030589,
+                    99843269,
+                    239675784,
+                    574279822,
+                    745546035,
+                    597167782,
+                    665892074,
+                    977630066,
+                    780655033,
+                    54794048,
+                    516576315,
+                    723943236,
+                    938190440,
+                    781864760,
+                    950035529,
+                    148002783,
+                    601142669,
+                    97786778,
+                    568811148,
+                    28168120,
+                    527558714,
+                    813246021,
+                    972673522,
+                    951940107,
+                    932207144,
+                    53717360,
+                    553640311,
+                    391898556,
+                    258107072,
+                    178604401,
+                    369419321,
+                    825105243,
+                    195064023,
+                    493112476,
+                    314448452,
+                    652478164,
+                    418176328,
+                    547037296,
+                    643593727,
+                    321097943,
+                    114780606,
+                    439790883,
+                    85980932,
+                    728157891,
+                    59050944,
+                    701043393,
+                    491674432,
+                    56282603,
+                    226966270,
+                    457454565,
+                    657646268,
+                    21184086,
+                    162638824,
+                    31747116,
+                    768062495,
+                    647658309,
+                    258644041,
+                    849866999,
+                    364280935,
+                    485507511,
+                    67114918,
+                    539937500,
+                    890151684,
+                    238249541,
+                    96205597,
+                    669938817,
+                    730835009,
+                    363242340,
+                    123246860,
+                    683653444,
+                    310469083,
+                    731152256,
+                    995438988,
+                    623377542,
+                    197191655,
+                    178857428,
+                    635097738,
+                    863160021,
+                    253835784,
+                    851611368,
+                    317859947,
+                    220618292,
+                    77057751,
+                    949117411,
+                    728087153,
+                    711018173,
+                    847597824,
+                    383262634,
+                    987583829,
+                    602209776,
+                    855806011,
+                    549618091,
+                    835383817,
+                    247542254,
+                    137057881,
+                    266198184,
+                    141164803,
+                    630367516,
+                    977486443,
+                    865791981,
+                    924279547,
+                    832437213,
+                    89224782,
+                    686316704,
+                    576584846,
+                    663903035,
+                    541251072,
+                    871843179,
+                    700659706,
+                    221835708,
+                    808399839,
+                    779516184,
+                    223130630,
+                    222196532,
+                    581793805,
+                    158148573,
+                    857332869,
+                    910499671,
+                    199589686,
+                    258932930,
+                    132580147,
+                    726874287,
+                    839457863,
+                    474405002,
+                    338225613,
+                    800869404,
+                    913366276,
+                    919320172,
+                    440420621,
+                    108181560,
+                    879082535,
+                    701506632,
+                    145002226,
+                    279559476,
+                    661101974,
+                    58566539,
+                    590271251,
+                    516669370,
+                    572585535,
+                    851670860,
+                    343122449,
+                    315173668,
+                    281906709,
+                    90670120,
+                    133961712,
+                    500117997,
+                    717271663,
+                    641398158,
+                    876739450,
+                    565852431,
+                    853936401,
+                    753771945,
+                    157196295,
+                    167837337,
+                    15226639,
+                    205758646,
+                    805803858,
+                    454381799,
+                    315118225,
+                    198783265,
+                    786915582,
+                    775170900,
+                    628220970,
+                    697904728,
+                    56431594,
+                    340024977,
+                    65780458,
+                    800857585,
+                    833663921,
+                    82093615,
+                    21477660,
+                    655851541,
+                    400555438,
+                    690638704,
+                    285440514,
+                    819299324,
+                    245889509,
+                    610553132,
+                    979008104,
+                    463359619,
+                    942843952,
+                    893544546,
+                    804850402,
+                    686982373,
+                    663917625,
+                    395263055,
+                    689323555,
+                    919614789,
+                    437467334,
+                    648248980,
+                    171399805,
+                    294914621,
+                    253218739,
+                    379672599,
+                    496977766,
+                    821954024,
+                    172211993,
+                    263833286,
+                    351861123,
+                    381370898,
+                    691323479,
+                    150609350,
+                    699966735,
+                    154936755,
+                    285749546,
+                    472934853,
+                    15168664,
+                    274815513,
+                    880265240,
+                    549296523,
+                    578758916,
+                    345629935,
+                    332449409,
+                    804305628,
+                    167625287,
+                    412150577,
+                    66506947,
+                    224160006,
+                    708313344,
+                    810072308,
+                    848089791,
+                    367669926,
+                    721130987,
+                    658587211,
+                    764088441,
+                    262958432,
+                    728442534,
+                    237586296,
+                    957103516,
+                    499922578,
+                    49081915,
+                    153795098,
+                    324804332,
+                    777848592,
+                    264589533,
+                    962434474,
+                    765815434,
+                    473492944,
+                    383699925,
+                    198749677,
+                    951553287,
+                    224558876,
+                    8819408,
+                    336134043,
+                    231778238,
+                    909337267,
+                    798685257,
+                    757344393,
+                    491692779,
+                    240097463,
+                    972753955,
+                    10223050,
+                    444409468,
+                    957928897,
+                    432275837,
+                    401860807,
+                    480380487,
+                    40366946,
+                    808781383,
+                    660604718,
+                    839648437,
+                    851160675,
+                    93424201,
+                    901698861,
+                    868462508,
+                    162688106,
+                    478540899,
+                    542494754,
+                    738987265,
+                    442682517,
+                    424656934,
+                    583451861,
+                    262344742,
+                    969970730,
+                    694420343,
+                    317343073,
+                    362117383,
+                    499951768,
+                    960761267,
+                    674147087,
+                    142142832,
+                    935540679,
+                    270836102,
+                    178906148,
+                    483842433,
+                    838258045,
+                    861827793,
+                    337987567,
+                    545742658,
+                    182324980,
+                    126302540,
+                    678107298,
+                    198102089,
+                    651655378,
+                    626070274,
+                    221637509,
+                    523034704,
+                    32669593,
+                    7817515,
+                    822845741,
+                    601844576,
+                    563045975,
+                    669360521,
+                    220435757,
+                    421096343,
+                    989985743,
+                    135839271,
+                    684431838,
+                    332155904,
+                    773791158,
+                    243099026,
+                    813356635,
+                    419076530,
+                    164764717,
+                    330928186,
+                    272424948,
+                    376952389,
+                    250448962,
+                    938390310,
+                    247855144,
+                    279597606,
+                    510318701,
+                    515133535,
+                    180256010,
+                    82920756,
+                    493017522,
+                    69171385,
+                    605775236,
+                    280886649,
+                    117229006,
+                    168537166,
+                    259533613,
+                    668161605,
+                    405168115,
+                    396693273,
+                    294717445,
+                    357056823,
+                    280689669,
+                    634339503,
+                    923820384,
+                    860066237,
+                    794732948,
+                    359547720,
+                    953498273,
+                    774696798,
+                    927851351,
+                    762355283,
+                    851958419,
+                    960811077,
+                    312643824,
+                    197820836,
+                    986414742,
+                    262304648,
+                    676486605,
+                    584187581,
+                    317758758,
+                    792915578,
+                    253837074,
+                    103731813,
+                    827317377,
+                    185670515,
+                    638276853,
+                    153253686,
+                    632144362,
+                    128533486,
+                    575325241,
+                    699628504,
+                    137652892,
+                    376784720,
+                    318762474,
+                    866347783,
+                    376660752,
+                    780514168,
+                    403663657,
+                    157361257,
+                    970837292,
+                    344599288,
+                    983200137,
+                    916013012,
+                    691286985,
+                    769319154,
+                    334536357,
+                    960388162,
+                    101832450,
+                    670362226,
+                    987891318,
+                    462169341,
+                    556669560,
+                    194885479,
+                    150701396,
+                    170293989,
+                    314908691,
+                    171043640,
+                    141428907,
+                    362364847,
+                    99507606,
+                    672021256,
+                    74052577,
+                    135266607,
+                    108527457,
+                    957860552,
+                    388013428,
+                    342352323,
+                    398517853,
+                    571381333,
+                    700281417,
+                    195360527,
+                    505674312,
+                    841115065,
+                    430929636,
+                    338164615,
+                    675756820,
+                    810718572,
+                    382525019,
+                    731683834,
+                    25876111,
+                    886036943,
+                    999400095,
+                    337897273,
+                    91238178,
+                    696619045,
+                    161879537,
+                    393782163,
+                    860343558,
+                    582610612,
+                    725021313,
+                    610564782,
+                    963577463,
+                    724608420,
+                    801901352,
+                    364275057,
+                    833123052,
+                    322492898,
+                    866804341,
+                    738198704,
+                    59045908,
+                    54389352,
+                    14476131,
+                    211688740,
+                    445724899,
+                    66997491,
+                    260113698,
+                    58730719,
+                    598620380,
+                    74111164,
+                    923667082,
+                    564784120,
+                    234010253,
+                    282591699,
+                    156089351,
+                    959719207,
+                    611101341,
+                    654343909,
+                    219420223,
+                    168538076,
+                    219596971,
+                    139520721,
+                    57212743,
+                    685528728,
+                    818359180,
+                    875542484,
+                    900418968,
+                    439878394,
+                    183346057,
+                    195658112,
+                    15738462,
+                    358353564,
+                    9993660,
+                    518014843,
+                    975310401,
+                    757462530,
+                    292264827,
+                    994043680,
+                    279021626,
+                    986775127,
+                    513005616,
+                    370911373,
+                    121785521,
+                    370416039,
+                    184051692,
+                    124604802,
+                    465194191,
+                    95273927,
+                    86844885,
+                    926120136,
+                    976996072,
+                    476659624,
+                    570205471,
+                    966595230,
+                    108014045,
+                    40474144,
+                    717056081,
+                    184852206,
+                    735571978,
+                    242667055,
+                    524074317,
+                    18035175,
+                    37742671,
+                    388778318,
+                    719898363,
+                    186209492,
+                    554016263,
+                    767108978,
+                    106487164,
+                    744345583,
+                    447302497,
+                    803008636,
+                    187716410,
+                    362397864,
+                    3229483,
+                    879664435,
+                    197565715,
+                    111119873,
+                    815327353,
+                    696956457,
+                    489917403,
+                    486505499,
+                    740815385,
+                    603941500,
+                    330792777,
+                    22631819,
+                    58692280,
+                    972476077,
+                    194443856,
+                    191642931,
+                    655447563,
+                    622877737,
+                    322250225,
+                    869328412,
+                    72786928,
+                    863138774,
+                    756074198,
+                    244516111,
+                    384503019,
+                    273579057,
+                    716736776,
+                    649753886,
+                    342100446,
+                    104599688,
+                    39170141,
+                    600847258,
+                    806011863,
+                    495199160,
+                    785432345,
+                    252478260,
+                    17665407,
+                    525888370,
+                    841315735,
+                    940552977,
+                    700218926,
+                    559812359,
+                    830854163,
+                    454052298,
+                    824960653,
+                    169414182,
+                    576293855,
+                    616068249,
+                    559866468,
+                    95473241,
+                    560254483,
+                    67343040,
+                    761084590,
+                    396797447,
+                    146520642,
+                    887909442,
+                    540324651,
+                    311550914,
+                    397311476,
+                    768668664,
+                    9038648,
+                    832365711,
+                    355728474,
+                    558552870,
+                    738911278,
+                    967580694,
+                    23719428,
+                    819294717,
+                    716068816,
+                    99090656,
+                    733741178,
+                    952534638,
+                    406220724,
+                    558807554,
+                    716572071,
+                    270272504,
+                    591968281,
+                    327757595,
+                    386908696,
+                    544620015,
+                    967748108,
+                    296589552,
+                    707304799,
+                    967462504,
+                    113357805,
+                    586858424,
+                    77153081,
+                    783461791,
+                    898585394,
+                    654827304,
+                    777495283,
+                    671884201,
+                    197994769,
+                    579933263,
+                    292799007,
+                    36681101,
+                    569040332,
+                    460436650,
+                    82173998,
+                    988789954,
+                    462806523,
+                    518208685,
+                    348405222,
+                    466063073,
+                    131089089,
+                    793942133,
+                    645111160,
+                    461289582,
+                    68330996,
+                    828093707,
+                    214076041,
+                    511381630,
+                    214470120,
+                    194849454,
+                    866522765,
+                    386136245,
+                    805476920,
+                    30778403,
+                    84265896,
+                    564087728,
+                    631271855,
+                    147769039,
+                    382765478,
+                    697529032,
+                    48100999,
+                    18001946,
+                    995265412,
+                    381073750,
+                    354312883,
+                    443059983,
+                    435998067,
+                    533497578,
+                    850653273,
+                    649827803,
+                    595781644,
+                    650505877,
+                    302917757,
+                    917320419,
+                    776883444,
+                    909282297,
+                    241996483,
+                    450183548,
+                    392305333,
+                    994657567,
+                    924480573,
+                    342198394,
+                    877322959,
+                    160508767,
+                    952257084,
+                    784921753,
+                    943188575,
+                    631938172,
+                    326663070,
+                    218612285,
+                    60451922,
+                    243867735,
+                    784738012,
+                    738605440,
+                    892733785,
+                    465026336,
+                    189516783,
+                    547866042,
+                    136872539,
+                    267665261,
+                    648957052,
+                    627404636,
+                    874226608,
+                    950105517,
+                    173162876,
+                    606810412,
+                    953434399,
+                    434851407,
+                    550659864,
+                    820597564,
+                    33020189,
+                    790362681,
+                    70336990,
+                    470847449,
+                    770142640,
+                    989784746,
+                    235712717,
+                    502662405,
+                    387238252,
+                    984694610,
+                    855813000,
+                    260194004,
+                    860475502,
+                    811401899,
+                    318155398,
+                    255913955,
+                    375739274,
+                    267510703,
+                    314457131,
+                    113957108,
+                    526002678,
+                    504767576,
+                    635921782,
+                    508664341,
+                    464211655,
+                    778769651,
+                    286774238,
+                    584416105,
+                    677333465,
+                    621660919,
+                    478340442,
+                    838660728,
+                    410276587,
+                    797627902,
+                    667066260,
+                    811101914,
+                    991356155,
+                    920504039,
+                    137009929,
+                    468638122,
+                    898059583,
+                    389834701,
+                    385877542,
+                    654571928,
+                    821696097,
+                    261533862,
+                    369964287,
+                    241623427,
+                    487937991,
+                    609328634,
+                    221377434,
+                    565486294,
+                    312863942,
+                    13930721,
+                    195968957,
+                    471639243,
+                    556528266,
+                    160209026,
+                    118338136,
+                    24213939,
+                    947914835,
+                    850491402,
+                    88039510,
+                    305235381,
+                    581788403,
+                    498391760,
+                    556097620,
+                    804390128,
+                    138188059,
+                    357779086,
+                    838884757,
+                    244279701,
+                    557975361,
+                    509629020,
+                    58602309,
+                    24665549,
+                    275211128,
+                    21339350,
+                    682912619,
+                    974081241,
+                    920492676,
+                    132765199,
+                    198321976,
+                    537608352,
+                    889454441,
+                    912690116,
+                    569977783,
+                    151969745,
+                    959367986,
+                    769271276,
+                    705311866,
+                    944202755,
+                    785120996,
+                    784664230,
+                    548517235,
+                    692847802,
+                    587621836,
+                    166241101,
+                    501714341,
+                    120324535,
+                    737067763,
+                    671936921,
+                    601190534,
+                    554533874,
+                    847622821,
+                    26711959,
+                    817695707,
+                    630039038,
+                    900262388,
+                    714734099,
+                    124186358,
+                    156843359,
+                    368670461,
+                    36056156,
+                    941447694,
+                    274268311,
+                    826504985,
+                    270347712,
+                    920707668,
+                    241721701,
+                    99257863,
+                    82346379,
+                    421861243,
+                    642449329,
+                    617063984,
+                    167103719,
+                    155409061,
+                    368774034,
+                    370677802,
+                    226285025,
+                    134403850,
+                    831558567,
+                    156299049,
+                    735224829,
+                    334052841,
+                    346490213,
+                    595192647,
+                    977826775,
+                    766457256,
+                    444378728,
+                    809842606,
+                    326574309,
+                    706754620,
+                    884009363,
+                    930918780,
+                    231342734,
+                    222932849,
+                    300479134,
+                    240703369,
+                    858984214,
+                    669329576,
+                    30590081,
+                    702526489,
+                    662126327,
+                    910331637,
+                    589892122,
+                    909072297,
+                    983150061,
+                    274723200,
+                    662943453,
+                    359858996,
+                    120203978,
+                    489429352,
+                    161291730,
+                    547422833,
+                    190139855,
+                    26286759,
+                    712899550,
+                    457902581,
+                    928832512,
+                    961603152,
+                    343678817,
+                    259933122,
+                    268970861,
+                    984460471,
+                    631483207,
+                    66808402,
+                    769130150,
+                    945816971,
+                    71711230,
+                    720654582,
+                    76008202,
+                    168282333,
+                    159349153,
+                    298115932,
+                    372663731,
+                    813050951,
+                    838864824,
+                    847880332,
+                    217403417,
+                    757490064,
+                    497328218,
+                    120036368,
+                    587338597,
+                    627316902,
+                    751654423,
+                    188269806,
+                    47285597,
+                    239221972,
+                    615070828,
+                    341891533,
+                    657411328,
+                    630807593,
+                    997158493,
+                    966966110,
+                    545567770,
+                    675430955,
+                    65830710,
+                    341204602,
+                    533410159,
+                    452640754,
+                    775894191,
+                    150755207,
+                    166160553,
+                    761803897,
+                    122289133,
+                    325524403,
+                    850653128,
+                    859186270,
+                    126654027,
+                    370264982,
+                    39450865,
+                    252117802,
+                    805623750,
+                    980978936,
+                    365754982,
+                    397775909,
+                    344723696,
+                    820474758,
+                    30614090,
+                    700600730,
+                    407674911,
+                    124625781,
+                    296220867,
+                    958382551,
+                    52791641,
+                    673356631,
+                    407693650,
+                    477123521,
+                    168946864,
+                    789291074,
+                    949979902,
+                    907830968,
+                    148270622,
+                    26811594,
+                    390215808,
+                    258179622,
+                    695249260,
+                    674534516,
+                    939319747,
+                    643287609,
+                    582349211,
+                    380705950,
+                    930278400,
+                    224258206,
+                    802595764,
+                    820737827,
+                    470385759,
+                    189111860,
+                    723440071,
+                    945104339,
+                    686688207,
+                    789566906,
+                    923597917,
+                    340542634,
+                    350777197,
+                    397125535,
+                    38955027,
+                    578929807,
+                    77442357,
+                    533843522,
+                    391048693,
+                    465666329,
+                    218149176,
+                    372841013,
+                    529873690,
+                    343004457,
+                    202665409,
+                    763580288,
+                    19928635,
+                    386387231,
+                    294334786,
+                    315787638,
+                    835626321,
+                    191862273,
+                    172495734,
+                    885414602,
+                    511114323,
+                    254381502,
+                    449283745,
+                    161470140,
+                    901902018,
+                    692025118,
+                    556426246,
+                    64908584,
+                    643360988,
+                    324859267,
+                    810596625,
+                    33878789,
+                    736412123,
+                    933221872,
+                    504474967,
+                    177831343,
+                    124556070,
+                    523422530,
+                    650713827,
+                    957711514,
+                    218261758,
+                    923062711,
+                    844994715,
+                    673127398,
+                    615066441,
+                    768567460,
+                    270211763,
+                    310588533,
+                    337518106,
+                    710712477,
+                    456208110,
+                    841523926,
+                    765371589,
+                    902942698,
+                    803338172,
+                    192662171,
+                    823491258,
+                    969590089,
+                    848517996,
+                    730238266,
+                    21955006,
+                    134782498,
+                    441950579,
+                    511659451,
+                    499263805,
+                    515098281,
+                    46452887,
+                    744037871,
+                    664710426,
+                    578912928,
+                    428339274,
+                    542126124,
+                    891801417,
+                    618905553,
+                    498861748,
+                    568714157,
+                    838938490,
+                    941492442,
+                    435127210,
+                    624131151,
+                    510331096,
+                    883082435,
+                    651894788,
+                    456145255,
+                    174433317,
+                    452372254,
+                    471233781,
+                    780573848,
+                    89517575,
+                    280416967,
+                    316678833,
+                    966536055,
+                    157288781,
+                    697678599,
+                    828192769,
+                    272454423,
+                    162845805,
+                    970802342,
+                    240631996,
+                    579082461,
+                    539902274,
+                    476032181,
+                    478988396,
+                    554639968,
+                    539690023,
+                    255660055,
+                    23067789,
+                    63376848,
+                    78990843,
+                    434790244,
+                    696726981,
+                    99634589,
+                    615197914,
+                    157644954,
+                    942209662,
+                    753726549,
+                    999417326,
+                    443152804,
+                    429337614,
+                    17283649,
+                    794748699,
+                    740469110,
+                    65658062,
+                    474257353,
+                    747352931,
+                    365096355,
+                    694280481,
+                    417877725,
+                    356062280,
+                    494452837,
+                    247639811,
+                    959479546,
+                    998683550,
+                    199102334,
+                    217312372,
+                    615333733,
+                    478322470,
+                    711872331,
+                    536088479,
+                    445120260,
+                    837263083,
+                    422898670,
+                    37154082,
+                    127089544,
+                    178451829,
+                    761477803,
+                    355711834,
+                    221646210,
+                    441484330,
+                    197731511,
+                    832727395,
+                    180204241,
+                    845991835,
+                    176570830,
+                    204786968,
+                    559851877,
+                    96186925,
+                    964926040,
+                    811766764,
+                    654820188,
+                    876089872,
+                    288909148,
+                    771236930,
+                    799565530,
+                    729374442,
+                    589502690,
+                    310225009,
+                    786491865,
+                    341804542,
+                    880842240,
+                    956622558,
+                    754731085,
+                    196329134,
+                    835508451,
+                    336640632,
+                    646715845,
+                    637728811,
+                    194241851,
+                    478765511,
+                    535215275,
+                    308703815,
+                    526344755,
+                    828213251,
+                    848355081,
+                    298545117,
+                    655252600,
+                    412322383,
+                    444210517,
+                    165805775,
+                    646537410,
+                    338903141,
+                    364385293,
+                    654375724,
+                    726615909,
+                    562698434,
+                    653481161,
+                    618948703,
+                    403613118,
+                    792194026,
+                    969129596,
+                    998432503,
+                    162554106,
+                    977777310,
+                    122427648,
+                    234373912,
+                    630607236,
+                    643651902,
+                    262645261,
+                    466969725,
+                    250524601,
+                    213294048,
+                    947563935,
+                    728648032,
+                    489405413,
+                    15899722,
+                    575322569,
+                    952704443,
+                    611300250,
+                    104029689,
+                    898077956,
+                    13154709,
+                    398086270,
+                    565202245,
+                    551110355,
+                    198287997,
+                    416615988,
+                    491091122,
+                    170404152,
+                    663557396,
+                    260995551,
+                    148075982,
+                    211551189,
+                    561582947,
+                    770984143,
+                    213216901,
+                    587482244,
+                    60251256,
+                    245990866,
+                    306779467,
+                    470557250,
+                    171604360,
+                    112994728,
+                    569377385,
+                    430670147,
+                    658793485,
+                    944153534,
+                    160819873,
+                    738642182,
+                    411927462,
+                    91959141,
+                    915906290,
+                    913833947,
+                    589968024,
+                    566657688,
+                    210005818,
+                    210363147,
+                    754051655,
+                    832613933,
+                    429718520,
+                    464368894,
+                    250087378,
+                    815527654,
+                    513264056,
+                    702939242,
+                    809169688,
+                    442785251,
+                    377281147,
+                    604554432,
+                    860338794,
+                    812847702,
+                    940426413,
+                    639826687,
+                    233969632,
+                    852616574,
+                    476611804,
+                    266654044,
+                    687943958,
+                    945502390,
+                    264171160,
+                    272764980,
+                    785418029,
+                    622211090,
+                    516570468,
+                    300594466,
+                    492736710,
+                    131353039,
+                    41636576,
+                    955571254,
+                    240056564,
+                    491777423,
+                    71329233,
+                    384460015,
+                    43512778,
+                    166846867,
+                    237179105,
+                    124826404,
+                    502514424,
+                    437694270,
+                    308459366,
+                    160874485,
+                    913166781,
+                    471590711,
+                    805084951,
+                    537020147,
+                    254821197,
+                    171590036,
+                    657011514
+                ],
+                [
+                    795,
+                    812,
+                    723,
+                    867,
+                    792,
+                    910,
+                    241,
+                    673,
+                    1172,
+                    252,
+                    605,
+                    1194,
+                    208,
+                    833,
+                    1069,
+                    995,
+                    1140,
+                    330,
+                    1090,
+                    563,
+                    993,
+                    716,
+                    569,
+                    475,
+                    381,
+                    875,
+                    19,
+                    793,
+                    358,
+                    919,
+                    663,
+                    214,
+                    1225,
+                    1139,
+                    669,
+                    1037,
+                    555,
+                    293,
+                    563,
+                    153,
+                    746,
+                    1135,
+                    511,
+                    929,
+                    878,
+                    607,
+                    351,
+                    1097,
+                    126,
+                    1080,
+                    567,
+                    956,
+                    283,
+                    439,
+                    448,
+                    557,
+                    494,
+                    1219,
+                    658,
+                    803,
+                    305,
+                    420,
+                    1153,
+                    1227,
+                    980,
+                    1006,
+                    335,
+                    1257,
+                    204,
+                    1268,
+                    930,
+                    1201,
+                    505,
+                    61,
+                    1087,
+                    729,
+                    1141,
+                    435,
+                    186,
+                    49,
+                    958,
+                    903,
+                    1085,
+                    377,
+                    603,
+                    1057,
+                    1199,
+                    955,
+                    947,
+                    979,
+                    99,
+                    589,
+                    411,
+                    986,
+                    783,
+                    1190,
+                    767,
+                    337,
+                    614,
+                    1262,
+                    77,
+                    422,
+                    1124,
+                    566,
+                    1094,
+                    1035,
+                    780,
+                    701,
+                    893,
+                    65,
+                    621,
+                    1230,
+                    325,
+                    743,
+                    1124,
+                    692,
+                    864,
+                    195,
+                    287,
+                    610,
+                    449,
+                    740,
+                    595,
+                    331,
+                    1273,
+                    774,
+                    940,
+                    794,
+                    436,
+                    917,
+                    721,
+                    1077,
+                    554,
+                    211,
+                    943,
+                    865,
+                    460,
+                    483,
+                    421,
+                    920,
+                    64,
+                    293,
+                    978,
+                    943,
+                    218,
+                    850,
+                    1248,
+                    748,
+                    1046,
+                    905,
+                    1211,
+                    139,
+                    984,
+                    241,
+                    92,
+                    1182,
+                    248,
+                    895,
+                    809,
+                    367,
+                    211,
+                    1232,
+                    1074,
+                    1046,
+                    187,
+                    1160,
+                    690,
+                    617,
+                    873,
+                    348,
+                    1111,
+                    48,
+                    860,
+                    209,
+                    733,
+                    980,
+                    410,
+                    197,
+                    880,
+                    103,
+                    36,
+                    258,
+                    78,
+                    687,
+                    1201,
+                    1120,
+                    329,
+                    29,
+                    75,
+                    883,
+                    675,
+                    152,
+                    986,
+                    267,
+                    472,
+                    256,
+                    173,
+                    1019,
+                    486,
+                    100,
+                    1199,
+                    803,
+                    659,
+                    99,
+                    1098,
+                    483,
+                    1219,
+                    374,
+                    889,
+                    814,
+                    924,
+                    529,
+                    918,
+                    611,
+                    58,
+                    248,
+                    1141,
+                    695,
+                    64,
+                    340,
+                    953,
+                    434,
+                    736,
+                    316,
+                    335,
+                    645,
+                    827,
+                    902,
+                    438,
+                    1087,
+                    1217,
+                    1050,
+                    880,
+                    141,
+                    112,
+                    659,
+                    63,
+                    698,
+                    126,
+                    368,
+                    190,
+                    241,
+                    471,
+                    936,
+                    293,
+                    780,
+                    567,
+                    1044,
+                    844,
+                    941,
+                    1130,
+                    482,
+                    507,
+                    1017,
+                    719,
+                    352,
+                    706,
+                    356,
+                    433,
+                    166,
+                    122,
+                    155,
+                    975,
+                    159,
+                    145,
+                    362,
+                    1010,
+                    907,
+                    1040,
+                    929,
+                    595,
+                    279,
+                    607,
+                    829,
+                    1140,
+                    1239,
+                    1022,
+                    543,
+                    1120,
+                    103,
+                    1038,
+                    97,
+                    250,
+                    559,
+                    253,
+                    934,
+                    1097,
+                    823,
+                    977,
+                    478,
+                    1123,
+                    36,
+                    957,
+                    499,
+                    584,
+                    519,
+                    914,
+                    299,
+                    14,
+                    1234,
+                    1083,
+                    342,
+                    1232,
+                    530,
+                    409,
+                    873,
+                    1237,
+                    493,
+                    1211,
+                    88,
+                    354,
+                    717,
+                    317,
+                    322,
+                    912,
+                    568,
+                    351,
+                    693,
+                    1018,
+                    626,
+                    430,
+                    46,
+                    751,
+                    978,
+                    1068,
+                    40,
+                    23,
+                    382,
+                    829,
+                    442,
+                    1119,
+                    1023,
+                    522,
+                    627,
+                    502,
+                    554,
+                    897,
+                    176,
+                    615,
+                    178,
+                    211,
+                    1232,
+                    1226,
+                    354,
+                    419,
+                    346,
+                    642,
+                    346,
+                    394,
+                    401,
+                    24,
+                    878,
+                    781,
+                    1195,
+                    625,
+                    1033,
+                    706,
+                    1247,
+                    405,
+                    34,
+                    1093,
+                    914,
+                    1221,
+                    50,
+                    292,
+                    1232,
+                    715,
+                    529,
+                    165,
+                    581,
+                    1164,
+                    67,
+                    85,
+                    574,
+                    63,
+                    734,
+                    1008,
+                    920,
+                    570,
+                    734,
+                    849,
+                    1207,
+                    791,
+                    275,
+                    555,
+                    141,
+                    675,
+                    881,
+                    340,
+                    605,
+                    893,
+                    914,
+                    332,
+                    182,
+                    718,
+                    1268,
+                    606,
+                    388,
+                    128,
+                    416,
+                    56,
+                    95,
+                    565,
+                    873,
+                    626,
+                    312,
+                    695,
+                    649,
+                    1228,
+                    569,
+                    373,
+                    819,
+                    682,
+                    408,
+                    981,
+                    230,
+                    1201,
+                    1000,
+                    771,
+                    1183,
+                    420,
+                    1101,
+                    726,
+                    1063,
+                    967,
+                    449,
+                    956,
+                    1169,
+                    400,
+                    894,
+                    141,
+                    699,
+                    584,
+                    842,
+                    777,
+                    553,
+                    17,
+                    730,
+                    843,
+                    943,
+                    824,
+                    574,
+                    209,
+                    1250,
+                    529,
+                    400,
+                    1131,
+                    250,
+                    352,
+                    823,
+                    837,
+                    707,
+                    427,
+                    513,
+                    1182,
+                    738,
+                    245,
+                    1112,
+                    93,
+                    513,
+                    578,
+                    634,
+                    665,
+                    1064,
+                    617,
+                    842,
+                    3,
+                    1055,
+                    761,
+                    370,
+                    434,
+                    1150,
+                    49,
+                    498,
+                    382,
+                    1011,
+                    150,
+                    436,
+                    1234,
+                    442,
+                    472,
+                    1014,
+                    215,
+                    587,
+                    61,
+                    644,
+                    358,
+                    1103,
+                    768,
+                    723,
+                    866,
+                    995,
+                    1221,
+                    238,
+                    181,
+                    1253,
+                    212,
+                    750,
+                    800,
+                    745,
+                    549,
+                    480,
+                    155,
+                    982,
+                    58,
+                    640,
+                    52,
+                    434,
+                    1189,
+                    1227,
+                    1055,
+                    446,
+                    632,
+                    259,
+                    1120,
+                    597,
+                    653,
+                    874,
+                    210,
+                    304,
+                    1161,
+                    1263,
+                    88,
+                    112,
+                    982,
+                    742,
+                    167,
+                    791,
+                    597,
+                    1102,
+                    892,
+                    1056,
+                    603,
+                    506,
+                    60,
+                    1134,
+                    498,
+                    65,
+                    230,
+                    748,
+                    702,
+                    315,
+                    483,
+                    392,
+                    979,
+                    496,
+                    1148,
+                    1031,
+                    26,
+                    879,
+                    992,
+                    1072,
+                    78,
+                    312,
+                    208,
+                    1207,
+                    596,
+                    624,
+                    13,
+                    612,
+                    41,
+                    186,
+                    762,
+                    449,
+                    652,
+                    1203,
+                    65,
+                    682,
+                    543,
+                    76,
+                    194,
+                    449,
+                    459,
+                    731,
+                    622,
+                    425,
+                    566,
+                    253,
+                    261,
+                    261,
+                    98,
+                    508,
+                    1048,
+                    871,
+                    842,
+                    58,
+                    1226,
+                    1193,
+                    5,
+                    951,
+                    445,
+                    858,
+                    263,
+                    564,
+                    729,
+                    686,
+                    1152,
+                    801,
+                    1127,
+                    390,
+                    219,
+                    1128,
+                    157,
+                    883,
+                    900,
+                    1013,
+                    331,
+                    359,
+                    341,
+                    274,
+                    334,
+                    1264,
+                    144,
+                    114,
+                    938,
+                    1013,
+                    403,
+                    886,
+                    687,
+                    1214,
+                    72,
+                    796,
+                    720,
+                    1217,
+                    1175,
+                    1160,
+                    1094,
+                    1148,
+                    63,
+                    1270,
+                    654,
+                    136,
+                    455,
+                    574,
+                    871,
+                    794,
+                    890,
+                    437,
+                    660,
+                    637,
+                    1052,
+                    1002,
+                    222,
+                    333,
+                    710,
+                    515,
+                    637,
+                    848,
+                    61,
+                    940,
+                    517,
+                    520,
+                    882,
+                    871,
+                    399,
+                    524,
+                    131,
+                    330,
+                    486,
+                    903,
+                    1235,
+                    538,
+                    1032,
+                    878,
+                    150,
+                    673,
+                    988,
+                    917,
+                    218,
+                    1257,
+                    233,
+                    947,
+                    137,
+                    1117,
+                    752,
+                    456,
+                    1054,
+                    544,
+                    70,
+                    52,
+                    193,
+                    976,
+                    53,
+                    729,
+                    749,
+                    426,
+                    989,
+                    922,
+                    981,
+                    891,
+                    772,
+                    261,
+                    385,
+                    104,
+                    424,
+                    1183,
+                    344,
+                    164,
+                    460,
+                    18,
+                    280,
+                    258,
+                    336,
+                    809,
+                    1112,
+                    1153,
+                    956,
+                    94,
+                    800,
+                    1069,
+                    1206,
+                    707,
+                    700,
+                    561,
+                    1145,
+                    351,
+                    118,
+                    429,
+                    1115,
+                    523,
+                    1133,
+                    394,
+                    662,
+                    605,
+                    1203,
+                    1003,
+                    542,
+                    711,
+                    1045,
+                    872,
+                    610,
+                    653,
+                    105,
+                    784,
+                    1217,
+                    645,
+                    985,
+                    646,
+                    38,
+                    955,
+                    586,
+                    1237,
+                    64,
+                    300,
+                    102,
+                    387,
+                    1245,
+                    294,
+                    499,
+                    295,
+                    1021,
+                    320,
+                    1268,
+                    229,
+                    25,
+                    88,
+                    352,
+                    1240,
+                    812,
+                    362,
+                    1,
+                    328,
+                    328,
+                    993,
+                    813,
+                    144,
+                    903,
+                    964,
+                    862,
+                    1159,
+                    985,
+                    38,
+                    379,
+                    216,
+                    1035,
+                    39,
+                    502,
+                    801,
+                    752,
+                    923,
+                    622,
+                    622,
+                    506,
+                    73,
+                    716,
+                    625,
+                    750,
+                    483,
+                    1044,
+                    478,
+                    870,
+                    313,
+                    225,
+                    275,
+                    635,
+                    320,
+                    1256,
+                    1084,
+                    580,
+                    862,
+                    484,
+                    999,
+                    1259,
+                    1245,
+                    197,
+                    197,
+                    421,
+                    948,
+                    746,
+                    319,
+                    676,
+                    1158,
+                    329,
+                    1026,
+                    556,
+                    548,
+                    1200,
+                    528,
+                    87,
+                    68,
+                    1163,
+                    1015,
+                    679,
+                    189,
+                    363,
+                    1048,
+                    144,
+                    305,
+                    911,
+                    1099,
+                    994,
+                    887,
+                    1117,
+                    885,
+                    1157,
+                    1125,
+                    619,
+                    654,
+                    352,
+                    1116,
+                    660,
+                    447,
+                    1271,
+                    489,
+                    1074,
+                    1186,
+                    1186,
+                    423,
+                    1233,
+                    363,
+                    426,
+                    553,
+                    1150,
+                    340,
+                    619,
+                    394,
+                    838,
+                    679,
+                    894,
+                    851,
+                    713,
+                    1091,
+                    1186,
+                    285,
+                    748,
+                    523,
+                    867,
+                    699,
+                    80,
+                    83,
+                    214,
+                    805,
+                    618,
+                    830,
+                    210,
+                    1242,
+                    834,
+                    1076,
+                    1242,
+                    329,
+                    757,
+                    1180,
+                    1245,
+                    1199,
+                    104,
+                    766,
+                    1016,
+                    388,
+                    838,
+                    287,
+                    616,
+                    775,
+                    893,
+                    895,
+                    1206,
+                    427,
+                    557,
+                    106,
+                    672,
+                    348,
+                    942,
+                    233,
+                    579,
+                    557,
+                    269,
+                    131,
+                    372,
+                    1234,
+                    396,
+                    353,
+                    605,
+                    107,
+                    846,
+                    386,
+                    726,
+                    543,
+                    560,
+                    29,
+                    1181,
+                    961,
+                    268,
+                    923,
+                    748,
+                    122,
+                    786,
+                    951,
+                    84,
+                    385,
+                    265,
+                    761,
+                    602,
+                    944,
+                    134,
+                    957,
+                    494,
+                    921,
+                    1240,
+                    678,
+                    618,
+                    1185,
+                    909,
+                    269,
+                    996,
+                    1057,
+                    1114,
+                    733,
+                    709,
+                    623,
+                    781,
+                    872,
+                    939,
+                    713,
+                    759,
+                    302,
+                    421,
+                    6,
+                    246,
+                    771,
+                    430,
+                    91,
+                    720,
+                    808,
+                    281,
+                    1032,
+                    660,
+                    705,
+                    1254,
+                    108,
+                    1082,
+                    408,
+                    828,
+                    724,
+                    818,
+                    938,
+                    915,
+                    601,
+                    1097,
+                    490,
+                    638,
+                    35,
+                    83,
+                    469,
+                    246,
+                    982,
+                    753,
+                    907,
+                    483,
+                    56,
+                    1208,
+                    901,
+                    1035,
+                    1028,
+                    1076,
+                    359,
+                    308,
+                    370,
+                    373,
+                    266,
+                    398,
+                    470,
+                    496,
+                    558,
+                    440,
+                    303,
+                    93,
+                    857,
+                    767,
+                    786,
+                    1225,
+                    441,
+                    789,
+                    840,
+                    401,
+                    301,
+                    1248,
+                    1007,
+                    573,
+                    808,
+                    1260,
+                    793,
+                    345,
+                    19,
+                    1057,
+                    481,
+                    846,
+                    100,
+                    854,
+                    475,
+                    540,
+                    10,
+                    883,
+                    758,
+                    492,
+                    687,
+                    826,
+                    802,
+                    421,
+                    781,
+                    1250,
+                    907,
+                    258,
+                    591,
+                    606,
+                    909,
+                    94,
+                    276,
+                    1208,
+                    1059,
+                    10,
+                    3,
+                    592,
+                    1032,
+                    965,
+                    615,
+                    21,
+                    775,
+                    853,
+                    364,
+                    302,
+                    1113,
+                    7,
+                    847,
+                    33,
+                    750,
+                    95,
+                    810,
+                    531,
+                    242,
+                    678,
+                    654,
+                    266,
+                    715,
+                    756,
+                    1034,
+                    756,
+                    1053,
+                    1022,
+                    53,
+                    986,
+                    64,
+                    19,
+                    49,
+                    346,
+                    1110,
+                    1272,
+                    89,
+                    62,
+                    1036,
+                    64,
+                    479,
+                    774,
+                    849,
+                    707,
+                    645,
+                    701,
+                    1078,
+                    791,
+                    619,
+                    1218,
+                    192,
+                    234,
+                    535,
+                    1174,
+                    550,
+                    649,
+                    717,
+                    1118,
+                    192,
+                    799,
+                    486,
+                    373,
+                    473,
+                    640,
+                    80,
+                    447,
+                    809,
+                    1052,
+                    959,
+                    474,
+                    47,
+                    497,
+                    1139,
+                    1228,
+                    428,
+                    612,
+                    139,
+                    1257,
+                    847,
+                    146,
+                    357,
+                    461,
+                    1094,
+                    363,
+                    223,
+                    159,
+                    374,
+                    302,
+                    618,
+                    418,
+                    171,
+                    56,
+                    547,
+                    24,
+                    316,
+                    586,
+                    613,
+                    3,
+                    181,
+                    1198,
+                    857,
+                    17,
+                    546,
+                    1185,
+                    1185,
+                    400,
+                    782,
+                    1067,
+                    778,
+                    322,
+                    93,
+                    46,
+                    436,
+                    308,
+                    859,
+                    1,
+                    287,
+                    139,
+                    172,
+                    118,
+                    280,
+                    869,
+                    1128,
+                    104,
+                    743,
+                    757,
+                    818,
+                    1194,
+                    932,
+                    952,
+                    335,
+                    147,
+                    436,
+                    146,
+                    390,
+                    887,
+                    1117,
+                    1146,
+                    617,
+                    187,
+                    189,
+                    86,
+                    70,
+                    736,
+                    1044,
+                    212,
+                    379,
+                    602,
+                    762,
+                    700,
+                    857,
+                    1152,
+                    855,
+                    284,
+                    949,
+                    1210,
+                    631,
+                    1247,
+                    212,
+                    414,
+                    3,
+                    466,
+                    232,
+                    351,
+                    1194,
+                    696,
+                    1029,
+                    558,
+                    891,
+                    372,
+                    980,
+                    297,
+                    151,
+                    330,
+                    733,
+                    749,
+                    8,
+                    1272,
+                    156,
+                    579,
+                    678,
+                    131,
+                    503,
+                    1252,
+                    829,
+                    760,
+                    570,
+                    93,
+                    608,
+                    320,
+                    460,
+                    1078,
+                    581,
+                    818,
+                    923,
+                    654,
+                    253,
+                    295,
+                    1220,
+                    944,
+                    1120,
+                    228,
+                    1201,
+                    719,
+                    941,
+                    656,
+                    1068,
+                    1230,
+                    27,
+                    987,
+                    969,
+                    727,
+                    1097,
+                    623
+                ]
+            ],
+            "output": -1
+        },
+        {
+            "input": [
+                [
+                    390623884,
+                    894936491,
+                    651392896,
+                    620164087,
+                    363713974,
+                    588372330,
+                    634266125,
+                    176300029,
+                    347108978,
+                    59494446,
+                    769910255,
+                    86285045,
+                    648195961,
+                    367734468,
+                    911264593,
+                    371364604,
+                    697247157,
+                    333743994,
+                    579041309,
+                    439347260,
+                    722761504,
+                    686649778,
+                    578707073,
+                    408117906,
+                    612200238,
+                    649710597,
+                    278076949,
+                    772130220,
+                    937793803,
+                    466876087,
+                    254949833,
+                    285335673,
+                    665687389,
+                    145639300,
+                    919474588,
+                    279201294,
+                    318154831,
+                    935665534,
+                    890684792,
+                    825923082,
+                    357690679,
+                    65027876,
+                    783379311,
+                    33432620,
+                    355270533,
+                    525677278,
+                    203966834,
+                    264111203,
+                    467652736,
+                    360743223,
+                    778854047,
+                    901639035,
+                    847114256,
+                    309915548,
+                    997877973,
+                    211181605,
+                    647821697,
+                    396910753,
+                    613744764,
+                    879644253,
+                    155017908,
+                    549329098,
+                    926723127,
+                    288842591,
+                    261888608,
+                    106224475,
+                    849457228,
+                    566283891,
+                    679845603,
+                    969653895,
+                    621000236,
+                    232628890,
+                    952334699,
+                    227444724,
+                    87749814,
+                    23230407,
+                    243360392,
+                    790131688,
+                    746431445,
+                    931170252,
+                    674374368,
+                    613875250,
+                    262227444,
+                    685762934,
+                    618335933,
+                    673852755,
+                    591078187,
+                    878813325,
+                    75884433,
+                    491178841,
+                    831342004,
+                    234680907,
+                    729383910,
+                    102083324,
+                    260750789,
+                    943328612,
+                    705716181,
+                    731444056,
+                    207690645,
+                    684914391,
+                    554729974,
+                    888030948,
+                    401150807,
+                    169613666,
+                    746313555,
+                    660471602,
+                    536292796,
+                    744689174,
+                    269459480,
+                    362231762,
+                    422764582,
+                    496999657,
+                    301123088,
+                    503624549,
+                    585559832,
+                    395421801,
+                    337053046,
+                    805771170,
+                    950298574,
+                    254271223,
+                    959066262,
+                    768949517,
+                    364176435,
+                    641148079,
+                    190522831,
+                    44267468,
+                    2007532,
+                    576734922,
+                    404361198,
+                    716413659,
+                    643893665,
+                    568405573,
+                    644879722,
+                    935747919,
+                    281541733,
+                    809032301,
+                    22061205,
+                    843477364,
+                    770562382,
+                    655881967,
+                    976742395,
+                    36726883,
+                    838442365,
+                    425372741,
+                    261597003,
+                    935947560,
+                    912926275,
+                    758712038,
+                    827684280,
+                    783492092,
+                    492480728,
+                    750268605,
+                    86111163,
+                    705542247,
+                    971768684,
+                    826955395,
+                    209065695,
+                    881981295,
+                    442546582,
+                    828446229,
+                    349026926,
+                    6555052,
+                    695302838,
+                    906213576,
+                    138715973,
+                    531198752,
+                    964186380,
+                    616802498,
+                    392382026,
+                    402754693,
+                    121952355,
+                    222940155,
+                    62103498,
+                    627332302,
+                    816631811,
+                    984154888,
+                    26633616,
+                    365672348,
+                    218670097,
+                    65805538,
+                    670518774,
+                    109825697,
+                    667881947,
+                    614665651,
+                    434043257,
+                    388483450,
+                    156944943,
+                    959581606,
+                    293873022,
+                    938498932,
+                    883897716,
+                    897624420,
+                    118459795,
+                    747080663,
+                    58970444,
+                    107956806,
+                    862601730,
+                    682141912,
+                    331106365,
+                    868030643,
+                    666809063,
+                    646781675,
+                    486337716,
+                    556374478,
+                    670816634,
+                    423817009,
+                    500826447,
+                    448584129,
+                    754741647,
+                    503527974,
+                    176078348,
+                    5580301,
+                    151249089,
+                    584738645,
+                    230786136,
+                    5877303,
+                    298999119,
+                    397353769,
+                    30756042,
+                    462984805,
+                    98369947,
+                    93288566,
+                    890061450,
+                    707309392,
+                    186802465,
+                    977942985,
+                    490692641,
+                    163669330,
+                    377662390,
+                    608413366,
+                    613307420,
+                    550285747,
+                    523244266,
+                    969003750,
+                    194547303,
+                    136967139,
+                    222022774,
+                    144016165,
+                    520122642,
+                    464650240,
+                    737639982,
+                    905506175,
+                    506918162,
+                    741976396,
+                    457683321,
+                    470889645,
+                    554059904,
+                    267995886,
+                    339783262,
+                    608207494,
+                    533895278,
+                    980251924,
+                    359467038,
+                    674279741,
+                    6059690,
+                    278239144,
+                    126084651,
+                    649570269,
+                    420222100,
+                    622998539,
+                    202879961,
+                    7354284,
+                    270465491,
+                    518432564,
+                    307766970,
+                    809172744,
+                    763646581,
+                    727798391,
+                    33621881,
+                    292688254,
+                    264011636,
+                    845309854,
+                    781337677,
+                    823487791,
+                    543634812,
+                    214529391,
+                    789192349,
+                    906490500,
+                    399167002,
+                    417875549,
+                    961354273,
+                    202261693,
+                    483908343,
+                    351558199,
+                    446327235,
+                    52216145,
+                    953484585,
+                    953289465,
+                    323434531,
+                    215679917,
+                    88900704,
+                    883175975,
+                    765548829,
+                    369893951,
+                    274591297,
+                    906101893,
+                    374526524,
+                    321189165,
+                    558623775,
+                    804561542,
+                    985885253,
+                    152106756,
+                    307507699,
+                    536351472,
+                    176534548,
+                    705624724,
+                    2472237,
+                    857976977,
+                    426635649,
+                    297378480,
+                    922806753,
+                    917292475,
+                    994272259,
+                    431454757,
+                    967840675,
+                    867052741,
+                    879875437,
+                    197851387,
+                    601010768,
+                    522038079,
+                    958919697,
+                    756647782,
+                    730357304,
+                    866094926,
+                    473727590,
+                    792866416,
+                    131246861,
+                    358963542,
+                    269920258,
+                    224924576,
+                    88201011,
+                    706110261,
+                    940308716,
+                    161804432,
+                    603231371,
+                    463791611,
+                    323538955,
+                    994793397,
+                    958787659,
+                    620642820,
+                    561379743,
+                    39957512,
+                    179383775,
+                    833560140,
+                    785151620,
+                    96227317,
+                    711826963,
+                    262060836,
+                    962743766,
+                    149309007,
+                    817031696,
+                    710622320,
+                    211509497,
+                    761196911,
+                    706078750,
+                    364215321,
+                    347413842,
+                    668486740,
+                    567895019,
+                    575393340,
+                    320509467,
+                    857968689,
+                    717789320,
+                    476980578,
+                    885554355,
+                    194979017,
+                    432941493,
+                    447498315,
+                    65743652,
+                    25108074,
+                    708714261,
+                    77199587,
+                    290432465,
+                    855203953,
+                    663291524,
+                    286352529,
+                    413829143,
+                    882901202,
+                    804663120,
+                    580660593,
+                    927253685,
+                    67816485,
+                    713926216,
+                    556103616,
+                    134115108,
+                    665381517,
+                    95240766,
+                    518436196,
+                    508692624,
+                    153243342,
+                    251323796,
+                    78975660,
+                    976426071,
+                    932117770,
+                    830011654,
+                    141655596,
+                    623455400,
+                    100308075,
+                    743172516,
+                    219898439,
+                    255703624,
+                    382073619,
+                    683221194,
+                    829697770,
+                    345128438,
+                    486929479,
+                    308692114,
+                    27426673,
+                    220798259,
+                    845272784,
+                    22190466,
+                    707154746,
+                    715496953,
+                    695896366,
+                    633633422,
+                    59742981,
+                    861068227,
+                    416844474,
+                    737122160,
+                    615030079,
+                    378247847,
+                    32459713,
+                    172159123,
+                    644741560,
+                    475625450,
+                    779130001,
+                    211915271,
+                    899477009,
+                    341547635,
+                    158498089,
+                    450644447,
+                    41546536,
+                    404771183,
+                    898828868,
+                    71629879,
+                    487528221,
+                    223316647,
+                    483402350,
+                    651257078,
+                    981041484,
+                    606811957,
+                    81885424,
+                    670176262,
+                    232830373,
+                    720651841,
+                    26168463,
+                    611526849,
+                    636097060,
+                    253626735,
+                    567104609,
+                    201961427,
+                    76722083,
+                    939120515,
+                    283152887,
+                    144645810,
+                    519728684,
+                    148362151,
+                    228123080,
+                    190657794,
+                    9635469,
+                    659623735,
+                    239013366,
+                    291059511,
+                    382968962,
+                    649400621,
+                    124040954,
+                    532652629,
+                    61072303,
+                    404265372,
+                    438999449,
+                    265279505,
+                    337723168,
+                    794102660,
+                    463055818,
+                    234809688,
+                    584486093,
+                    466038239,
+                    787023389,
+                    281755368,
+                    406057231,
+                    391391733,
+                    44686294,
+                    819720420,
+                    89402409,
+                    340334244,
+                    104763026,
+                    681729461,
+                    864516891,
+                    764841957,
+                    356945509,
+                    144157773,
+                    22597640,
+                    462156263,
+                    402820459,
+                    319566569,
+                    829588728,
+                    177830468,
+                    436545863,
+                    959646109,
+                    696909200,
+                    717578191,
+                    767271922,
+                    458932299,
+                    690242941,
+                    487094609,
+                    558169734,
+                    479015525,
+                    599018668,
+                    86494073,
+                    383013415,
+                    239954360,
+                    589264013,
+                    720200537,
+                    169643545,
+                    478720071,
+                    23991740,
+                    505686850,
+                    499484403,
+                    178472763,
+                    149227445,
+                    513789019,
+                    917316501,
+                    687182709,
+                    645900097,
+                    69500382,
+                    232989722,
+                    964027363,
+                    687843623,
+                    823106486,
+                    704971061,
+                    727420443,
+                    311315948,
+                    417804794,
+                    877071313,
+                    561800665,
+                    683338893,
+                    782726055,
+                    944058000,
+                    192488849,
+                    97368906,
+                    16720067,
+                    335520303,
+                    418767886,
+                    786144347,
+                    385586149,
+                    733566874,
+                    690752478,
+                    46642054,
+                    361988365,
+                    124015964,
+                    565001096,
+                    516907625,
+                    306804840,
+                    407984752,
+                    125008644,
+                    336987210,
+                    509213188,
+                    801039423,
+                    767885904,
+                    405921561,
+                    283974068,
+                    337377399,
+                    522189386,
+                    124196410,
+                    682454651,
+                    6969827,
+                    234590555,
+                    575790633,
+                    442364682,
+                    692851265,
+                    952093451,
+                    163863348,
+                    714216183,
+                    909168561,
+                    276417201,
+                    547303580,
+                    688870008,
+                    732333400,
+                    799228806,
+                    224388612,
+                    221392109,
+                    952223849,
+                    947003558,
+                    40537032,
+                    817934708,
+                    301707825,
+                    95454602,
+                    46627256,
+                    47392341,
+                    80602044,
+                    326915947,
+                    156583332,
+                    683084489,
+                    856497998,
+                    345817929,
+                    249140796,
+                    573039341,
+                    541906467,
+                    142381296,
+                    68860447,
+                    532690289,
+                    174215533,
+                    747752056,
+                    181716053,
+                    275157190,
+                    273233221,
+                    687130508,
+                    978594971,
+                    206266097,
+                    372199412,
+                    309763162,
+                    105599809,
+                    456348084,
+                    706789390,
+                    438399011,
+                    370929077,
+                    232166283,
+                    617295989,
+                    537291740,
+                    274849851,
+                    507671631,
+                    233348649,
+                    425776259,
+                    556935691,
+                    159340253,
+                    73497092,
+                    716726285,
+                    550727331
+                ],
+                [
+                    504,
+                    135,
+                    179,
+                    418,
+                    477,
+                    315,
+                    31,
+                    551,
+                    319,
+                    182,
+                    83,
+                    595,
+                    297,
+                    275,
+                    512,
+                    592,
+                    56,
+                    130,
+                    231,
+                    600,
+                    601,
+                    288,
+                    364,
+                    46,
+                    355,
+                    56,
+                    498,
+                    21,
+                    185,
+                    494,
+                    141,
+                    110,
+                    375,
+                    494,
+                    520,
+                    294,
+                    248,
+                    431,
+                    440,
+                    374,
+                    584,
+                    493,
+                    379,
+                    37,
+                    88,
+                    524,
+                    64,
+                    150,
+                    124,
+                    408,
+                    129,
+                    299,
+                    37,
+                    472,
+                    33,
+                    396,
+                    295,
+                    227,
+                    128,
+                    21,
+                    319,
+                    444,
+                    454,
+                    550,
+                    309,
+                    180,
+                    81,
+                    17,
+                    603,
+                    326,
+                    405,
+                    402,
+                    481,
+                    63,
+                    229,
+                    366,
+                    628,
+                    474,
+                    571,
+                    459,
+                    554,
+                    379,
+                    63,
+                    52,
+                    449,
+                    39,
+                    122,
+                    296,
+                    332,
+                    92,
+                    151,
+                    535,
+                    39,
+                    294,
+                    1,
+                    611,
+                    597,
+                    196,
+                    464,
+                    495,
+                    514,
+                    248,
+                    567,
+                    64,
+                    292,
+                    74,
+                    521,
+                    394,
+                    108,
+                    198,
+                    435,
+                    116,
+                    135,
+                    263,
+                    53,
+                    364,
+                    192,
+                    342,
+                    449,
+                    93,
+                    347,
+                    67,
+                    249,
+                    572,
+                    478,
+                    305,
+                    403,
+                    325,
+                    264,
+                    396,
+                    32,
+                    63,
+                    525,
+                    461,
+                    564,
+                    363,
+                    246,
+                    186,
+                    25,
+                    10,
+                    273,
+                    616,
+                    414,
+                    212,
+                    615,
+                    181,
+                    622,
+                    489,
+                    444,
+                    524,
+                    315,
+                    437,
+                    338,
+                    29,
+                    237,
+                    312,
+                    141,
+                    604,
+                    211,
+                    541,
+                    560,
+                    593,
+                    508,
+                    475,
+                    556,
+                    346,
+                    303,
+                    462,
+                    311,
+                    496,
+                    434,
+                    396,
+                    594,
+                    489,
+                    561,
+                    335,
+                    603,
+                    254,
+                    465,
+                    558,
+                    611,
+                    57,
+                    200,
+                    35,
+                    150,
+                    585,
+                    311,
+                    600,
+                    499,
+                    515,
+                    247,
+                    386,
+                    10,
+                    372,
+                    75,
+                    182,
+                    23,
+                    502,
+                    579,
+                    96,
+                    52,
+                    574,
+                    475,
+                    47,
+                    440,
+                    251,
+                    448,
+                    20,
+                    395,
+                    330,
+                    312,
+                    504,
+                    260,
+                    535,
+                    71,
+                    349,
+                    25,
+                    200,
+                    444,
+                    292,
+                    109,
+                    549,
+                    116,
+                    374,
+                    56,
+                    89,
+                    562,
+                    269,
+                    339,
+                    47,
+                    245,
+                    499
+                ]
+            ],
+            "output": -1
+        },
+        {
+            "input": [
+                [
+                    541663488,
+                    450021561,
+                    602976101,
+                    491674536,
+                    79897607,
+                    14307639,
+                    707176216,
+                    650701848,
+                    348409214,
+                    580485984,
+                    344379774,
+                    716150711,
+                    918403668,
+                    384521592,
+                    946543514,
+                    232520300,
+                    762393847,
+                    438940975,
+                    579836667,
+                    583141260,
+                    565080655,
+                    431894651,
+                    131327573,
+                    328810313,
+                    81663827,
+                    378416543,
+                    152926586,
+                    224528242,
+                    176414673,
+                    459010459,
+                    881110204,
+                    380301182,
+                    23463207,
+                    332327197,
+                    2695619,
+                    352904698,
+                    9581422,
+                    241560072,
+                    725938561,
+                    715230335,
+                    986144229,
+                    661853746,
+                    352248366,
+                    773359905,
+                    789384493,
+                    552164698,
+                    501358382,
+                    559872888,
+                    702964119,
+                    30464642,
+                    261662623,
+                    825442464,
+                    29626807,
+                    1246205,
+                    90382734,
+                    424396951,
+                    951985125,
+                    171637182,
+                    52597848,
+                    385407974,
+                    41338098,
+                    371232546,
+                    663399501,
+                    507297477,
+                    546226098,
+                    580881411,
+                    377010206,
+                    907149416,
+                    908447638,
+                    345009173,
+                    618278530,
+                    788313362,
+                    803144154,
+                    805927265,
+                    824921734,
+                    181895884,
+                    565250956,
+                    765992783,
+                    721314739,
+                    25875112,
+                    281887392,
+                    153562934,
+                    427944762,
+                    204536328,
+                    683338774,
+                    722268696,
+                    905106043,
+                    714949589,
+                    287179563,
+                    597399836,
+                    152469294,
+                    587669827,
+                    738699396,
+                    432101517,
+                    113376936,
+                    693533184,
+                    7846385,
+                    188430439,
+                    56525715,
+                    220938805,
+                    392718754,
+                    38413331,
+                    79323160,
+                    951208601,
+                    58262226,
+                    796946950,
+                    209366874,
+                    513660517,
+                    255529102,
+                    107381309,
+                    134027087,
+                    897886440,
+                    29771658,
+                    363711166,
+                    985219767,
+                    402333398,
+                    963564101,
+                    215062864,
+                    770559402,
+                    867746424,
+                    246279370,
+                    275136515,
+                    676859738,
+                    267446674,
+                    206632646,
+                    496211606,
+                    651192730,
+                    349544022,
+                    245278808,
+                    8560320,
+                    176385889,
+                    349441785,
+                    84206234,
+                    448035417,
+                    565416077,
+                    118812722,
+                    574287376,
+                    140137207,
+                    829362082,
+                    475188176,
+                    729806399,
+                    687170446,
+                    615657604,
+                    907122623,
+                    653265131,
+                    544279765,
+                    324416190,
+                    264110076,
+                    538042055,
+                    73541209,
+                    790442822,
+                    153571642,
+                    429912775,
+                    494361439,
+                    758658173,
+                    870913779,
+                    835442248,
+                    418121016,
+                    509406423,
+                    727448284,
+                    317495320,
+                    682917408,
+                    156045172,
+                    772472874,
+                    525662352,
+                    619933937,
+                    736742289,
+                    172838352,
+                    988910251,
+                    880107334,
+                    579776632,
+                    585495665,
+                    926223888,
+                    280215537,
+                    959254018,
+                    749572275,
+                    70552975,
+                    612450702,
+                    241072337,
+                    965597890,
+                    89531558,
+                    422902655,
+                    14402489,
+                    67047714,
+                    191824489,
+                    913619054,
+                    916055499,
+                    209028792,
+                    426944202,
+                    585131740,
+                    321633998,
+                    821764144,
+                    824227141,
+                    369347599,
+                    316002939,
+                    725581396,
+                    887201841,
+                    501021176,
+                    704825081,
+                    606540260,
+                    716754940,
+                    936203927,
+                    245871774,
+                    597687386,
+                    538196366,
+                    576291042,
+                    836743436,
+                    135366821,
+                    429473555,
+                    118515228,
+                    612872683,
+                    329993690,
+                    36191448,
+                    565454735,
+                    301504619,
+                    578208249,
+                    506261249,
+                    682528647,
+                    676687725,
+                    134636607,
+                    974615814,
+                    34361555,
+                    368829057,
+                    100258973,
+                    667398136,
+                    887749965,
+                    851883895,
+                    893249852,
+                    870534969,
+                    706845995,
+                    862111736,
+                    419489001,
+                    527632918,
+                    822360067,
+                    300489233,
+                    125277970,
+                    741656509,
+                    662166994,
+                    163433419,
+                    162017907,
+                    22817315,
+                    88780728,
+                    178177807,
+                    130136291,
+                    567397509,
+                    203107201,
+                    105106138,
+                    973900731,
+                    710400390,
+                    391545285,
+                    261618298,
+                    495593298,
+                    835584553,
+                    995955102,
+                    480511837,
+                    312524837,
+                    321088745,
+                    980999354,
+                    68504073,
+                    207493437,
+                    914268518,
+                    295656900,
+                    69289014,
+                    512266885,
+                    968402967,
+                    844971219,
+                    965932716,
+                    710416706,
+                    854025248,
+                    812668075,
+                    922900534,
+                    439185069,
+                    963161674,
+                    596590798,
+                    181743287,
+                    127973498,
+                    104000438,
+                    245385404,
+                    587600142,
+                    670552093,
+                    600382418,
+                    131631319,
+                    11037966,
+                    573248151,
+                    196982524,
+                    504996785,
+                    870389508,
+                    353644132,
+                    387397790,
+                    20593754,
+                    626340201,
+                    142882297,
+                    326704355,
+                    802893401,
+                    277768845,
+                    567426756,
+                    945582565,
+                    21735864,
+                    83498727,
+                    838084649,
+                    918367337,
+                    990410468,
+                    880587528,
+                    761381251,
+                    917686047,
+                    245004555,
+                    953451067,
+                    745539862,
+                    802418771,
+                    5714903,
+                    107996222,
+                    668424155,
+                    638645145,
+                    12969191,
+                    311550260,
+                    517008009,
+                    176286428,
+                    678137676,
+                    846982264,
+                    663772314,
+                    796641050,
+                    752696612,
+                    556063077,
+                    924354787,
+                    347599008,
+                    57519705,
+                    506625639,
+                    811382446,
+                    317998034,
+                    871250964,
+                    56722525,
+                    23868197,
+                    152744679,
+                    449580746,
+                    248575187,
+                    688148164,
+                    647284852,
+                    445220712,
+                    676394998,
+                    523590605,
+                    398039351,
+                    137466302,
+                    409442850,
+                    857291849,
+                    2880354,
+                    921901179,
+                    545516849,
+                    484943626,
+                    282541473,
+                    527745313,
+                    379808612,
+                    241252255,
+                    398905011,
+                    761072336,
+                    836059755,
+                    100432189,
+                    999198332,
+                    339098172,
+                    793266789,
+                    669866068,
+                    481065848,
+                    141584774,
+                    188202429,
+                    470964542,
+                    163248066,
+                    443600354,
+                    746735654,
+                    886209143,
+                    91407472,
+                    820086140,
+                    282043243,
+                    228604933,
+                    214355752,
+                    63368280,
+                    365745389,
+                    321254995,
+                    187792949,
+                    726053435,
+                    892242537,
+                    768079856,
+                    227704884,
+                    387051719,
+                    576564046,
+                    974153452,
+                    318483033,
+                    475180392,
+                    214859627,
+                    416636314,
+                    139528045,
+                    492123445,
+                    203631796,
+                    160895909,
+                    690638254,
+                    144119255,
+                    108339324,
+                    835667933,
+                    227157152,
+                    593455723,
+                    279517281,
+                    318052021,
+                    468366906,
+                    947121933,
+                    423899468,
+                    268246403,
+                    34150454,
+                    866746303,
+                    743287816,
+                    835120777,
+                    179734083,
+                    404890891,
+                    343638188,
+                    258049113,
+                    921878243,
+                    736262075,
+                    35796232,
+                    235007136,
+                    293642733,
+                    401972064,
+                    487145076,
+                    338604158,
+                    670992039,
+                    373816248,
+                    932286413,
+                    6168085,
+                    965909005,
+                    262886509,
+                    396627794,
+                    710871592,
+                    537243535,
+                    299835678,
+                    215071930,
+                    799779353,
+                    101595371,
+                    909561056,
+                    784896100,
+                    159767863,
+                    173108339,
+                    182112366,
+                    967100499,
+                    935155177,
+                    970895926,
+                    351077013,
+                    645368124,
+                    83233793,
+                    421964248,
+                    220338549,
+                    65693789,
+                    510705892,
+                    496166250,
+                    694563806,
+                    695148382,
+                    903395060,
+                    984319280,
+                    828613336,
+                    407597314,
+                    999223163,
+                    426684485,
+                    5700424,
+                    622839500,
+                    518751500,
+                    87365823,
+                    934092271,
+                    296268949,
+                    292756934,
+                    837777781,
+                    28327020,
+                    842171898,
+                    819643333,
+                    854518163,
+                    159145075,
+                    977700334,
+                    996788217,
+                    584758657,
+                    410561221,
+                    997272143,
+                    105669715,
+                    27239725,
+                    734510427,
+                    865070375,
+                    795419689,
+                    959458962,
+                    26232724,
+                    708660967,
+                    991900249,
+                    972199198,
+                    991153942,
+                    773928032,
+                    773398662,
+                    732081952,
+                    392769671,
+                    525829353,
+                    63327424,
+                    535968789,
+                    257077890,
+                    835716990,
+                    808937264,
+                    416799196,
+                    527539771,
+                    429359674,
+                    229393690,
+                    920508195,
+                    713813371,
+                    652562533,
+                    464280051,
+                    699595760,
+                    701447573,
+                    189729446,
+                    337310631,
+                    244387881,
+                    866205154,
+                    657185301,
+                    801919963,
+                    137495260,
+                    669859825,
+                    858293315,
+                    587730352,
+                    976135548,
+                    81715142,
+                    413035837,
+                    790925254,
+                    235618473,
+                    32902862,
+                    30454389,
+                    850290790,
+                    410056032,
+                    607415089,
+                    617987693,
+                    110896515,
+                    347146973,
+                    249353527,
+                    128511853,
+                    211012552,
+                    629014246,
+                    280456456,
+                    526007143,
+                    413070269,
+                    412682363,
+                    924510609,
+                    226429695,
+                    301358129,
+                    283326652,
+                    443657783,
+                    134531052,
+                    589910762,
+                    51055113,
+                    972707493,
+                    751921431,
+                    397393156,
+                    18227234,
+                    765376045,
+                    410566929,
+                    551665699,
+                    56304225,
+                    698792818,
+                    490517223,
+                    460488598,
+                    889013400,
+                    120363375,
+                    666289118,
+                    774273707,
+                    570300611,
+                    918792289,
+                    392342682,
+                    922583407,
+                    848657442,
+                    767024624,
+                    974784743,
+                    440459824,
+                    994221168,
+                    664370805,
+                    204116316,
+                    983304091,
+                    836750737,
+                    604315604,
+                    109616017,
+                    828601045,
+                    372612586,
+                    533435816,
+                    373615830,
+                    574810719,
+                    481838957,
+                    731949349,
+                    555798464,
+                    160732226,
+                    85439375,
+                    843467437,
+                    257626693,
+                    570897333,
+                    253457074,
+                    497354690,
+                    224333493,
+                    900857362,
+                    494852522,
+                    68622838,
+                    42535205,
+                    27205075,
+                    545198794,
+                    843069670,
+                    565492439,
+                    660344063,
+                    407921677,
+                    489872224,
+                    571187378,
+                    977488209,
+                    973692666,
+                    475460432,
+                    950293001,
+                    530761840,
+                    480604218,
+                    925856871,
+                    613950696,
+                    667733887,
+                    573337908,
+                    799033874,
+                    158275542,
+                    948309127,
+                    300848318,
+                    276375600,
+                    821993167,
+                    519694895,
+                    163749321,
+                    15572098,
+                    426534784,
+                    711669724,
+                    135559759,
+                    786051690,
+                    482694471,
+                    379998476,
+                    181437898,
+                    369650456,
+                    478557983,
+                    389908179,
+                    182221944,
+                    128714346,
+                    428822962,
+                    614035971,
+                    151659831,
+                    356277843,
+                    917419753,
+                    306333886,
+                    703439167,
+                    925384156,
+                    785258730,
+                    358083627,
+                    514833326,
+                    510201997,
+                    868829221,
+                    282588235,
+                    958156055,
+                    506801964,
+                    172636811,
+                    118816971,
+                    162186288,
+                    538748294,
+                    763738863,
+                    897954390,
+                    152304653,
+                    757544579,
+                    95476414,
+                    414413636,
+                    180596826,
+                    187504073,
+                    555621325,
+                    556905354,
+                    103546835,
+                    461184451,
+                    513048568,
+                    765584847,
+                    657883638,
+                    15815634,
+                    530810109,
+                    811905932,
+                    14610167,
+                    635256236,
+                    714438189,
+                    964155823,
+                    494933497,
+                    413978052,
+                    456479477,
+                    794061668,
+                    853988394,
+                    958120466,
+                    5796909,
+                    913238363,
+                    457897175,
+                    297116933,
+                    42733984,
+                    955185161,
+                    619553593,
+                    530341291,
+                    861007311,
+                    529084962,
+                    494096136,
+                    49229276,
+                    189443974,
+                    955052255,
+                    605909006,
+                    603055870,
+                    617616081,
+                    127939454,
+                    165330139,
+                    448484650,
+                    256412086,
+                    200680693,
+                    296630194,
+                    358098030,
+                    832535736,
+                    861780122,
+                    643776461,
+                    394223512,
+                    473835532,
+                    231124251,
+                    676410644,
+                    877816138,
+                    569498866,
+                    599192843,
+                    647854603,
+                    959544616,
+                    228838455,
+                    547875818,
+                    469695251,
+                    211660851,
+                    813570147,
+                    639311541,
+                    197682954,
+                    323866611,
+                    53207760,
+                    85199621,
+                    137687721,
+                    113509513,
+                    401222068,
+                    666496732,
+                    500723918,
+                    296808319,
+                    469154731,
+                    421948581,
+                    212959526,
+                    136993431,
+                    460755213,
+                    932521493,
+                    517299172,
+                    914111625,
+                    809872657,
+                    724729722,
+                    201695285,
+                    920581158,
+                    55457504,
+                    563617729,
+                    571609908,
+                    447514908,
+                    775423074,
+                    461869805,
+                    564135178,
+                    467944075,
+                    853438406,
+                    254924012,
+                    944721559,
+                    106699101,
+                    92421606,
+                    635318153,
+                    857138107,
+                    187144105,
+                    78430369,
+                    958458883,
+                    580053310,
+                    447946643,
+                    636592767,
+                    289261070,
+                    926531482,
+                    404849431,
+                    687115877,
+                    892463608,
+                    561671186,
+                    562210516,
+                    423430225,
+                    326835123,
+                    782899984,
+                    308127819,
+                    713083541,
+                    426633836,
+                    620446322,
+                    38065992,
+                    951539843,
+                    157170675,
+                    337302025,
+                    727332137,
+                    993671424,
+                    177005037,
+                    671772428,
+                    895831616,
+                    565630482,
+                    209443244,
+                    450436022,
+                    881800163,
+                    52954896,
+                    320278547,
+                    207466139,
+                    325173039,
+                    287000858,
+                    597217696,
+                    52150197,
+                    116190129,
+                    320637499,
+                    845009047,
+                    756175352,
+                    838363226,
+                    724889323,
+                    756011653,
+                    952108990,
+                    794249776,
+                    695071927,
+                    410963986,
+                    817361256,
+                    889463814,
+                    929302022,
+                    572444645,
+                    265180897,
+                    512079475,
+                    217748202,
+                    81327663,
+                    899499228,
+                    745668760,
+                    173219456,
+                    78053099,
+                    696107745,
+                    509773769,
+                    895689811,
+                    420870880,
+                    207871952,
+                    143219724,
+                    506884446,
+                    562826727,
+                    445462241,
+                    560449828,
+                    841514981,
+                    475991957,
+                    257206267,
+                    775437168,
+                    447037887,
+                    582843052,
+                    608238601,
+                    991991052,
+                    851695647,
+                    849619514,
+                    727089819,
+                    553814669,
+                    159044765,
+                    215737125,
+                    406864077,
+                    582245599,
+                    442358990,
+                    212831660,
+                    578295513,
+                    162817651,
+                    684916235,
+                    649297603,
+                    672394952,
+                    742584106,
+                    451745684,
+                    824336115,
+                    732708873,
+                    248195747,
+                    177878607,
+                    22165240,
+                    952879272,
+                    922553450,
+                    700328483,
+                    928717827,
+                    904914289,
+                    326669789,
+                    464565113,
+                    467117829,
+                    862287239,
+                    346517053,
+                    482639785,
+                    742990755,
+                    509951729,
+                    900694470,
+                    110895733,
+                    836068412,
+                    431728021,
+                    941638597,
+                    118318832,
+                    88077781,
+                    522525768,
+                    639755591,
+                    661764684,
+                    45813803,
+                    403510266,
+                    169233007,
+                    889886875,
+                    940743190,
+                    70412829,
+                    498067224,
+                    876523319,
+                    889934796,
+                    789795956,
+                    864762069,
+                    622724616,
+                    147447497,
+                    786236353,
+                    19222068,
+                    475960394,
+                    503493114,
+                    757855863,
+                    445271238,
+                    704415027,
+                    183878767,
+                    55440869,
+                    295448986,
+                    614167638,
+                    444116772,
+                    379106958,
+                    875227371,
+                    22424048,
+                    637339044,
+                    466301130,
+                    833911540,
+                    84677310,
+                    790725405,
+                    738726623,
+                    857132337,
+                    292982126,
+                    992443392,
+                    125571246,
+                    425984480,
+                    338716220,
+                    91595106,
+                    721997646,
+                    862108559,
+                    667255577,
+                    48000129,
+                    953043273,
+                    3160102,
+                    530070365,
+                    703405467,
+                    658528505,
+                    796319954,
+                    714984588,
+                    771099712,
+                    904536496,
+                    156866425,
+                    607119252,
+                    735162769,
+                    683189171,
+                    74792237,
+                    629585437,
+                    96153740,
+                    580152740,
+                    199698496,
+                    979353035,
+                    166788122,
+                    84344595,
+                    740039402,
+                    573785599,
+                    475292387,
+                    436300979,
+                    139646740,
+                    129178517,
+                    680409834,
+                    869458309,
+                    947207229,
+                    207779433,
+                    922890925,
+                    914577827,
+                    462123963,
+                    699673525,
+                    940153869,
+                    969620604,
+                    532453075,
+                    166399916,
+                    5573577,
+                    183238636,
+                    429500976,
+                    226926445,
+                    689044179,
+                    625053021,
+                    984369246,
+                    191318178,
+                    95234092,
+                    616707279,
+                    575478440,
+                    185146595,
+                    316776272,
+                    225829074,
+                    757361277,
+                    495210200,
+                    504502208,
+                    114281437,
+                    315943476,
+                    979305412,
+                    866010410,
+                    533885657,
+                    221311202,
+                    796650617,
+                    607112360,
+                    105530824,
+                    480791364,
+                    911980256,
+                    600847167,
+                    800375166,
+                    749657866,
+                    607767624,
+                    890569889,
+                    630406022,
+                    562649144,
+                    98172337,
+                    467065806,
+                    568565929,
+                    336196884,
+                    674933535,
+                    476498942,
+                    901109412,
+                    855704825,
+                    486115679,
+                    170913394,
+                    73310618,
+                    346769823,
+                    199962212,
+                    125477531,
+                    184331268,
+                    768133775,
+                    273703454,
+                    242874311,
+                    89161089,
+                    504694875,
+                    526234503,
+                    733510674,
+                    186310005,
+                    871077733,
+                    835744424,
+                    149802423,
+                    95200894,
+                    476703595,
+                    228219216,
+                    45733684,
+                    414975081,
+                    677290913,
+                    956471168,
+                    185439609,
+                    791158839,
+                    789091568,
+                    363617789,
+                    745238122,
+                    982784560,
+                    853754025,
+                    932895434,
+                    304513079,
+                    647263166,
+                    969177814,
+                    304600004,
+                    860759591,
+                    201897993,
+                    204614340,
+                    48783616,
+                    976868167,
+                    404869322,
+                    818735857,
+                    97742799,
+                    359930485,
+                    926091268,
+                    776690782,
+                    599834570,
+                    47512582,
+                    747895554,
+                    560026453,
+                    5074306,
+                    283980456,
+                    695670576,
+                    337834089,
+                    193407871,
+                    613188245,
+                    67231800,
+                    870776833,
+                    646207562,
+                    609850947,
+                    404748041,
+                    629260155,
+                    93587274,
+                    494957655,
+                    217447934,
+                    534793934,
+                    891826459,
+                    430945172,
+                    721713929,
+                    307556005,
+                    162790181,
+                    719876081,
+                    59621016,
+                    317799246,
+                    221366724,
+                    84407141,
+                    996640579,
+                    504511166,
+                    647750020,
+                    735460728,
+                    549544260,
+                    53088068,
+                    176057017,
+                    603559509,
+                    605324505,
+                    823204292,
+                    389607960,
+                    738714090,
+                    155166582,
+                    848925880,
+                    415192476,
+                    54786967,
+                    595172416,
+                    82314143,
+                    96577896,
+                    757822073,
+                    895667782,
+                    417680251,
+                    22586166,
+                    122098669,
+                    946712510,
+                    525545551,
+                    546784034,
+                    496088655,
+                    959078539,
+                    730366260,
+                    388433158,
+                    260499167,
+                    972687533,
+                    613114620,
+                    120576902,
+                    173819608,
+                    225605755,
+                    897847825,
+                    727171096,
+                    278035432,
+                    404044726,
+                    337940219,
+                    714654811,
+                    510935960,
+                    124391726,
+                    594447592,
+                    611227105,
+                    676214519,
+                    272587079,
+                    176907153,
+                    565584691,
+                    859151314,
+                    388601004,
+                    577877083,
+                    270981223,
+                    768837111,
+                    183440004,
+                    409559807,
+                    991198289,
+                    28413402,
+                    332787307,
+                    680987134,
+                    129557404,
+                    106679358,
+                    582012416,
+                    750154758,
+                    384212182,
+                    130287274,
+                    592940323,
+                    595397996,
+                    352885715,
+                    884126456,
+                    346815149,
+                    906604747,
+                    457100709,
+                    286826743,
+                    497076278,
+                    93320059,
+                    494068597,
+                    468222189,
+                    162231982,
+                    934486911,
+                    986461660,
+                    970726754,
+                    758065353,
+                    853936246,
+                    21140771,
+                    373020568,
+                    348432832,
+                    954013161,
+                    183728825,
+                    151029370,
+                    132992099,
+                    320035716,
+                    19122765,
+                    84918564,
+                    432031745,
+                    99285370,
+                    85328023,
+                    324216934,
+                    280876051,
+                    450929262,
+                    430039508,
+                    785073449,
+                    868461455,
+                    73427405,
+                    200498201,
+                    328509241,
+                    573667319,
+                    25027313,
+                    403239029,
+                    85653778,
+                    199995359,
+                    479669516,
+                    342420605,
+                    961961678,
+                    722107091,
+                    787472863,
+                    139744812,
+                    776374142,
+                    310822240,
+                    672830779,
+                    441357200,
+                    997235642,
+                    694668078,
+                    412640361,
+                    39735079,
+                    334662577,
+                    957111946,
+                    275192325,
+                    151360127,
+                    162519042,
+                    951599460,
+                    712037465,
+                    43752300,
+                    163411026,
+                    12344468,
+                    67279465,
+                    483746741,
+                    35449159,
+                    627008334,
+                    777526948,
+                    617500814,
+                    154338602,
+                    501091609,
+                    648884060,
+                    11551830,
+                    377611217,
+                    9706952,
+                    812331132,
+                    390563709,
+                    630224366,
+                    117763565,
+                    34706001,
+                    823748705,
+                    70120444,
+                    876996361,
+                    967974076,
+                    266870992,
+                    351046082,
+                    173628240,
+                    37984870,
+                    116332398,
+                    201782759,
+                    605356525,
+                    789430571,
+                    923162480,
+                    642345239,
+                    572332445,
+                    871276339,
+                    122042047,
+                    483227745,
+                    862116944,
+                    977275799,
+                    183260988,
+                    899003301,
+                    17474521,
+                    494950259,
+                    805150535,
+                    680428779,
+                    698797434,
+                    521468774,
+                    204563694,
+                    585391183,
+                    77547719,
+                    128166458,
+                    441343966,
+                    981383249,
+                    747813743,
+                    554608822,
+                    494604343,
+                    417480488,
+                    750799230,
+                    635985114,
+                    595319059,
+                    11013176,
+                    610883581,
+                    53810142,
+                    904015728,
+                    580711440,
+                    386385177,
+                    673017830,
+                    337430730,
+                    111168381,
+                    256968792,
+                    862690225,
+                    614833666,
+                    347884774,
+                    617605452,
+                    497330528,
+                    182338290,
+                    291290277,
+                    468585328,
+                    173096773,
+                    777372331,
+                    206469592,
+                    677012528,
+                    330881643,
+                    589014429,
+                    308202581,
+                    444114854,
+                    775211582,
+                    933864147,
+                    85996726,
+                    353247187,
+                    78248370,
+                    649648332,
+                    5461094,
+                    192051061,
+                    978764750,
+                    863282848,
+                    872280735,
+                    38134662,
+                    853626515,
+                    915597623,
+                    423181510,
+                    428316267,
+                    637467258,
+                    550158428,
+                    278448626,
+                    749328549,
+                    785864776,
+                    665201641,
+                    702517744,
+                    551073328,
+                    486040863,
+                    930172051,
+                    488813571,
+                    545210026,
+                    944723066,
+                    776753365,
+                    456783544,
+                    797934863,
+                    102108712,
+                    39741502,
+                    378690479,
+                    647447085,
+                    968808479,
+                    163398390,
+                    647421938,
+                    222309589,
+                    616383995,
+                    731027586,
+                    24282053,
+                    772886125,
+                    792087400,
+                    634227054,
+                    761002632,
+                    278131166,
+                    319241970,
+                    736441729,
+                    971379176,
+                    943953234,
+                    524494511,
+                    401330263,
+                    722731260,
+                    201184085,
+                    976886634,
+                    194303338,
+                    329137359,
+                    503630374,
+                    463692256,
+                    923697639,
+                    858086616,
+                    445569520,
+                    73648871,
+                    2149983,
+                    994715135,
+                    374440263,
+                    118270949,
+                    780229856,
+                    800161322,
+                    45839602,
+                    455858142,
+                    956981174,
+                    390586428,
+                    396307723,
+                    47114584,
+                    877642136,
+                    815423508,
+                    209207998,
+                    49031544,
+                    788484207,
+                    359103573,
+                    56558561,
+                    45548761,
+                    170644229,
+                    674082067,
+                    381033476,
+                    69555200,
+                    225287219,
+                    706220082,
+                    618444833,
+                    856476677,
+                    401689706,
+                    900592027,
+                    362978702,
+                    520848182,
+                    621286709,
+                    453262306,
+                    157237775,
+                    215185312,
+                    622767451,
+                    421326906,
+                    741861471,
+                    426873786,
+                    537226861,
+                    804038483,
+                    663896880
+                ],
+                [
+                    213,
+                    1002,
+                    1055,
+                    1298,
+                    361,
+                    299,
+                    1153,
+                    494,
+                    47,
+                    348,
+                    1209,
+                    1053,
+                    443,
+                    518,
+                    1194,
+                    1393,
+                    1072,
+                    393,
+                    11,
+                    772,
+                    975,
+                    249,
+                    788,
+                    1381,
+                    632,
+                    347,
+                    1418,
+                    308,
+                    225,
+                    600,
+                    486,
+                    817,
+                    812,
+                    1391,
+                    584,
+                    514,
+                    1149,
+                    553,
+                    260,
+                    27,
+                    968,
+                    894,
+                    696,
+                    884,
+                    351,
+                    57,
+                    1113,
+                    617,
+                    1185,
+                    3,
+                    1200,
+                    452,
+                    438,
+                    250,
+                    1192,
+                    778,
+                    1010,
+                    984,
+                    1119,
+                    902,
+                    844,
+                    180,
+                    120,
+                    1128,
+                    1272,
+                    847,
+                    1367,
+                    997,
+                    960,
+                    1135,
+                    576,
+                    656,
+                    874,
+                    1248,
+                    919,
+                    235,
+                    111,
+                    1214,
+                    809,
+                    121,
+                    1002,
+                    1272,
+                    956,
+                    762,
+                    653,
+                    110,
+                    573,
+                    848,
+                    368,
+                    1333,
+                    103,
+                    344,
+                    1337,
+                    127,
+                    320,
+                    841,
+                    97,
+                    877,
+                    545,
+                    437,
+                    274,
+                    319,
+                    1333,
+                    199,
+                    283,
+                    64,
+                    777,
+                    1065,
+                    955,
+                    553,
+                    49,
+                    1034,
+                    139,
+                    1020,
+                    620,
+                    561,
+                    727,
+                    262,
+                    1328,
+                    1386,
+                    836,
+                    1292,
+                    851,
+                    281,
+                    684,
+                    946,
+                    455,
+                    338,
+                    284,
+                    807,
+                    946,
+                    420,
+                    1244,
+                    523,
+                    1355,
+                    1118,
+                    845,
+                    129,
+                    268,
+                    222,
+                    750,
+                    150,
+                    94,
+                    819,
+                    1081,
+                    992,
+                    644,
+                    53,
+                    795,
+                    1130,
+                    681,
+                    243,
+                    399,
+                    814,
+                    230,
+                    310,
+                    372,
+                    62,
+                    497,
+                    145,
+                    400,
+                    1372,
+                    450,
+                    738,
+                    1162,
+                    622,
+                    1336,
+                    1417,
+                    12,
+                    820,
+                    4,
+                    1046,
+                    549,
+                    1325,
+                    407,
+                    646,
+                    1260,
+                    323,
+                    1278,
+                    1348,
+                    159,
+                    1251,
+                    759,
+                    540,
+                    626,
+                    569,
+                    527,
+                    992,
+                    551,
+                    460,
+                    593,
+                    651,
+                    420,
+                    630,
+                    533,
+                    1014,
+                    112,
+                    153,
+                    988,
+                    83,
+                    363,
+                    1388,
+                    241,
+                    469,
+                    395,
+                    363,
+                    353,
+                    1314,
+                    404,
+                    829,
+                    1331,
+                    1201,
+                    624,
+                    1066,
+                    1007,
+                    513,
+                    892,
+                    1353,
+                    596,
+                    228,
+                    1261,
+                    828,
+                    37,
+                    177,
+                    7,
+                    222,
+                    378,
+                    947,
+                    669,
+                    1137,
+                    1284,
+                    891,
+                    1002,
+                    142,
+                    709,
+                    324,
+                    136,
+                    541,
+                    44,
+                    148,
+                    1372,
+                    648,
+                    202,
+                    626,
+                    835,
+                    358,
+                    991,
+                    995,
+                    1283,
+                    560,
+                    95,
+                    459,
+                    321,
+                    1120,
+                    839,
+                    1055,
+                    733,
+                    1346,
+                    849,
+                    101,
+                    44,
+                    990,
+                    574,
+                    642,
+                    907,
+                    639,
+                    1037,
+                    4,
+                    903,
+                    770,
+                    400,
+                    754,
+                    659,
+                    515,
+                    1028,
+                    175,
+                    782,
+                    126,
+                    1253,
+                    692,
+                    488,
+                    201,
+                    1304,
+                    1017,
+                    394,
+                    945,
+                    426,
+                    1314,
+                    560,
+                    1406,
+                    821,
+                    93,
+                    765,
+                    734,
+                    972,
+                    1036,
+                    1196,
+                    981,
+                    1035,
+                    1352,
+                    38,
+                    1180,
+                    633,
+                    62,
+                    61,
+                    1103,
+                    1168,
+                    1285,
+                    1286,
+                    361,
+                    359,
+                    1330,
+                    255,
+                    283,
+                    429,
+                    465,
+                    1048,
+                    506,
+                    1147,
+                    755,
+                    875,
+                    1070,
+                    1186,
+                    1408,
+                    839,
+                    72,
+                    80,
+                    1066,
+                    350,
+                    916,
+                    23,
+                    1031,
+                    504,
+                    442,
+                    14,
+                    980,
+                    1380,
+                    322,
+                    184,
+                    1393,
+                    36,
+                    1140,
+                    817,
+                    108,
+                    1317,
+                    844,
+                    487,
+                    1385,
+                    373,
+                    11,
+                    430,
+                    1340,
+                    839,
+                    1008,
+                    1389,
+                    96,
+                    805,
+                    1230,
+                    1130,
+                    673,
+                    1296,
+                    92,
+                    1418,
+                    569,
+                    1056,
+                    286,
+                    1237,
+                    1098,
+                    1278,
+                    388,
+                    912,
+                    1134,
+                    780,
+                    351,
+                    366,
+                    1161,
+                    490,
+                    1363,
+                    1271,
+                    412,
+                    1110,
+                    429,
+                    620,
+                    1368,
+                    796,
+                    853,
+                    699,
+                    784,
+                    650,
+                    481,
+                    1206,
+                    413,
+                    1197,
+                    1316,
+                    918,
+                    1416,
+                    1314,
+                    1148,
+                    1334,
+                    1215,
+                    1268,
+                    1224,
+                    1081,
+                    731,
+                    35,
+                    16,
+                    785,
+                    860,
+                    563,
+                    140,
+                    1075,
+                    760,
+                    578,
+                    810,
+                    165,
+                    934,
+                    1108,
+                    246,
+                    503,
+                    341,
+                    308,
+                    1100,
+                    1320,
+                    571,
+                    1223,
+                    947,
+                    1135,
+                    102,
+                    914,
+                    26,
+                    1417,
+                    857,
+                    864,
+                    694,
+                    1037,
+                    900,
+                    317,
+                    1252,
+                    747,
+                    278,
+                    792,
+                    1411,
+                    687,
+                    635,
+                    720,
+                    1000,
+                    1039,
+                    886,
+                    239,
+                    909,
+                    157,
+                    265,
+                    1178,
+                    989,
+                    1010,
+                    402,
+                    1416,
+                    356,
+                    238,
+                    519,
+                    305,
+                    736,
+                    242,
+                    321,
+                    674,
+                    342,
+                    1204,
+                    783,
+                    38,
+                    322,
+                    384,
+                    599,
+                    885,
+                    1234,
+                    946,
+                    13,
+                    79,
+                    1420,
+                    910,
+                    432,
+                    1409,
+                    423,
+                    1407,
+                    435,
+                    779,
+                    208,
+                    163,
+                    208,
+                    1378,
+                    1148,
+                    206,
+                    443,
+                    113,
+                    478,
+                    1194,
+                    1336,
+                    639,
+                    9,
+                    38,
+                    72,
+                    38,
+                    550,
+                    267,
+                    318,
+                    957,
+                    92,
+                    1289,
+                    156,
+                    1104,
+                    371,
+                    1363,
+                    960,
+                    235,
+                    663,
+                    1303,
+                    1123,
+                    1159,
+                    428,
+                    964,
+                    302,
+                    392,
+                    1399,
+                    582,
+                    562,
+                    524,
+                    526,
+                    1132,
+                    803,
+                    1382,
+                    402,
+                    837,
+                    534,
+                    922,
+                    1028,
+                    358,
+                    1066,
+                    976,
+                    201,
+                    1179,
+                    1222,
+                    814,
+                    590,
+                    911,
+                    885,
+                    877,
+                    134,
+                    1341,
+                    917,
+                    1252,
+                    363,
+                    1096,
+                    772,
+                    610,
+                    286,
+                    106,
+                    318,
+                    932,
+                    623,
+                    895,
+                    393,
+                    1178,
+                    1390,
+                    1391,
+                    85,
+                    829,
+                    736,
+                    775,
+                    162,
+                    1187,
+                    1123,
+                    492,
+                    1092,
+                    613,
+                    87,
+                    736,
+                    276,
+                    408,
+                    96,
+                    1258,
+                    273,
+                    856,
+                    825,
+                    1034,
+                    882,
+                    555,
+                    625,
+                    875,
+                    1245,
+                    1151,
+                    232,
+                    653,
+                    56,
+                    209,
+                    974,
+                    504,
+                    1303,
+                    783,
+                    1419,
+                    168,
+                    1161,
+                    585,
+                    860,
+                    707,
+                    157,
+                    771,
+                    624,
+                    517,
+                    371,
+                    936
+                ]
+            ],
+            "output": -1
+        },
+        {
+            "input": [
+                [
+                    515440776,
+                    602842699,
+                    597192975,
+                    289519659,
+                    779259557,
+                    296342891,
+                    112026735,
+                    675952747,
+                    854801761,
+                    361503536,
+                    178668830,
+                    742408107,
+                    844375444,
+                    68163070,
+                    486046231,
+                    965056982,
+                    82331848,
+                    58086726,
+                    511159594,
+                    609749805,
+                    529344794,
+                    743854082,
+                    427514538,
+                    59168764,
+                    376928674,
+                    361357469,
+                    826648799,
+                    100254685,
+                    849143466,
+                    58837566,
+                    756641173,
+                    766577231,
+                    421583398,
+                    515569965,
+                    894795362,
+                    458168502,
+                    245233798,
+                    885564378,
+                    749758344,
+                    956707151,
+                    709125547,
+                    976779799,
+                    665288834,
+                    849178587,
+                    344825561,
+                    604565068,
+                    772917907,
+                    611426980,
+                    45529779,
+                    239862906,
+                    73953002,
+                    291375840,
+                    711006036,
+                    645758767,
+                    33553903,
+                    501987274,
+                    732243519,
+                    549819055,
+                    775074238,
+                    109230359,
+                    613836728,
+                    674817295,
+                    678982897,
+                    4621474,
+                    831813607,
+                    755298617,
+                    857732912,
+                    240091718,
+                    824732336,
+                    263065042,
+                    436125799,
+                    613653857,
+                    421058454,
+                    848449279,
+                    549194026,
+                    390400708,
+                    520357750,
+                    201714473,
+                    310908320,
+                    291076272,
+                    750419624,
+                    499397744,
+                    366291675,
+                    194548935,
+                    249475527,
+                    981145387,
+                    830764108,
+                    488906619,
+                    936046762,
+                    273116590,
+                    223475535,
+                    26909743,
+                    377131597,
+                    255618,
+                    901236629,
+                    249363328,
+                    38633596,
+                    553867400,
+                    880083263,
+                    767944708,
+                    929153832,
+                    338226574,
+                    758488912,
+                    624018034,
+                    436227912,
+                    757885954,
+                    886561224,
+                    760162263,
+                    985967874,
+                    446123643,
+                    747098236,
+                    637789910,
+                    465718723,
+                    396625245,
+                    690091670,
+                    204893834,
+                    771614806,
+                    675764329,
+                    518031333,
+                    253963590,
+                    179655397,
+                    755628428,
+                    248635597,
+                    655826937,
+                    711638122,
+                    87089747,
+                    100827346,
+                    886212850,
+                    150066958,
+                    720093549,
+                    963470658,
+                    431290100,
+                    591994765,
+                    996160046,
+                    375483514,
+                    187942979,
+                    198170348,
+                    354561875,
+                    460455969,
+                    33330957,
+                    717511783,
+                    280790600,
+                    682358041,
+                    221577045,
+                    721385186,
+                    121062153,
+                    45801005,
+                    937129842,
+                    753581938,
+                    835779914,
+                    801707972,
+                    956107212,
+                    404170880,
+                    81911598,
+                    867391537,
+                    968790701,
+                    851660520,
+                    280707062,
+                    970823070,
+                    100820672,
+                    433203275,
+                    31597384,
+                    605442041,
+                    630866454,
+                    18868516,
+                    176187551,
+                    783727279,
+                    929318370,
+                    997268426,
+                    337281568,
+                    928555309,
+                    139745358,
+                    297002900,
+                    394306243,
+                    508643557,
+                    125314576,
+                    22598790,
+                    151934672,
+                    110156488,
+                    549240306,
+                    726484932,
+                    804248276,
+                    683108577,
+                    460913255,
+                    986555034,
+                    752061484,
+                    937422955,
+                    35467887,
+                    84317904,
+                    559893870,
+                    793308049,
+                    949187533,
+                    7075392,
+                    72275071,
+                    315788473,
+                    554124140,
+                    933369501,
+                    440555873,
+                    885702299,
+                    271479875,
+                    407366682,
+                    528642724,
+                    991472828,
+                    737092418,
+                    528558148,
+                    687979167,
+                    648348973,
+                    412358902,
+                    231520423,
+                    406439292,
+                    317834226,
+                    228628625,
+                    562588318,
+                    870674574,
+                    800936008,
+                    468377190,
+                    518336885,
+                    607178760,
+                    39776697,
+                    884767731,
+                    639025625,
+                    61205528,
+                    559340692,
+                    236398366,
+                    137564904,
+                    362490088,
+                    572577535,
+                    247994103,
+                    744757997,
+                    608907394,
+                    556799325,
+                    354884355,
+                    607138497,
+                    100957648,
+                    844607929,
+                    640548565,
+                    189897592,
+                    929012868,
+                    72753012,
+                    860506015,
+                    998423550,
+                    936598075,
+                    12660654,
+                    678039826,
+                    697694778,
+                    981861493,
+                    469246729,
+                    477863511,
+                    903800442,
+                    982586041,
+                    826489677,
+                    440092768,
+                    638835563,
+                    220900608,
+                    401976543,
+                    541089434,
+                    924489986,
+                    171978936,
+                    190799297,
+                    238429922,
+                    363247427,
+                    508736578,
+                    345375735,
+                    392542469,
+                    357212429,
+                    423566800,
+                    84528775,
+                    367296050,
+                    540056196,
+                    708626122,
+                    784454371,
+                    916138184,
+                    258597947,
+                    466311875,
+                    677554191,
+                    821786488,
+                    407865430,
+                    700235080,
+                    107239546,
+                    906363976,
+                    774439297,
+                    117968149,
+                    305107099,
+                    817459511,
+                    804264801,
+                    302672558,
+                    66518381,
+                    996035630,
+                    278552174,
+                    529764261,
+                    597159973,
+                    489987883,
+                    846302148,
+                    296424965,
+                    760827445,
+                    264940514,
+                    605973313,
+                    974702636,
+                    160266275,
+                    148664231,
+                    417942258,
+                    343388417,
+                    499676771,
+                    577744272,
+                    407111555,
+                    46170325,
+                    618654459,
+                    874484500,
+                    679474589,
+                    466427025,
+                    209514110,
+                    550455083,
+                    485370031,
+                    427864937,
+                    825926724,
+                    217806854,
+                    19901717,
+                    758271529,
+                    184790131,
+                    931766158,
+                    456869764,
+                    983707263,
+                    991376832,
+                    981946934,
+                    672345225,
+                    464230036,
+                    378464292,
+                    362141434,
+                    749063121,
+                    11421377,
+                    299537068,
+                    478670952,
+                    233891287,
+                    645096852,
+                    825139000,
+                    950981876,
+                    11911916,
+                    368715799,
+                    771372459,
+                    873692432,
+                    624837225,
+                    910601872,
+                    917516352,
+                    970864950,
+                    378673807,
+                    940015622,
+                    294663053,
+                    658362932,
+                    920132636,
+                    81953933,
+                    81386945,
+                    101751214,
+                    268342735,
+                    759270126,
+                    324349715,
+                    723944297,
+                    377419363,
+                    396791057,
+                    309850203,
+                    785615309,
+                    848749398,
+                    477755831,
+                    593664896,
+                    908053488,
+                    971426473,
+                    216641595,
+                    353954791,
+                    438837005,
+                    555618992,
+                    778792497,
+                    595933057,
+                    209329805,
+                    97574521,
+                    338011809,
+                    636721230,
+                    998578774,
+                    681933912,
+                    525170250,
+                    582343029,
+                    856255955,
+                    929922595,
+                    427411341,
+                    338544746,
+                    202141922,
+                    235748292,
+                    457649040,
+                    124053176
+                ],
+                [
+                    32,
+                    173,
+                    178,
+                    249,
+                    177,
+                    44,
+                    223,
+                    142,
+                    362,
+                    115,
+                    188,
+                    344,
+                    249,
+                    308,
+                    56,
+                    33,
+                    167,
+                    69,
+                    328,
+                    190,
+                    110,
+                    307,
+                    326,
+                    246,
+                    363,
+                    283,
+                    35,
+                    197,
+                    104,
+                    259,
+                    269,
+                    354,
+                    29,
+                    314,
+                    214,
+                    276,
+                    52,
+                    153,
+                    292,
+                    283,
+                    299,
+                    7,
+                    11,
+                    166,
+                    203,
+                    311,
+                    319,
+                    263,
+                    133,
+                    167,
+                    41,
+                    252,
+                    168,
+                    17,
+                    355,
+                    253,
+                    296,
+                    162,
+                    230,
+                    62,
+                    308,
+                    155,
+                    330,
+                    314,
+                    54,
+                    327,
+                    106,
+                    50,
+                    35,
+                    258,
+                    319,
+                    167,
+                    259,
+                    171,
+                    108,
+                    232,
+                    124,
+                    93,
+                    151,
+                    191,
+                    346,
+                    90,
+                    362,
+                    53,
+                    34,
+                    268,
+                    41,
+                    237,
+                    97,
+                    124,
+                    327,
+                    54,
+                    250,
+                    356,
+                    2,
+                    250,
+                    29,
+                    347,
+                    114,
+                    49,
+                    379,
+                    165,
+                    380,
+                    290,
+                    281,
+                    281,
+                    165,
+                    279,
+                    110,
+                    69,
+                    149,
+                    276,
+                    56,
+                    224,
+                    205,
+                    85,
+                    5,
+                    280,
+                    334,
+                    276,
+                    118,
+                    66,
+                    260,
+                    143,
+                    113,
+                    206,
+                    147,
+                    69,
+                    253,
+                    208,
+                    251,
+                    67,
+                    206,
+                    340,
+                    178,
+                    211,
+                    185,
+                    124,
+                    168,
+                    154,
+                    87,
+                    349,
+                    24,
+                    348,
+                    250,
+                    280,
+                    181,
+                    18,
+                    253,
+                    193,
+                    257,
+                    264,
+                    40,
+                    224,
+                    52,
+                    350,
+                    317,
+                    278,
+                    320,
+                    219,
+                    346,
+                    154,
+                    371,
+                    324,
+                    327,
+                    187,
+                    137,
+                    69,
+                    376,
+                    149,
+                    357,
+                    318,
+                    154,
+                    53,
+                    209,
+                    354,
+                    111,
+                    78,
+                    217,
+                    269,
+                    28,
+                    384,
+                    257,
+                    218,
+                    186,
+                    328,
+                    179,
+                    322,
+                    346,
+                    323,
+                    349,
+                    11,
+                    209,
+                    256,
+                    258,
+                    37,
+                    375,
+                    208,
+                    359,
+                    39,
+                    320,
+                    67,
+                    269,
+                    136,
+                    9,
+                    380,
+                    307,
+                    288,
+                    262,
+                    385,
+                    119,
+                    267,
+                    101,
+                    336,
+                    113,
+                    235,
+                    100,
+                    310,
+                    278,
+                    254,
+                    230,
+                    356,
+                    279,
+                    327,
+                    116,
+                    196,
+                    165,
+                    121,
+                    5,
+                    287,
+                    220,
+                    191,
+                    272,
+                    160,
+                    237,
+                    10,
+                    39,
+                    184,
+                    86,
+                    33,
+                    126,
+                    222,
+                    241,
+                    200,
+                    304,
+                    121,
+                    43,
+                    373,
+                    243,
+                    203,
+                    118,
+                    31,
+                    4,
+                    118,
+                    364,
+                    165,
+                    99,
+                    213,
+                    232,
+                    350,
+                    45,
+                    249,
+                    128,
+                    255,
+                    326,
+                    252,
+                    89,
+                    36,
+                    254,
+                    92,
+                    3,
+                    345,
+                    123,
+                    16,
+                    31,
+                    77,
+                    350,
+                    326,
+                    300,
+                    383,
+                    262,
+                    292,
+                    10,
+                    136,
+                    316,
+                    29,
+                    11,
+                    214,
+                    181,
+                    30,
+                    318,
+                    303,
+                    273,
+                    237,
+                    97,
+                    267,
+                    218,
+                    186,
+                    2,
+                    358,
+                    167,
+                    35,
+                    292,
+                    49,
+                    218,
+                    129,
+                    377,
+                    267,
+                    333,
+                    25,
+                    314,
+                    281,
+                    188,
+                    116,
+                    381,
+                    201,
+                    43,
+                    99,
+                    174,
+                    58,
+                    293,
+                    251,
+                    371,
+                    230,
+                    130,
+                    22,
+                    326,
+                    97,
+                    95,
+                    31,
+                    212,
+                    256,
+                    30,
+                    352,
+                    241,
+                    147,
+                    163,
+                    4,
+                    296,
+                    228,
+                    168,
+                    226,
+                    109,
+                    171,
+                    68,
+                    53,
+                    194,
+                    181,
+                    358,
+                    384,
+                    314,
+                    280,
+                    173,
+                    380,
+                    9,
+                    92,
+                    136,
+                    14,
+                    383,
+                    25,
+                    128,
+                    25,
+                    319,
+                    155,
+                    94,
+                    70,
+                    275,
+                    200,
+                    163,
+                    121,
+                    118,
+                    94,
+                    281,
+                    123,
+                    295,
+                    335,
+                    119,
+                    197,
+                    214,
+                    109,
+                    381,
+                    247,
+                    205,
+                    192,
+                    367,
+                    375,
+                    321,
+                    193,
+                    99,
+                    24,
+                    266,
+                    223,
+                    53,
+                    106,
+                    304,
+                    16,
+                    293,
+                    203,
+                    326,
+                    89,
+                    40,
+                    343,
+                    26,
+                    281,
+                    351,
+                    58,
+                    232,
+                    351,
+                    375,
+                    190,
+                    243,
+                    38,
+                    339,
+                    318,
+                    203,
+                    130,
+                    128,
+                    39,
+                    183,
+                    299,
+                    364,
+                    306,
+                    269,
+                    294,
+                    107,
+                    289,
+                    56,
+                    379,
+                    213,
+                    297,
+                    264,
+                    28,
+                    185,
+                    243,
+                    327,
+                    295,
+                    349,
+                    122,
+                    12,
+                    23,
+                    253,
+                    3,
+                    168,
+                    242,
+                    158,
+                    7,
+                    45,
+                    147,
+                    189,
+                    247,
+                    316,
+                    59,
+                    208,
+                    278,
+                    79,
+                    210,
+                    107,
+                    361,
+                    110,
+                    358,
+                    310,
+                    94,
+                    174,
+                    199,
+                    120,
+                    311,
+                    266,
+                    164,
+                    91,
+                    157,
+                    173,
+                    257,
+                    98,
+                    349,
+                    160,
+                    162,
+                    221,
+                    41,
+                    50,
+                    384,
+                    270,
+                    327,
+                    338,
+                    216,
+                    315,
+                    89,
+                    205,
+                    281,
+                    248,
+                    50,
+                    34,
+                    134,
+                    269,
+                    339,
+                    218,
+                    3,
+                    297,
+                    382,
+                    62,
+                    255,
+                    362,
+                    22,
+                    259,
+                    186,
+                    172,
+                    202,
+                    28,
+                    240,
+                    172,
+                    343,
+                    229,
+                    307,
+                    380,
+                    332,
+                    268,
+                    189,
+                    265,
+                    183,
+                    188,
+                    210,
+                    176,
+                    191,
+                    141,
+                    313,
+                    363,
+                    204,
+                    90,
+                    126,
+                    105,
+                    330,
+                    25,
+                    270,
+                    241,
+                    187,
+                    380,
+                    43,
+                    202,
+                    331,
+                    238,
+                    187,
+                    134,
+                    159,
+                    28,
+                    283,
+                    208,
+                    376,
+                    33,
+                    152,
+                    320,
+                    366,
+                    250,
+                    178,
+                    97,
+                    312,
+                    104,
+                    289,
+                    384,
+                    242,
+                    167,
+                    266,
+                    157,
+                    222,
+                    274,
+                    275,
+                    196,
+                    124,
+                    23,
+                    373,
+                    188,
+                    304,
+                    157,
+                    337,
+                    376,
+                    257,
+                    295,
+                    239,
+                    372,
+                    190,
+                    85,
+                    305,
+                    12,
+                    179,
+                    330,
+                    82,
+                    288,
+                    153,
+                    115,
+                    357,
+                    68,
+                    287,
+                    39,
+                    353,
+                    366,
+                    12,
+                    368,
+                    164,
+                    266,
+                    5,
+                    37,
+                    340,
+                    320,
+                    115,
+                    111,
+                    281,
+                    387,
+                    284,
+                    355,
+                    148,
+                    69,
+                    357,
+                    65,
+                    274,
+                    71,
+                    254,
+                    57,
+                    297,
+                    72,
+                    235,
+                    97,
+                    68,
+                    20,
+                    108,
+                    10,
+                    314,
+                    38,
+                    131,
+                    341,
+                    111,
+                    4,
+                    287,
+                    127,
+                    133,
+                    7,
+                    33,
+                    369,
+                    19,
+                    39,
+                    222,
+                    242,
+                    84,
+                    132,
+                    304,
+                    136,
+                    215,
+                    302,
+                    176,
+                    355,
+                    217,
+                    82,
+                    195,
+                    166,
+                    38,
+                    350,
+                    312,
+                    49,
+                    186,
+                    295,
+                    353,
+                    162,
+                    123,
+                    364,
+                    322,
+                    111,
+                    270,
+                    70,
+                    331,
+                    140,
+                    342,
+                    293,
+                    316,
+                    114,
+                    57,
+                    33,
+                    87,
+                    64,
+                    73,
+                    332,
+                    17,
+                    117,
+                    216,
+                    264,
+                    93,
+                    360,
+                    198,
+                    158,
+                    102,
+                    65,
+                    336,
+                    358,
+                    383,
+                    214,
+                    383,
+                    339,
+                    344,
+                    151,
+                    84,
+                    335,
+                    79,
+                    367,
+                    263,
+                    235,
+                    148,
+                    143,
+                    245,
+                    372,
+                    32,
+                    189,
+                    161,
+                    295,
+                    82,
+                    45,
+                    325,
+                    353,
+                    122,
+                    244,
+                    356,
+                    56,
+                    339,
+                    101,
+                    79,
+                    71,
+                    179,
+                    339,
+                    123,
+                    36,
+                    169,
+                    201,
+                    137,
+                    109,
+                    275,
+                    74,
+                    237,
+                    384,
+                    251,
+                    102,
+                    198,
+                    17,
+                    250,
+                    158,
+                    246,
+                    49,
+                    335,
+                    181,
+                    83,
+                    362,
+                    302,
+                    93,
+                    343,
+                    253,
+                    354,
+                    227,
+                    264,
+                    106,
+                    198,
+                    336,
+                    289,
+                    231,
+                    185,
+                    111,
+                    348,
+                    210,
+                    85,
+                    184,
+                    109,
+                    245,
+                    26,
+                    272,
+                    113,
+                    176,
+                    205,
+                    164,
+                    218,
+                    94,
+                    69,
+                    247,
+                    379,
+                    149,
+                    54,
+                    354,
+                    361,
+                    235,
+                    377,
+                    194,
+                    115,
+                    45,
+                    319,
+                    306,
+                    195,
+                    67,
+                    74,
+                    207,
+                    193,
+                    4,
+                    113,
+                    209,
+                    365,
+                    123,
+                    46,
+                    300,
+                    246,
+                    259,
+                    256,
+                    349,
+                    187,
+                    194,
+                    301,
+                    124,
+                    94,
+                    23,
+                    242,
+                    41,
+                    189,
+                    221,
+                    279,
+                    146,
+                    238,
+                    116,
+                    158,
+                    313,
+                    349,
+                    275,
+                    22,
+                    159,
+                    85,
+                    86,
+                    191,
+                    373,
+                    28,
+                    233,
+                    201,
+                    328,
+                    21,
+                    288,
+                    357,
+                    185,
+                    339,
+                    20,
+                    378,
+                    203,
+                    235,
+                    146,
+                    233,
+                    366,
+                    373,
+                    195,
+                    58,
+                    88,
+                    73,
+                    341,
+                    334,
+                    263,
+                    22,
+                    44,
+                    240,
+                    273,
+                    159,
+                    341,
+                    141,
+                    73,
+                    289,
+                    287,
+                    211,
+                    94,
+                    345,
+                    273,
+                    112,
+                    287,
+                    316,
+                    91,
+                    289,
+                    279,
+                    63,
+                    234,
+                    250,
+                    158,
+                    178,
+                    40,
+                    141,
+                    48,
+                    162,
+                    178,
+                    194,
+                    246,
+                    77,
+                    45,
+                    5,
+                    75,
+                    325,
+                    364,
+                    11,
+                    143,
+                    375,
+                    110,
+                    192,
+                    307,
+                    290,
+                    94,
+                    210,
+                    132,
+                    132,
+                    138,
+                    383,
+                    5,
+                    273,
+                    260,
+                    159,
+                    106,
+                    331,
+                    213,
+                    233,
+                    99,
+                    135,
+                    114,
+                    44,
+                    161,
+                    301,
+                    210,
+                    186,
+                    84,
+                    131,
+                    370,
+                    380,
+                    372,
+                    188,
+                    339,
+                    8,
+                    315,
+                    159,
+                    355,
+                    260,
+                    355,
+                    194,
+                    64,
+                    154,
+                    383,
+                    365,
+                    57,
+                    342,
+                    138,
+                    81,
+                    298,
+                    319,
+                    74,
+                    194,
+                    326,
+                    270,
+                    373,
+                    336,
+                    354,
+                    182,
+                    268,
+                    45,
+                    286,
+                    381,
+                    22,
+                    127,
+                    83,
+                    59,
+                    119,
+                    45,
+                    249,
+                    169,
+                    6,
+                    247,
+                    139,
+                    278,
+                    287,
+                    289,
+                    329,
+                    74,
+                    312,
+                    212,
+                    207,
+                    326,
+                    270,
+                    40,
+                    251,
+                    143,
+                    88,
+                    89,
+                    268,
+                    211,
+                    305,
+                    241,
+                    115,
+                    31,
+                    197,
+                    368,
+                    84,
+                    350,
+                    202,
+                    20,
+                    64,
+                    246,
+                    326,
+                    13,
+                    190,
+                    273,
+                    275,
+                    60,
+                    103,
+                    104,
+                    361,
+                    248,
+                    270,
+                    294,
+                    204,
+                    108,
+                    219,
+                    207,
+                    247,
+                    209,
+                    178,
+                    164,
+                    361,
+                    316,
+                    245,
+                    288,
+                    344,
+                    288,
+                    237,
+                    71,
+                    387,
+                    75,
+                    369,
+                    314,
+                    246,
+                    305,
+                    118,
+                    221,
+                    315,
+                    309,
+                    17,
+                    246,
+                    356,
+                    41,
+                    73,
+                    260,
+                    267,
+                    52,
+                    174,
+                    152,
+                    380,
+                    3,
+                    221,
+                    315,
+                    10,
+                    31,
+                    194,
+                    244,
+                    179,
+                    268,
+                    27,
+                    164,
+                    174,
+                    385,
+                    267,
+                    372,
+                    239,
+                    377,
+                    113,
+                    12,
+                    284,
+                    314,
+                    232,
+                    296,
+                    154,
+                    18,
+                    158,
+                    256,
+                    288,
+                    342,
+                    165,
+                    170,
+                    19,
+                    310,
+                    237,
+                    217,
+                    115,
+                    108,
+                    11,
+                    382,
+                    31,
+                    65,
+                    186,
+                    162,
+                    130,
+                    342,
+                    207,
+                    338,
+                    133,
+                    146,
+                    14,
+                    346,
+                    263,
+                    247,
+                    114,
+                    23,
+                    322,
+                    40,
+                    31,
+                    27,
+                    152,
+                    222,
+                    222,
+                    198,
+                    166,
+                    232,
+                    122,
+                    5,
+                    150
+                ]
+            ],
+            "output": -1
+        },
+        {
+            "input": [
+                [
+                    275345304,
+                    684050530,
+                    907816636,
+                    492367036,
+                    540947588,
+                    383633415,
+                    127222373,
+                    592269165,
+                    881372102,
+                    760385719,
+                    353489878,
+                    133016163,
+                    977116355,
+                    521234250,
+                    136604166,
+                    20820441,
+                    493598494,
+                    16631998,
+                    725028784,
+                    599209364,
+                    778596646,
+                    674498013,
+                    697987943,
+                    106408054,
+                    957123395,
+                    232364810,
+                    4096702,
+                    764953041,
+                    471792863,
+                    746315972,
+                    653782335,
+                    565788233,
+                    486792377,
+                    502751670,
+                    83742596,
+                    609509979,
+                    219132145,
+                    427629009,
+                    31728970,
+                    401829548,
+                    15582143,
+                    8429419,
+                    709470609,
+                    395351302,
+                    411506168,
+                    5055100,
+                    885745434,
+                    495379370,
+                    467861336,
+                    836378950,
+                    792806620,
+                    33046293,
+                    981845693,
+                    315521857,
+                    30440553,
+                    537687069,
+                    705352355,
+                    587533428,
+                    878463574,
+                    794712180,
+                    617721637,
+                    139937177,
+                    931071010,
+                    437875415,
+                    715622411,
+                    377019774,
+                    460661748,
+                    507934966,
+                    336821929,
+                    887375708,
+                    381649837,
+                    89944031,
+                    213788538,
+                    365068390,
+                    516397214,
+                    418422332,
+                    161370790,
+                    897679431,
+                    773590453,
+                    146474878,
+                    968913100,
+                    595645472,
+                    806685564,
+                    308593382,
+                    405591515,
+                    300177918,
+                    94828308,
+                    702037248,
+                    165928807,
+                    618838573,
+                    787066847,
+                    238031821,
+                    617934052,
+                    175853533,
+                    52175974,
+                    835982532,
+                    533719896,
+                    133564493,
+                    450632802,
+                    964020799,
+                    951525400,
+                    100254297,
+                    998152140,
+                    783674559,
+                    769103842,
+                    989671712,
+                    278014439,
+                    358007347,
+                    619958714,
+                    103616611,
+                    375468367,
+                    222848507,
+                    728416591,
+                    838460051,
+                    675556234,
+                    601629199,
+                    672607049,
+                    413529965,
+                    620567780,
+                    185624278,
+                    796719570,
+                    506400430,
+                    120638848,
+                    110051454,
+                    329897415,
+                    783468035,
+                    536352169,
+                    750946119,
+                    287112876,
+                    117345825,
+                    888827979,
+                    839269751,
+                    647137638,
+                    333110786,
+                    76172739,
+                    543069104,
+                    311706843,
+                    259372987,
+                    941188667,
+                    131694640,
+                    598616736,
+                    20009445,
+                    477742220,
+                    88275296,
+                    822663494,
+                    266512286,
+                    873879275,
+                    635128016,
+                    814436816,
+                    312222551,
+                    684347951,
+                    577084381,
+                    479472330,
+                    835608638,
+                    34791863,
+                    872936694,
+                    538831923,
+                    820676183,
+                    424627841,
+                    426622586,
+                    605759725,
+                    362152257,
+                    366700733,
+                    659097049,
+                    853684034,
+                    101401291,
+                    2926725,
+                    851595176,
+                    430178148,
+                    786305153,
+                    611629313,
+                    525897203,
+                    398498905,
+                    24871940,
+                    915124649,
+                    614703444,
+                    237402341,
+                    22119539,
+                    701474265,
+                    749131498,
+                    83429925,
+                    435898203,
+                    294109777,
+                    202197853,
+                    916466469,
+                    69236014,
+                    227116563,
+                    229962849,
+                    795485534,
+                    827133668,
+                    167259933,
+                    898916608,
+                    933873815,
+                    572885751,
+                    225981053,
+                    667105981,
+                    622585087,
+                    279904392,
+                    967348879,
+                    646753400,
+                    976977762,
+                    321105563,
+                    387702711,
+                    912001318,
+                    898052318,
+                    204366534,
+                    813915089,
+                    272932139,
+                    385369702,
+                    929061161,
+                    12282757,
+                    792933834,
+                    976399995,
+                    380900424,
+                    866329034,
+                    848671112,
+                    64025309,
+                    269980092,
+                    880719248,
+                    7239038,
+                    179973152,
+                    229246669,
+                    619276250,
+                    950138045,
+                    631727784,
+                    217398445,
+                    652944834,
+                    526290108,
+                    667615135,
+                    858650058,
+                    659633973,
+                    971220083,
+                    684970775,
+                    459675085,
+                    55378111,
+                    453933301,
+                    615993054,
+                    930704194,
+                    593638805,
+                    519336674,
+                    594523312,
+                    177763151,
+                    606917167,
+                    768934025,
+                    212539629,
+                    150803009,
+                    515548854,
+                    641498859,
+                    366664864,
+                    199511317,
+                    631279649,
+                    477749337,
+                    906323663,
+                    31984110,
+                    496858405,
+                    136418372,
+                    913471604,
+                    181398531,
+                    113654476,
+                    220398397,
+                    961789248,
+                    922239832,
+                    173640282,
+                    504160103,
+                    541689070,
+                    542896953,
+                    240918442,
+                    389461287,
+                    238131206,
+                    574654533,
+                    242640180,
+                    134962195,
+                    72937404,
+                    260124761,
+                    138183927,
+                    508835481,
+                    832916289,
+                    28943521,
+                    616831671,
+                    512558589,
+                    375093484,
+                    936895347,
+                    871594966
+                ],
+                [
+                    65,
+                    50,
+                    278,
+                    188,
+                    182,
+                    164,
+                    186,
+                    121,
+                    112,
+                    241,
+                    86,
+                    157,
+                    78,
+                    225,
+                    101,
+                    19,
+                    210,
+                    55,
+                    136,
+                    62,
+                    278,
+                    228,
+                    147,
+                    24,
+                    69,
+                    129,
+                    212,
+                    274,
+                    40,
+                    89,
+                    105,
+                    61,
+                    25,
+                    78,
+                    9,
+                    88,
+                    130,
+                    34,
+                    82,
+                    4,
+                    38,
+                    115,
+                    83,
+                    208,
+                    37,
+                    85,
+                    182,
+                    99,
+                    166,
+                    151,
+                    108,
+                    233,
+                    101,
+                    230,
+                    167,
+                    42,
+                    163,
+                    32,
+                    263,
+                    94,
+                    135,
+                    217,
+                    52,
+                    8,
+                    116,
+                    92,
+                    281,
+                    82,
+                    224,
+                    71,
+                    174,
+                    266,
+                    247,
+                    81,
+                    88,
+                    134,
+                    223,
+                    40,
+                    56,
+                    165,
+                    99,
+                    180,
+                    227,
+                    139,
+                    69,
+                    203,
+                    111,
+                    16,
+                    24,
+                    153,
+                    106,
+                    47,
+                    210,
+                    2,
+                    240,
+                    162,
+                    53,
+                    157,
+                    30,
+                    94,
+                    22,
+                    276,
+                    137,
+                    166,
+                    172,
+                    249,
+                    120,
+                    21,
+                    204,
+                    153,
+                    228,
+                    203,
+                    13,
+                    11,
+                    279,
+                    237,
+                    38,
+                    237,
+                    107,
+                    266,
+                    16,
+                    147,
+                    216,
+                    174,
+                    216,
+                    152,
+                    104,
+                    137,
+                    67,
+                    221,
+                    207,
+                    132,
+                    174,
+                    203,
+                    118,
+                    226,
+                    145,
+                    98,
+                    35,
+                    55,
+                    147,
+                    174,
+                    51,
+                    9,
+                    242,
+                    206,
+                    136,
+                    28,
+                    29,
+                    106,
+                    259,
+                    192,
+                    178,
+                    158,
+                    101,
+                    121,
+                    111,
+                    174,
+                    88,
+                    155,
+                    169,
+                    90,
+                    269,
+                    199,
+                    231,
+                    27,
+                    278,
+                    125,
+                    184,
+                    204,
+                    189,
+                    148,
+                    220,
+                    25,
+                    121,
+                    108,
+                    269,
+                    16,
+                    109,
+                    39,
+                    116,
+                    7,
+                    153,
+                    96,
+                    260,
+                    180,
+                    188,
+                    73,
+                    97,
+                    234,
+                    168,
+                    69,
+                    145,
+                    141,
+                    183,
+                    18,
+                    31,
+                    234,
+                    68,
+                    95,
+                    93,
+                    120,
+                    161,
+                    278,
+                    231,
+                    247,
+                    206,
+                    26,
+                    181,
+                    215,
+                    126,
+                    53,
+                    153,
+                    239,
+                    148,
+                    87,
+                    235,
+                    268,
+                    203,
+                    206,
+                    105,
+                    177,
+                    68,
+                    84,
+                    222,
+                    116,
+                    177,
+                    174,
+                    230,
+                    228,
+                    278,
+                    262,
+                    167,
+                    186,
+                    70,
+                    157,
+                    8,
+                    147,
+                    110,
+                    9,
+                    93,
+                    193,
+                    179,
+                    245,
+                    142,
+                    222,
+                    145,
+                    130,
+                    272,
+                    249,
+                    101,
+                    14,
+                    263,
+                    226,
+                    252,
+                    16,
+                    147,
+                    148,
+                    57,
+                    185,
+                    4,
+                    233,
+                    180,
+                    145,
+                    263,
+                    28,
+                    25,
+                    112,
+                    224,
+                    79,
+                    279,
+                    96,
+                    92,
+                    27,
+                    232,
+                    202,
+                    54,
+                    122,
+                    90,
+                    6,
+                    224,
+                    38,
+                    252,
+                    162,
+                    87,
+                    44,
+                    231,
+                    77,
+                    150,
+                    203,
+                    6,
+                    176,
+                    275,
+                    108,
+                    4,
+                    37,
+                    142,
+                    21,
+                    76,
+                    103,
+                    8,
+                    91,
+                    91,
+                    54,
+                    4,
+                    62,
+                    200,
+                    191,
+                    61,
+                    258,
+                    238,
+                    138,
+                    116,
+                    185,
+                    16,
+                    83,
+                    192,
+                    47,
+                    247,
+                    226,
+                    180,
+                    240,
+                    3,
+                    1,
+                    36,
+                    167,
+                    271,
+                    171,
+                    80,
+                    11,
+                    1,
+                    167,
+                    54,
+                    267,
+                    222,
+                    27,
+                    71,
+                    282,
+                    154,
+                    212,
+                    277,
+                    93,
+                    147,
+                    78,
+                    237,
+                    188,
+                    87,
+                    126,
+                    122,
+                    182,
+                    283,
+                    211,
+                    163,
+                    218,
+                    248,
+                    244,
+                    246,
+                    141,
+                    48,
+                    121,
+                    186,
+                    61,
+                    163,
+                    39,
+                    208,
+                    26,
+                    131,
+                    3,
+                    177,
+                    110,
+                    214,
+                    202,
+                    277,
+                    218,
+                    31,
+                    214,
+                    47,
+                    199,
+                    262,
+                    282,
+                    149,
+                    77,
+                    49,
+                    263,
+                    97,
+                    31,
+                    77,
+                    209,
+                    210,
+                    126,
+                    123,
+                    54,
+                    273,
+                    222,
+                    268,
+                    255,
+                    256,
+                    10,
+                    253,
+                    138,
+                    271,
+                    47,
+                    188,
+                    269,
+                    70,
+                    11,
+                    128,
+                    78,
+                    163,
+                    129,
+                    214,
+                    90,
+                    90,
+                    13,
+                    223,
+                    26,
+                    119,
+                    178,
+                    211,
+                    176,
+                    153,
+                    68,
+                    216,
+                    130,
+                    111,
+                    281,
+                    209,
+                    33,
+                    163,
+                    189,
+                    217,
+                    236,
+                    212,
+                    241,
+                    166,
+                    39,
+                    20,
+                    132,
+                    159,
+                    237,
+                    74,
+                    264,
+                    78,
+                    47,
+                    81,
+                    229,
+                    12,
+                    238,
+                    129,
+                    53,
+                    47,
+                    30,
+                    88,
+                    110,
+                    48,
+                    88,
+                    14,
+                    194,
+                    268,
+                    256,
+                    138,
+                    72,
+                    28,
+                    215,
+                    244,
+                    175,
+                    118,
+                    195,
+                    274,
+                    12,
+                    108,
+                    121,
+                    60,
+                    97,
+                    138,
+                    158,
+                    27,
+                    54,
+                    31,
+                    63,
+                    162,
+                    204,
+                    242,
+                    19,
+                    283,
+                    132,
+                    99,
+                    143,
+                    34,
+                    210,
+                    264,
+                    170
+                ]
+            ],
+            "output": -1
+        },
+        {
+            "input": [
+                [
+                    345206373,
+                    504492415,
+                    517562883,
+                    146792274,
+                    485948431,
+                    355953024,
+                    353055177,
+                    952419650,
+                    683156901,
+                    996890769,
+                    351112260,
+                    244247091,
+                    101946472,
+                    2207299,
+                    247020645,
+                    251235297,
+                    962432389,
+                    739454333,
+                    788704827,
+                    312315276,
+                    309116164,
+                    645856933,
+                    26513980,
+                    781266151,
+                    217330701,
+                    877369063,
+                    516602532,
+                    635113640,
+                    400206933,
+                    985139529,
+                    995544826,
+                    497645171,
+                    219411473,
+                    740995358,
+                    998227933,
+                    812474418,
+                    637525061,
+                    551576055,
+                    701346433,
+                    177131335,
+                    594123964,
+                    308513792,
+                    96331622,
+                    170082076,
+                    555164180,
+                    956496221,
+                    102797484,
+                    841766260,
+                    984490730,
+                    517462724,
+                    254046204,
+                    388889292,
+                    692296216,
+                    50722274,
+                    249889515,
+                    562787306,
+                    933300123,
+                    623060527,
+                    59931380,
+                    666669499,
+                    318094518,
+                    856521219,
+                    262854540,
+                    21657825,
+                    400208170,
+                    964761732,
+                    311205114,
+                    626330895,
+                    91989660,
+                    309951799,
+                    850881041,
+                    356405694,
+                    687233075,
+                    649984751,
+                    856168273,
+                    765069663,
+                    972913241,
+                    696866654,
+                    828222492,
+                    788561426,
+                    497615226,
+                    576364573,
+                    554994261,
+                    350354744,
+                    593803370,
+                    286413169,
+                    212502609,
+                    347098308,
+                    424792717,
+                    497279582,
+                    595809703,
+                    109299280,
+                    74442093,
+                    382420131,
+                    380334683,
+                    730205978,
+                    395702948,
+                    474993334,
+                    584771608,
+                    314723511,
+                    63842698,
+                    462687266,
+                    586633976,
+                    651137152,
+                    769780569,
+                    299139625,
+                    72435967,
+                    808494056,
+                    316412756,
+                    6833232,
+                    492610386,
+                    433538776,
+                    484802691,
+                    82064254,
+                    384897743,
+                    929087306,
+                    494407838,
+                    153747314,
+                    473241956,
+                    995916626,
+                    730775185,
+                    429833008,
+                    876247531,
+                    139031635,
+                    724163272,
+                    408290805,
+                    598329273,
+                    289849483,
+                    464953652,
+                    571259225,
+                    458544527,
+                    980627713,
+                    998464914,
+                    33145396,
+                    471830127,
+                    977849292,
+                    338399793,
+                    442860203,
+                    482998806,
+                    664390745,
+                    365387645,
+                    22287207,
+                    369248025,
+                    309873500,
+                    283430593,
+                    966207962,
+                    243159504,
+                    514721379,
+                    896704408,
+                    906435496,
+                    214869933,
+                    186771110,
+                    116989160,
+                    768420197,
+                    28097356,
+                    923975788,
+                    578787168,
+                    713701637,
+                    493522092,
+                    378479596,
+                    825871181,
+                    823576902,
+                    25612854,
+                    647869385,
+                    288436602,
+                    260767158,
+                    854698667,
+                    423779678,
+                    515669909,
+                    554815972,
+                    851358667,
+                    953865837,
+                    972103638,
+                    584540198,
+                    406443067,
+                    551491059,
+                    621573651,
+                    1429557,
+                    199162841,
+                    50517737,
+                    865911606,
+                    7360010,
+                    35267707,
+                    598273825,
+                    584011056,
+                    750952654,
+                    88776910,
+                    27974037,
+                    476976112,
+                    828869707,
+                    510948290,
+                    361819401,
+                    38673838,
+                    869854002,
+                    286260928,
+                    466812553,
+                    566445841,
+                    969974522,
+                    296247481,
+                    4802532,
+                    504557275,
+                    278411939,
+                    303304897,
+                    396299177,
+                    499694351,
+                    295018610,
+                    475681405,
+                    112851468,
+                    570571194,
+                    134556392,
+                    756479358,
+                    563002458,
+                    121078632,
+                    387915496,
+                    270557513,
+                    422852982,
+                    863964238,
+                    927350683,
+                    858008459,
+                    81197635,
+                    144434512,
+                    918571756,
+                    167749397,
+                    675749740,
+                    295749381,
+                    827884856,
+                    620280242,
+                    874012528,
+                    822768160,
+                    610884250,
+                    977118105,
+                    626267907,
+                    884046813,
+                    257109598,
+                    33541739,
+                    227640867,
+                    750873326,
+                    238245698,
+                    951121303,
+                    19597806,
+                    647067999,
+                    318153366,
+                    874855475,
+                    226642627,
+                    19774533,
+                    765426951,
+                    549663831,
+                    847386371,
+                    536200031,
+                    370072115,
+                    271805569,
+                    955917987,
+                    601131252,
+                    531858179,
+                    168540346,
+                    232372125,
+                    356383101,
+                    308244787,
+                    762571335,
+                    554725354,
+                    242745332,
+                    445798383,
+                    999786827,
+                    697513168,
+                    353223657,
+                    635339360,
+                    927870081,
+                    889109257,
+                    190857489,
+                    15049521,
+                    848770644,
+                    702229378,
+                    284142116,
+                    989118622,
+                    477506738,
+                    355054475,
+                    64819202,
+                    77330682,
+                    681037238,
+                    109865802,
+                    703058836,
+                    707247089,
+                    543254914,
+                    664360482,
+                    499750631,
+                    100684433,
+                    133445412,
+                    576721485,
+                    829915693,
+                    883813414,
+                    956113657,
+                    742597008,
+                    271079614,
+                    572262275,
+                    768521407,
+                    244016280,
+                    704301316,
+                    56399682,
+                    388325829,
+                    838530078,
+                    884456553,
+                    796749839,
+                    387552444,
+                    925455407,
+                    398847679,
+                    480536154,
+                    272463361,
+                    441786256,
+                    369223635,
+                    486933922,
+                    279582552,
+                    12064036,
+                    777144608,
+                    984699175,
+                    95334837,
+                    404629203,
+                    946802433,
+                    968186567,
+                    73886846,
+                    814312267,
+                    287709900,
+                    841942745,
+                    311724741,
+                    496306817,
+                    840154106,
+                    412424932,
+                    21418938,
+                    361802854,
+                    901291696,
+                    764205774,
+                    186376195,
+                    964248461,
+                    871786256,
+                    649446238,
+                    488108595,
+                    82193481,
+                    425230656,
+                    756516662,
+                    736966436,
+                    451202886,
+                    567438703,
+                    299500980,
+                    170613072,
+                    142071461,
+                    694802189,
+                    735900024,
+                    495744843,
+                    579030033,
+                    109410289,
+                    456653529,
+                    391477300,
+                    113368581,
+                    957245403,
+                    380607701,
+                    298902502,
+                    579716665,
+                    234429880,
+                    822802813,
+                    142510839,
+                    34256515,
+                    436588620,
+                    152680848,
+                    411032619,
+                    602164004,
+                    793631057,
+                    231793778,
+                    159024316,
+                    282491374,
+                    452044577,
+                    423079411,
+                    448954287,
+                    795565220,
+                    739443614,
+                    200180270
+                ],
+                [
+                    35,
+                    292,
+                    148,
+                    340,
+                    129,
+                    162,
+                    370,
+                    131,
+                    186,
+                    155,
+                    149,
+                    223,
+                    214,
+                    262,
+                    108,
+                    343,
+                    157,
+                    356,
+                    317,
+                    209,
+                    129,
+                    325,
+                    68,
+                    42,
+                    56,
+                    173,
+                    267,
+                    329,
+                    236,
+                    20,
+                    312,
+                    219,
+                    351,
+                    133,
+                    170,
+                    69,
+                    125,
+                    262,
+                    257,
+                    328,
+                    151,
+                    102,
+                    94,
+                    228,
+                    159,
+                    5,
+                    340,
+                    29,
+                    177,
+                    181,
+                    203,
+                    51,
+                    56,
+                    117,
+                    238,
+                    142,
+                    75,
+                    164,
+                    254,
+                    176,
+                    39,
+                    242,
+                    182,
+                    372,
+                    144,
+                    352,
+                    269,
+                    128,
+                    331,
+                    283,
+                    227,
+                    302,
+                    222,
+                    292,
+                    33,
+                    138,
+                    20,
+                    120,
+                    53,
+                    254,
+                    293,
+                    192,
+                    4,
+                    130,
+                    41,
+                    21,
+                    374,
+                    140,
+                    5,
+                    42,
+                    152,
+                    56,
+                    133,
+                    22,
+                    138,
+                    99,
+                    297,
+                    273,
+                    356,
+                    356,
+                    119,
+                    10,
+                    361,
+                    363,
+                    232,
+                    355,
+                    322,
+                    305,
+                    67,
+                    205,
+                    301,
+                    19,
+                    2,
+                    372,
+                    191,
+                    264,
+                    293,
+                    214,
+                    373,
+                    70,
+                    305,
+                    341,
+                    346,
+                    71,
+                    27,
+                    93,
+                    341,
+                    228,
+                    330,
+                    56,
+                    190,
+                    305,
+                    344,
+                    194,
+                    186,
+                    46,
+                    246,
+                    31,
+                    341,
+                    64,
+                    89,
+                    265,
+                    137,
+                    320,
+                    181,
+                    348,
+                    362,
+                    214,
+                    18,
+                    80,
+                    144,
+                    307,
+                    61,
+                    343,
+                    246,
+                    149,
+                    218,
+                    61,
+                    86,
+                    85,
+                    25,
+                    201,
+                    75,
+                    295,
+                    7,
+                    55,
+                    141,
+                    48,
+                    68,
+                    290,
+                    245,
+                    370,
+                    89,
+                    179,
+                    151,
+                    310,
+                    251,
+                    174,
+                    159,
+                    282,
+                    239,
+                    150,
+                    63,
+                    49,
+                    128,
+                    294,
+                    70,
+                    61,
+                    373,
+                    40,
+                    10,
+                    23,
+                    52,
+                    251,
+                    255,
+                    80,
+                    136,
+                    32,
+                    367,
+                    48,
+                    125,
+                    279,
+                    325,
+                    297,
+                    161,
+                    285,
+                    42,
+                    83,
+                    72,
+                    318,
+                    145,
+                    67,
+                    201,
+                    360,
+                    356,
+                    26,
+                    324,
+                    177,
+                    69,
+                    39,
+                    210,
+                    198,
+                    307,
+                    23,
+                    318,
+                    364,
+                    93,
+                    304,
+                    360,
+                    113,
+                    226,
+                    107,
+                    299,
+                    342,
+                    72,
+                    334,
+                    129,
+                    53,
+                    208,
+                    312,
+                    87,
+                    144,
+                    293,
+                    25,
+                    305,
+                    59,
+                    83,
+                    325,
+                    261,
+                    15,
+                    176,
+                    1,
+                    292,
+                    324,
+                    127,
+                    249,
+                    274,
+                    296,
+                    40,
+                    279,
+                    319,
+                    10,
+                    8,
+                    293,
+                    313,
+                    255,
+                    228,
+                    13,
+                    83,
+                    326,
+                    319,
+                    54,
+                    71,
+                    161,
+                    321,
+                    64,
+                    11,
+                    12,
+                    89,
+                    263,
+                    327,
+                    70,
+                    254,
+                    73,
+                    159,
+                    99,
+                    131,
+                    80,
+                    174,
+                    255,
+                    241,
+                    138,
+                    21,
+                    45,
+                    129,
+                    233,
+                    2,
+                    99,
+                    332,
+                    266,
+                    202,
+                    251,
+                    83,
+                    324,
+                    25,
+                    282,
+                    315,
+                    368,
+                    330,
+                    298,
+                    172,
+                    206,
+                    210,
+                    338,
+                    271,
+                    190,
+                    191,
+                    260,
+                    208,
+                    182,
+                    309,
+                    61,
+                    215,
+                    155,
+                    124,
+                    349,
+                    68,
+                    183,
+                    21,
+                    141,
+                    276,
+                    252,
+                    325,
+                    311,
+                    308,
+                    319,
+                    247,
+                    256,
+                    118,
+                    45,
+                    5,
+                    109,
+                    111,
+                    285,
+                    99,
+                    204,
+                    329,
+                    75,
+                    297,
+                    318,
+                    326,
+                    148,
+                    371,
+                    118,
+                    117,
+                    100,
+                    171,
+                    74,
+                    137,
+                    46,
+                    306,
+                    306,
+                    173,
+                    307,
+                    113,
+                    242,
+                    73,
+                    33,
+                    276,
+                    189,
+                    325,
+                    38,
+                    78,
+                    127,
+                    103,
+                    227,
+                    357,
+                    60,
+                    322,
+                    172,
+                    155,
+                    84,
+                    345,
+                    286,
+                    374,
+                    23,
+                    162,
+                    33,
+                    315,
+                    276,
+                    4,
+                    322,
+                    22,
+                    219,
+                    372,
+                    88,
+                    14,
+                    64,
+                    103,
+                    231,
+                    233,
+                    258,
+                    147,
+                    343,
+                    14,
+                    357,
+                    70,
+                    353,
+                    14,
+                    184,
+                    52,
+                    128,
+                    136,
+                    115,
+                    214,
+                    106,
+                    317,
+                    324,
+                    373,
+                    51,
+                    346,
+                    63,
+                    235,
+                    136,
+                    139,
+                    212,
+                    160,
+                    340,
+                    144,
+                    1,
+                    233,
+                    165,
+                    244,
+                    119,
+                    66,
+                    50,
+                    373,
+                    254,
+                    59,
+                    327,
+                    149,
+                    269,
+                    359,
+                    103,
+                    182,
+                    224,
+                    36,
+                    24,
+                    201,
+                    95,
+                    206,
+                    37,
+                    173,
+                    28,
+                    331,
+                    51,
+                    173,
+                    195,
+                    330,
+                    7,
+                    26,
+                    73,
+                    268,
+                    107,
+                    152,
+                    265,
+                    221,
+                    75,
+                    190,
+                    55,
+                    94,
+                    257,
+                    79,
+                    64,
+                    345,
+                    329,
+                    84,
+                    101,
+                    230,
+                    367,
+                    176,
+                    90,
+                    367,
+                    88,
+                    227,
+                    208,
+                    226,
+                    367,
+                    183,
+                    81,
+                    147,
+                    297,
+                    214,
+                    317,
+                    225,
+                    338,
+                    266,
+                    85,
+                    104,
+                    178,
+                    14,
+                    257,
+                    113,
+                    267,
+                    181,
+                    87,
+                    373,
+                    287,
+                    82,
+                    22,
+                    168,
+                    370,
+                    140,
+                    247,
+                    82,
+                    71,
+                    172,
+                    155,
+                    350,
+                    361,
+                    46,
+                    272,
+                    206,
+                    273,
+                    219,
+                    30,
+                    89,
+                    32,
+                    312,
+                    91,
+                    206,
+                    161,
+                    76,
+                    298,
+                    187,
+                    273,
+                    176,
+                    177,
+                    349,
+                    45,
+                    198,
+                    307,
+                    300,
+                    141,
+                    54,
+                    220,
+                    180,
+                    143,
+                    193,
+                    48,
+                    337,
+                    347,
+                    347,
+                    245,
+                    293,
+                    280,
+                    79,
+                    97,
+                    103,
+                    47,
+                    238,
+                    229,
+                    75,
+                    357,
+                    122,
+                    14,
+                    323,
+                    140,
+                    235,
+                    192,
+                    64,
+                    149,
+                    318,
+                    6,
+                    59,
+                    22,
+                    258,
+                    4,
+                    158,
+                    238,
+                    87,
+                    303,
+                    81,
+                    243,
+                    267,
+                    128,
+                    61,
+                    300,
+                    277,
+                    133,
+                    86,
+                    92,
+                    161,
+                    51,
+                    60,
+                    286,
+                    207,
+                    260,
+                    357,
+                    171,
+                    214,
+                    140,
+                    64,
+                    294,
+                    16,
+                    203,
+                    123,
+                    306,
+                    190,
+                    117,
+                    193,
+                    5,
+                    256,
+                    225,
+                    75,
+                    177,
+                    103,
+                    372,
+                    22,
+                    291,
+                    151,
+                    247,
+                    206,
+                    65,
+                    250,
+                    322,
+                    257,
+                    277,
+                    302,
+                    192,
+                    62,
+                    215,
+                    111,
+                    221,
+                    268,
+                    234,
+                    353,
+                    64,
+                    223,
+                    239,
+                    362,
+                    261,
+                    45,
+                    60,
+                    256,
+                    288,
+                    276,
+                    322,
+                    299,
+                    165,
+                    352,
+                    233,
+                    56,
+                    337,
+                    295,
+                    233,
+                    316,
+                    366,
+                    329,
+                    100,
+                    117,
+                    359,
+                    204,
+                    234,
+                    6,
+                    84,
+                    276,
+                    2,
+                    73,
+                    275,
+                    96,
+                    61,
+                    94,
+                    63,
+                    332,
+                    288,
+                    246,
+                    245,
+                    55,
+                    188,
+                    69,
+                    80,
+                    338,
+                    34,
+                    298,
+                    310,
+                    43,
+                    64,
+                    236,
+                    219,
+                    290,
+                    199,
+                    66,
+                    336,
+                    67,
+                    139,
+                    168,
+                    283,
+                    298,
+                    368,
+                    154,
+                    301,
+                    70,
+                    374,
+                    296,
+                    128,
+                    337,
+                    300,
+                    337,
+                    281,
+                    129,
+                    89,
+                    14,
+                    183,
+                    333,
+                    97,
+                    292,
+                    312,
+                    250,
+                    352,
+                    33,
+                    350,
+                    362,
+                    239,
+                    336,
+                    114,
+                    349,
+                    371,
+                    76,
+                    358,
+                    286,
+                    165,
+                    125,
+                    368,
+                    38,
+                    18,
+                    310,
+                    134,
+                    337,
+                    265,
+                    18,
+                    167,
+                    166,
+                    152,
+                    248,
+                    234,
+                    59,
+                    34,
+                    240,
+                    310,
+                    101,
+                    168,
+                    72,
+                    360,
+                    52,
+                    373,
+                    290,
+                    6,
+                    268,
+                    153,
+                    339,
+                    83,
+                    43,
+                    291,
+                    173,
+                    133,
+                    306,
+                    45,
+                    306,
+                    303,
+                    164,
+                    246,
+                    305,
+                    180,
+                    6,
+                    145,
+                    72,
+                    199,
+                    49,
+                    258,
+                    252,
+                    135,
+                    119,
+                    62,
+                    96,
+                    172,
+                    22,
+                    184,
+                    24,
+                    289,
+                    280,
+                    24,
+                    231,
+                    176,
+                    238,
+                    75,
+                    318,
+                    13,
+                    208,
+                    106,
+                    53,
+                    54,
+                    321,
+                    235,
+                    369,
+                    265,
+                    360,
+                    126,
+                    276,
+                    221,
+                    172,
+                    216,
+                    223,
+                    89,
+                    167,
+                    177,
+                    339,
+                    370,
+                    269,
+                    313,
+                    330,
+                    277,
+                    264,
+                    246,
+                    328,
+                    87,
+                    163,
+                    6,
+                    165,
+                    33,
+                    177,
+                    175,
+                    114,
+                    305,
+                    191,
+                    44,
+                    340,
+                    179,
+                    183,
+                    182,
+                    79,
+                    310,
+                    191,
+                    79,
+                    311,
+                    144,
+                    164,
+                    268,
+                    238,
+                    12,
+                    253,
+                    264,
+                    286,
+                    53,
+                    157,
+                    131,
+                    370,
+                    203,
+                    114,
+                    339,
+                    219,
+                    131,
+                    188,
+                    320,
+                    199,
+                    32,
+                    148,
+                    73,
+                    228,
+                    119,
+                    282,
+                    220,
+                    7,
+                    169,
+                    244,
+                    72,
+                    361,
+                    274,
+                    254,
+                    196,
+                    300,
+                    208,
+                    230,
+                    156,
+                    219,
+                    81,
+                    176,
+                    161,
+                    107,
+                    207,
+                    51,
+                    371,
+                    274,
+                    179,
+                    111,
+                    181,
+                    34,
+                    278,
+                    157,
+                    159,
+                    264,
+                    250,
+                    176,
+                    242,
+                    354,
+                    220,
+                    29,
+                    134,
+                    116,
+                    188,
+                    176,
+                    352,
+                    339,
+                    21,
+                    57,
+                    276,
+                    332,
+                    204,
+                    303,
+                    198,
+                    251,
+                    188,
+                    15,
+                    145,
+                    353,
+                    110,
+                    54,
+                    133,
+                    312,
+                    122,
+                    81,
+                    38,
+                    319,
+                    368,
+                    320,
+                    196,
+                    301,
+                    23,
+                    367,
+                    176,
+                    152,
+                    232,
+                    145,
+                    306,
+                    358,
+                    260,
+                    254,
+                    326,
+                    113,
+                    61,
+                    139,
+                    330,
+                    83,
+                    133,
+                    11,
+                    284,
+                    357,
+                    166,
+                    186,
+                    289,
+                    87,
+                    30,
+                    175,
+                    79,
+                    309,
+                    282,
+                    2,
+                    211,
+                    136,
+                    69,
+                    269,
+                    247,
+                    224,
+                    286,
+                    7,
+                    220,
+                    294,
+                    13,
+                    97,
+                    317,
+                    102,
+                    135,
+                    38,
+                    362,
+                    165,
+                    295,
+                    316,
+                    137,
+                    72,
+                    115,
+                    280,
+                    354,
+                    326,
+                    322,
+                    321,
+                    344,
+                    93,
+                    263,
+                    128,
+                    177,
+                    367,
+                    258,
+                    312,
+                    139,
+                    123,
+                    118,
+                    278,
+                    85,
+                    159,
+                    204,
+                    303,
+                    31,
+                    236,
+                    301,
+                    69,
+                    92,
+                    210,
+                    205,
+                    101,
+                    116,
+                    100,
+                    34,
+                    261,
+                    341,
+                    259,
+                    201,
+                    246,
+                    372,
+                    283,
+                    259,
+                    297,
+                    329,
+                    19,
+                    84,
+                    193,
+                    252,
+                    184,
+                    278,
+                    210,
+                    167,
+                    340,
+                    110,
+                    6,
+                    160,
+                    119,
+                    137,
+                    348,
+                    249,
+                    133,
+                    107,
+                    48,
+                    51,
+                    72,
+                    256,
+                    42,
+                    106,
+                    113,
+                    317,
+                    368,
+                    348,
+                    37,
+                    28,
+                    24,
+                    170,
+                    349,
+                    65,
+                    303,
+                    282,
+                    20,
+                    6,
+                    146,
+                    306,
+                    110,
+                    41,
+                    55,
+                    221,
+                    119,
+                    346,
+                    176,
+                    84,
+                    18,
+                    337,
+                    127,
+                    46,
+                    180,
+                    193,
+                    346,
+                    34,
+                    353,
+                    372,
+                    64,
+                    306,
+                    220,
+                    262,
+                    309,
+                    10,
+                    124,
+                    39,
+                    132,
+                    313,
+                    28,
+                    82,
+                    9,
+                    218,
+                    302,
+                    228,
+                    150,
+                    155,
+                    215,
+                    235,
+                    107,
+                    48,
+                    38,
+                    171,
+                    71,
+                    137,
+                    170,
+                    203,
+                    347,
+                    193,
+                    152,
+                    222,
+                    135,
+                    35,
+                    255,
+                    195,
+                    244,
+                    286,
+                    256,
+                    242,
+                    141,
+                    283,
+                    164,
+                    193,
+                    193,
+                    19,
+                    247,
+                    265,
+                    310,
+                    131,
+                    357,
+                    104,
+                    174,
+                    365,
+                    138,
+                    109,
+                    289,
+                    64,
+                    213,
+                    187,
+                    342,
+                    355,
+                    77,
+                    102,
+                    17,
+                    96,
+                    166,
+                    17,
+                    352,
+                    170,
+                    242,
+                    80,
+                    206,
+                    84,
+                    90,
+                    358,
+                    272,
+                    94,
+                    268,
+                    356,
+                    195,
+                    324,
+                    337,
+                    227,
+                    109,
+                    255,
+                    278,
+                    26,
+                    369,
+                    333,
+                    183,
+                    17,
+                    121,
+                    338,
+                    280,
+                    250,
+                    286,
+                    80,
+                    160,
+                    277,
+                    23,
+                    351,
+                    243,
+                    39,
+                    206,
+                    67,
+                    66,
+                    51,
+                    26,
+                    141,
+                    120,
+                    331,
+                    326,
+                    81,
+                    140,
+                    225,
+                    228,
+                    364,
+                    14,
+                    333,
+                    296,
+                    95,
+                    55,
+                    295,
+                    298,
+                    283,
+                    99,
+                    22,
+                    279,
+                    31,
+                    199,
+                    280,
+                    341,
+                    370,
+                    272,
+                    188,
+                    83,
+                    350,
+                    167,
+                    61,
+                    368,
+                    193,
+                    295,
+                    149,
+                    266,
+                    219,
+                    329,
+                    370,
+                    20,
+                    340,
+                    345,
+                    248,
+                    310,
+                    286,
+                    133,
+                    199,
+                    50,
+                    5,
+                    77,
+                    57,
+                    151,
+                    192,
+                    195,
+                    93,
+                    355,
+                    361,
+                    216,
+                    4,
+                    367,
+                    206,
+                    148,
+                    188,
+                    73,
+                    120,
+                    171,
+                    233,
+                    365,
+                    184,
+                    371,
+                    213,
+                    247,
+                    108,
+                    63,
+                    106,
+                    237,
+                    243,
+                    75,
+                    62,
+                    13,
+                    154,
+                    249,
+                    74,
+                    222,
+                    361,
+                    274,
+                    93,
+                    237,
+                    256,
+                    28,
+                    229,
+                    181,
+                    151,
+                    304,
+                    37,
+                    106,
+                    29,
+                    239,
+                    53,
+                    280,
+                    62,
+                    116,
+                    216,
+                    109,
+                    204,
+                    67,
+                    1,
+                    148,
+                    233,
+                    312,
+                    237,
+                    41,
+                    60,
+                    351,
+                    102,
+                    78,
+                    138,
+                    125,
+                    126,
+                    328,
+                    341,
+                    228,
+                    318,
+                    10,
+                    56,
+                    286,
+                    221,
+                    106,
+                    63,
+                    366,
+                    100,
+                    300,
+                    22,
+                    330,
+                    272,
+                    211,
+                    87,
+                    169,
+                    205,
+                    91,
+                    353,
+                    145,
+                    217,
+                    65,
+                    230,
+                    247,
+                    145,
+                    232,
+                    330,
+                    306,
+                    44,
+                    98,
+                    359,
+                    20,
+                    175,
+                    90,
+                    321,
+                    351,
+                    71,
+                    205,
+                    53,
+                    214,
+                    363,
+                    13,
+                    239,
+                    260,
+                    143,
+                    367,
+                    222,
+                    286,
+                    115,
+                    332,
+                    75,
+                    355,
+                    332,
+                    194,
+                    306,
+                    208,
+                    122,
+                    276,
+                    80,
+                    58,
+                    374,
+                    202,
+                    294,
+                    195,
+                    268,
+                    91,
+                    177,
+                    241,
+                    250,
+                    82,
+                    201,
+                    180,
+                    166,
+                    27,
+                    352,
+                    94,
+                    199,
+                    154,
+                    203,
+                    374,
+                    306,
+                    358,
+                    197,
+                    50,
+                    250,
+                    314,
+                    179,
+                    345,
+                    346,
+                    204,
+                    251,
+                    28,
+                    194,
+                    199,
+                    2,
+                    353,
+                    253,
+                    29,
+                    145,
+                    155,
+                    89,
+                    146,
+                    61,
+                    273,
+                    119,
+                    236,
+                    248,
+                    82,
+                    173,
+                    230,
+                    249,
+                    68,
+                    312,
+                    52,
+                    12,
+                    107,
+                    39,
+                    73,
+                    302,
+                    359,
+                    96,
+                    17,
+                    337,
+                    26,
+                    72,
+                    354,
+                    374,
+                    304,
+                    282,
+                    319,
+                    301,
+                    305,
+                    160,
+                    214,
+                    151,
+                    324,
+                    143,
+                    117,
+                    328,
+                    203,
+                    353,
+                    352,
+                    281,
+                    192,
+                    25,
+                    216,
+                    167,
+                    312,
+                    350,
+                    143,
+                    184,
+                    218,
+                    350,
+                    157,
+                    273,
+                    232,
+                    68,
+                    169,
+                    296,
+                    249,
+                    202,
+                    27,
+                    238,
+                    205,
+                    320,
+                    260,
+                    187,
+                    286,
+                    53,
+                    168,
+                    103,
+                    212,
+                    124,
+                    176,
+                    5,
+                    329,
+                    365,
+                    282,
+                    283,
+                    291,
+                    306,
+                    107,
+                    368,
+                    18,
+                    31,
+                    31,
+                    218,
+                    231,
+                    265,
+                    371,
+                    118,
+                    119,
+                    354,
+                    74,
+                    71,
+                    339,
+                    10,
+                    196,
+                    109,
+                    99,
+                    5,
+                    284,
+                    5,
+                    80,
+                    332,
+                    118,
+                    35,
+                    152,
+                    148,
+                    248,
+                    82,
+                    62,
+                    370,
+                    293,
+                    188,
+                    258,
+                    24,
+                    323,
+                    72,
+                    346,
+                    233,
+                    8,
+                    51,
+                    333,
+                    2,
+                    21,
+                    250,
+                    136,
+                    164,
+                    26,
+                    203,
+                    324,
+                    52,
+                    227,
+                    86,
+                    148,
+                    296,
+                    46,
+                    368,
+                    44,
+                    141,
+                    248,
+                    211,
+                    346,
+                    39,
+                    131,
+                    238,
+                    253,
+                    94,
+                    271,
+                    313,
+                    102,
+                    373,
+                    262,
+                    309,
+                    172,
+                    183,
+                    167,
+                    88,
+                    223,
+                    204,
+                    323,
+                    209,
+                    334,
+                    296,
+                    115,
+                    362,
+                    185,
+                    124,
+                    164,
+                    57,
+                    117,
+                    106,
+                    337,
+                    196,
+                    23,
+                    223,
+                    210,
+                    126,
+                    250,
+                    16,
+                    9,
+                    238,
+                    357,
+                    169,
+                    153,
+                    161,
+                    80,
+                    330,
+                    319,
+                    38,
+                    69,
+                    41,
+                    155,
+                    194,
+                    84,
+                    154,
+                    300,
+                    110,
+                    122,
+                    10,
+                    14,
+                    62,
+                    98,
+                    268,
+                    147,
+                    107,
+                    115,
+                    365,
+                    169,
+                    127,
+                    8,
+                    58,
+                    344,
+                    198,
+                    283,
+                    288,
+                    58,
+                    274,
+                    153,
+                    340,
+                    74,
+                    324,
+                    158,
+                    244,
+                    156,
+                    286,
+                    34,
+                    145,
+                    4,
+                    255,
+                    6,
+                    86,
+                    209,
+                    61,
+                    76
+                ]
+            ],
+            "output": -1
+        }
+    ],
+    "haskell_template": "earliestSecondToMarkIndices :: [Int] -> [Int] -> Int\nearliestSecondToMarkIndices nums changeIndices ",
+    "ocaml_template": "let earliestSecondToMarkIndices (nums: int list) (changeIndices: int list) : int =  ",
+    "scala_template": "def earliestSecondToMarkIndices(nums: List[Int],changeIndices: List[Int]): Int = { \n    \n}",
+    "java_template": "class Solution {\n    public int earliestSecondToMarkIndices(int[] nums, int[] changeIndices) {\n        \n    }\n}",
+    "python_template": "class Solution(object):\n    def earliestSecondToMarkIndices(self, nums, changeIndices):\n        \"\"\"\n        :type nums: List[int]\n        :type changeIndices: List[int]\n        :rtype: int\n        \"\"\"\n        "
+}
\ No newline at end of file