Datasets:
beta3
/
GridCorpus_9M_Sudoku_Puzzles_Enriched

Dataset card Data Studio Files
xet
Community
1
puzzle_grid
stringlengths
261
261
solution_grid
stringlengths
261
261
missing_cells
int64
4
58
given_cells
int64
23
77
given_ratio
float64
0.28
0.95
row_given_counts
stringlengths
27
27
col_given_counts
stringlengths
27
27
naked_singles_count
int64
0
26
hidden_singles_count
int64
0
27
initial_resolution_rate
float64
0
1
requires_backtrack
bool
2 classes
backtrack_depth
int64
0
18
constraint_propagation_steps
int64
4
3.15k
difficulty_tier
stringclasses
4 values
[[0, 7, 0, 0, 0, 0, 0, 4, 3], [0, 4, 0, 0, 0, 9, 6, 1, 0], [8, 0, 0, 6, 3, 4, 9, 0, 0], [0, 9, 4, 0, 5, 2, 0, 0, 0], [3, 5, 8, 4, 6, 0, 0, 2, 0], [0, 0, 0, 8, 0, 0, 5, 3, 0], [0, 8, 0, 0, 7, 0, 0, 9, 1], [9, 0, 2, 1, 0, 0, 0, 0, 5], [0, 0, 7, 0, 4, 0, 8, 0, 2]]
[[6, 7, 9, 5, 1, 8, 2, 4, 3], [5, 4, 3, 7, 2, 9, 6, 1, 8], [8, 2, 1, 6, 3, 4, 9, 5, 7], [7, 9, 4, 3, 5, 2, 1, 8, 6], [3, 5, 8, 4, 6, 1, 7, 2, 9], [2, 1, 6, 8, 9, 7, 5, 3, 4], [4, 8, 5, 2, 7, 6, 3, 9, 1], [9, 6, 2, 1, 8, 3, 4, 7, 5], [1, 3, 7, 9, 4, 5, 8, 6, 2]]
44
37
0.45679
[3, 4, 5, 4, 6, 3, 4, 4, 4]
[3, 5, 4, 4, 5, 3, 4, 5, 4]
4
15
0.431818
false
0
44
medium
[[3, 0, 1, 0, 8, 6, 5, 0, 4], [0, 4, 6, 5, 2, 1, 0, 7, 0], [5, 0, 0, 0, 0, 0, 0, 0, 1], [4, 0, 0, 8, 0, 0, 0, 0, 2], [0, 8, 0, 3, 4, 7, 9, 0, 0], [0, 0, 9, 0, 5, 0, 0, 3, 8], [0, 0, 4, 0, 9, 0, 2, 0, 0], [0, 0, 8, 7, 3, 4, 0, 9, 0], [0, 0, 7, 2, 0, 8, 1, 0, 3]]
[[3, 7, 1, 9, 8, 6, 5, 2, 4], [8, 4, 6, 5, 2, 1, 3, 7, 9], [5, 9, 2, 4, 7, 3, 8, 6, 1], [4, 6, 3, 8, 1, 9, 7, 5, 2], [2, 8, 5, 3, 4, 7, 9, 1, 6], [7, 1, 9, 6, 5, 2, 4, 3, 8], [6, 3, 4, 1, 9, 5, 2, 8, 7], [1, 2, 8, 7, 3, 4, 6, 9, 5], [9, 5, 7, 2, 6, 8, 1, 4, 3]]
42
39
0.481481
[6, 6, 2, 3, 5, 4, 3, 5, 5]
[3, 2, 6, 5, 6, 5, 4, 3, 5]
10
14
0.571429
false
0
42
medium
[[0, 4, 8, 3, 0, 1, 5, 6, 0], [3, 6, 0, 0, 0, 8, 0, 9, 0], [9, 1, 0, 6, 7, 0, 0, 0, 3], [0, 2, 0, 0, 0, 0, 9, 3, 5], [5, 0, 9, 0, 1, 0, 2, 0, 0], [6, 7, 0, 0, 2, 0, 0, 1, 0], [0, 0, 4, 0, 0, 2, 1, 0, 7], [0, 9, 0, 1, 0, 0, 0, 0, 8], [1, 5, 0, 8, 3, 4, 0, 2, 9]]
[[7, 4, 8, 3, 9, 1, 5, 6, 2], [3, 6, 5, 2, 4, 8, 7, 9, 1], [9, 1, 2, 6, 7, 5, 4, 8, 3], [4, 2, 1, 7, 8, 6, 9, 3, 5], [5, 8, 9, 4, 1, 3, 2, 7, 6], [6, 7, 3, 5, 2, 9, 8, 1, 4], [8, 3, 4, 9, 6, 2, 1, 5, 7], [2, 9, 6, 1, 5, 7, 3, 4, 8], [1, 5, 7, 8, 3, 4, 6, 2, 9]]
40
41
0.506173
[6, 4, 5, 4, 4, 4, 4, 3, 7]
[5, 7, 3, 4, 4, 4, 4, 5, 5]
9
16
0.625
false
0
40
medium
[[0, 0, 8, 3, 1, 7, 0, 0, 0], [0, 0, 4, 2, 0, 5, 1, 0, 9], [0, 0, 0, 0, 4, 0, 0, 7, 0], [3, 2, 7, 1, 6, 0, 9, 0, 4], [9, 0, 1, 4, 5, 0, 0, 0, 0], [0, 4, 5, 7, 0, 0, 8, 0, 0], [0, 3, 0, 0, 0, 1, 0, 6, 0], [8, 7, 2, 6, 0, 4, 0, 0, 0], [4, 1, 6, 0, 7, 0, 0, 8, 0]]
[[2, 9, 8, 3, 1, 7, 6, 4, 5], [7, 6, 4, 2, 8, 5, 1, 3, 9], [1, 5, 3, 9, 4, 6, 2, 7, 8], [3, 2, 7, 1, 6, 8, 9, 5, 4], [9, 8, 1, 4, 5, 3, 7, 2, 6], [6, 4, 5, 7, 9, 2, 8, 1, 3], [5, 3, 9, 8, 2, 1, 4, 6, 7], [8, 7, 2, 6, 3, 4, 5, 9, 1], [4, 1, 6, 5, 7, 9, 3, 8, 2]]
42
39
0.481481
[4, 5, 2, 7, 4, 4, 3, 5, 5]
[4, 5, 7, 6, 5, 4, 3, 3, 2]
8
10
0.428571
false
0
42
medium
[[0, 4, 0, 8, 9, 0, 6, 3, 0], [0, 0, 0, 1, 3, 6, 8, 2, 0], [8, 0, 0, 7, 4, 0, 5, 1, 9], [0, 0, 0, 4, 6, 7, 0, 5, 2], [4, 5, 0, 0, 2, 0, 7, 0, 0], [2, 6, 7, 0, 1, 0, 0, 0, 0], [5, 2, 0, 0, 0, 3, 4, 0, 0], [0, 1, 0, 2, 8, 0, 9, 7, 0], [0, 0, 4, 0, 5, 0, 0, 6, 3]]
[[1, 4, 2, 8, 9, 5, 6, 3, 7], [9, 7, 5, 1, 3, 6, 8, 2, 4], [8, 3, 6, 7, 4, 2, 5, 1, 9], [3, 9, 8, 4, 6, 7, 1, 5, 2], [4, 5, 1, 3, 2, 8, 7, 9, 6], [2, 6, 7, 5, 1, 9, 3, 4, 8], [5, 2, 9, 6, 7, 3, 4, 8, 1], [6, 1, 3, 2, 8, 4, 9, 7, 5], [7, 8, 4, 9, 5, 1, 2, 6, 3]]
39
42
0.518519
[5, 5, 6, 5, 4, 4, 4, 5, 4]
[4, 5, 2, 5, 8, 3, 6, 6, 3]
9
13
0.564103
false
0
39
medium
[[5, 6, 1, 0, 9, 2, 7, 3, 0], [0, 2, 0, 7, 8, 0, 0, 9, 0], [9, 0, 0, 0, 0, 5, 0, 4, 6], [6, 0, 0, 0, 0, 0, 4, 2, 7], [0, 1, 0, 0, 7, 0, 0, 0, 3], [0, 7, 3, 0, 0, 0, 8, 1, 9], [0, 3, 5, 9, 0, 0, 6, 7, 0], [7, 0, 0, 1, 0, 3, 0, 8, 0], [0, 0, 0, 0, 0, 0, 0, 5, 0]]
[[5, 6, 1, 4, 9, 2, 7, 3, 8], [3, 2, 4, 7, 8, 6, 1, 9, 5], [9, 8, 7, 3, 1, 5, 2, 4, 6], [6, 5, 9, 8, 3, 1, 4, 2, 7], [4, 1, 8, 2, 7, 9, 5, 6, 3], [2, 7, 3, 5, 6, 4, 8, 1, 9], [1, 3, 5, 9, 2, 8, 6, 7, 4], [7, 4, 6, 1, 5, 3, 9, 8, 2], [8, 9, 2, 6, 4, 7, 3, 5, 1]]
44
37
0.45679
[7, 4, 4, 4, 3, 5, 5, 4, 1]
[4, 5, 3, 3, 3, 3, 4, 8, 4]
7
9
0.363636
false
0
44
medium
[[3, 1, 0, 4, 5, 0, 9, 0, 0], [0, 7, 2, 9, 8, 6, 1, 4, 3], [9, 0, 6, 0, 1, 0, 5, 0, 8], [6, 3, 9, 1, 7, 8, 0, 2, 0], [1, 5, 0, 0, 9, 0, 8, 0, 6], [0, 0, 4, 0, 0, 3, 7, 0, 0], [0, 0, 5, 7, 3, 1, 0, 0, 9], [7, 0, 1, 8, 2, 9, 3, 5, 0], [0, 0, 0, 6, 4, 5, 0, 1, 0]]
[[3, 1, 8, 4, 5, 7, 9, 6, 2], [5, 7, 2, 9, 8, 6, 1, 4, 3], [9, 4, 6, 3, 1, 2, 5, 7, 8], [6, 3, 9, 1, 7, 8, 4, 2, 5], [1, 5, 7, 2, 9, 4, 8, 3, 6], [2, 8, 4, 5, 6, 3, 7, 9, 1], [4, 2, 5, 7, 3, 1, 6, 8, 9], [7, 6, 1, 8, 2, 9, 3, 5, 4], [8, 9, 3, 6, 4, 5, 2, 1, 7]]
32
49
0.604938
[5, 8, 5, 7, 5, 3, 5, 7, 4]
[5, 4, 6, 6, 8, 6, 6, 4, 4]
12
14
0.8125
false
0
32
easy
[[8, 0, 0, 1, 3, 4, 9, 0, 2], [0, 4, 1, 0, 9, 6, 0, 8, 0], [0, 0, 5, 0, 7, 0, 0, 1, 0], [0, 0, 8, 6, 0, 5, 0, 0, 0], [4, 0, 6, 3, 1, 0, 0, 0, 9], [0, 2, 3, 0, 4, 0, 8, 6, 0], [5, 0, 0, 7, 0, 9, 0, 0, 0], [0, 1, 0, 0, 8, 0, 0, 4, 0], [0, 0, 0, 4, 0, 1, 0, 0, 6]]
[[8, 6, 7, 1, 3, 4, 9, 5, 2], [2, 4, 1, 5, 9, 6, 7, 8, 3], [3, 9, 5, 8, 7, 2, 6, 1, 4], [9, 7, 8, 6, 2, 5, 4, 3, 1], [4, 5, 6, 3, 1, 8, 2, 7, 9], [1, 2, 3, 9, 4, 7, 8, 6, 5], [5, 3, 4, 7, 6, 9, 1, 2, 8], [6, 1, 9, 2, 8, 3, 5, 4, 7], [7, 8, 2, 4, 5, 1, 3, 9, 6]]
45
36
0.444444
[6, 5, 3, 3, 5, 5, 3, 3, 3]
[3, 3, 5, 5, 6, 5, 2, 4, 3]
4
16
0.444444
false
0
45
medium
[[1, 6, 5, 2, 9, 3, 0, 0, 4], [0, 0, 0, 0, 0, 1, 6, 3, 2], [0, 2, 3, 0, 6, 0, 0, 9, 0], [0, 0, 9, 1, 7, 5, 0, 0, 0], [5, 0, 0, 9, 0, 0, 0, 1, 8], [0, 0, 2, 0, 3, 0, 0, 4, 9], [0, 9, 8, 0, 0, 0, 0, 0, 6], [0, 0, 0, 0, 0, 0, 9, 5, 0], [0, 0, 0, 4, 2, 9, 3, 8, 1]]
[[1, 6, 5, 2, 9, 3, 8, 7, 4], [9, 7, 4, 8, 5, 1, 6, 3, 2], [8, 2, 3, 7, 6, 4, 1, 9, 5], [4, 8, 9, 1, 7, 5, 2, 6, 3], [5, 3, 6, 9, 4, 2, 7, 1, 8], [7, 1, 2, 6, 3, 8, 5, 4, 9], [3, 9, 8, 5, 1, 7, 4, 2, 6], [2, 4, 1, 3, 8, 6, 9, 5, 7], [6, 5, 7, 4, 2, 9, 3, 8, 1]]
43
38
0.469136
[7, 4, 4, 4, 4, 4, 3, 2, 6]
[2, 3, 5, 4, 5, 4, 3, 6, 6]
6
14
0.465116
false
0
43
medium
[[0, 0, 0, 0, 0, 3, 6, 1, 0], [0, 0, 0, 0, 1, 5, 0, 0, 7], [0, 0, 0, 0, 0, 8, 0, 9, 0], [0, 8, 6, 0, 0, 0, 7, 0, 0], [0, 3, 0, 8, 0, 0, 1, 0, 0], [5, 0, 0, 1, 2, 0, 3, 0, 9], [0, 0, 5, 0, 6, 0, 9, 0, 4], [0, 6, 0, 9, 0, 0, 5, 3, 0], [4, 0, 3, 7, 0, 1, 0, 0, 8]]
[[7, 2, 8, 4, 9, 3, 6, 1, 5], [3, 4, 9, 6, 1, 5, 8, 2, 7], [6, 5, 1, 2, 7, 8, 4, 9, 3], [1, 8, 6, 5, 3, 9, 7, 4, 2], [9, 3, 2, 8, 4, 7, 1, 5, 6], [5, 7, 4, 1, 2, 6, 3, 8, 9], [8, 1, 5, 3, 6, 2, 9, 7, 4], [2, 6, 7, 9, 8, 4, 5, 3, 1], [4, 9, 3, 7, 5, 1, 2, 6, 8]]
49
32
0.395062
[3, 3, 2, 3, 3, 5, 4, 4, 5]
[2, 3, 3, 4, 3, 4, 6, 3, 4]
3
16
0.387755
false
0
49
medium
[[4, 0, 5, 0, 0, 1, 0, 6, 8], [0, 7, 3, 6, 2, 8, 5, 0, 0], [0, 0, 9, 0, 0, 3, 0, 7, 0], [2, 4, 0, 7, 9, 0, 0, 3, 0], [0, 0, 6, 1, 0, 2, 0, 0, 5], [9, 5, 0, 0, 0, 0, 0, 2, 1], [5, 0, 7, 0, 6, 4, 2, 1, 3], [0, 8, 0, 2, 1, 7, 0, 5, 0], [6, 1, 2, 3, 0, 0, 0, 0, 7]]
[[4, 2, 5, 9, 7, 1, 3, 6, 8], [1, 7, 3, 6, 2, 8, 5, 9, 4], [8, 6, 9, 5, 4, 3, 1, 7, 2], [2, 4, 1, 7, 9, 5, 8, 3, 6], [7, 3, 6, 1, 8, 2, 9, 4, 5], [9, 5, 8, 4, 3, 6, 7, 2, 1], [5, 9, 7, 8, 6, 4, 2, 1, 3], [3, 8, 4, 2, 1, 7, 6, 5, 9], [6, 1, 2, 3, 5, 9, 4, 8, 7]]
37
44
0.54321
[5, 6, 3, 5, 4, 4, 7, 5, 5]
[5, 5, 6, 5, 4, 6, 2, 6, 5]
11
13
0.648649
false
0
37
medium
[[9, 6, 0, 4, 0, 5, 1, 0, 0], [0, 2, 0, 0, 6, 0, 5, 0, 4], [0, 0, 1, 7, 0, 3, 0, 0, 6], [1, 0, 0, 0, 0, 4, 0, 0, 0], [4, 9, 0, 1, 3, 0, 0, 5, 0], [0, 0, 2, 0, 0, 7, 6, 0, 1], [2, 0, 9, 0, 0, 6, 0, 3, 8], [0, 7, 0, 2, 1, 8, 9, 0, 5], [6, 0, 0, 0, 7, 9, 0, 0, 0]]
[[9, 6, 8, 4, 2, 5, 1, 7, 3], [7, 2, 3, 8, 6, 1, 5, 9, 4], [5, 4, 1, 7, 9, 3, 2, 8, 6], [1, 5, 7, 6, 8, 4, 3, 2, 9], [4, 9, 6, 1, 3, 2, 8, 5, 7], [8, 3, 2, 9, 5, 7, 6, 4, 1], [2, 1, 9, 5, 4, 6, 7, 3, 8], [3, 7, 4, 2, 1, 8, 9, 6, 5], [6, 8, 5, 3, 7, 9, 4, 1, 2]]
43
38
0.469136
[5, 4, 4, 2, 5, 4, 5, 6, 3]
[5, 4, 3, 4, 4, 7, 4, 2, 5]
5
14
0.44186
true
1
49
hard
[[9, 0, 4, 5, 2, 0, 0, 7, 0], [0, 0, 1, 8, 9, 0, 2, 4, 0], [0, 0, 2, 6, 4, 3, 0, 0, 0], [0, 7, 0, 9, 6, 0, 3, 8, 0], [0, 0, 0, 1, 0, 8, 7, 0, 0], [6, 0, 0, 0, 0, 0, 0, 1, 0], [0, 9, 0, 0, 8, 0, 0, 0, 0], [0, 0, 0, 7, 5, 0, 0, 3, 0], [0, 0, 0, 3, 1, 2, 5, 6, 9]]
[[9, 8, 4, 5, 2, 1, 6, 7, 3], [3, 6, 1, 8, 9, 7, 2, 4, 5], [7, 5, 2, 6, 4, 3, 8, 9, 1], [1, 7, 5, 9, 6, 4, 3, 8, 2], [4, 2, 9, 1, 3, 8, 7, 5, 6], [6, 3, 8, 2, 7, 5, 9, 1, 4], [5, 9, 3, 4, 8, 6, 1, 2, 7], [2, 1, 6, 7, 5, 9, 4, 3, 8], [8, 4, 7, 3, 1, 2, 5, 6, 9]]
46
35
0.432099
[5, 5, 4, 5, 3, 2, 2, 3, 6]
[2, 2, 3, 7, 7, 3, 4, 6, 1]
6
9
0.326087
false
0
46
medium
[[0, 0, 1, 4, 0, 8, 0, 0, 6], [0, 9, 3, 5, 2, 0, 7, 4, 1], [0, 0, 0, 0, 1, 0, 5, 2, 0], [6, 0, 2, 0, 8, 0, 3, 0, 0], [0, 0, 7, 0, 6, 0, 0, 0, 0], [0, 0, 5, 0, 3, 9, 0, 6, 0], [0, 6, 4, 0, 5, 2, 1, 0, 9], [0, 2, 0, 0, 0, 0, 6, 5, 4], [5, 0, 0, 6, 0, 7, 0, 8, 3]]
[[2, 5, 1, 4, 7, 8, 9, 3, 6], [8, 9, 3, 5, 2, 6, 7, 4, 1], [4, 7, 6, 9, 1, 3, 5, 2, 8], [6, 4, 2, 1, 8, 5, 3, 9, 7], [9, 3, 7, 2, 6, 4, 8, 1, 5], [1, 8, 5, 7, 3, 9, 4, 6, 2], [3, 6, 4, 8, 5, 2, 1, 7, 9], [7, 2, 8, 3, 9, 1, 6, 5, 4], [5, 1, 9, 6, 4, 7, 2, 8, 3]]
42
39
0.481481
[4, 7, 3, 4, 2, 4, 6, 4, 5]
[2, 3, 6, 3, 6, 4, 5, 5, 5]
9
11
0.47619
false
0
42
medium
[[0, 0, 7, 3, 0, 0, 0, 5, 4], [2, 4, 5, 0, 8, 0, 9, 0, 0], [0, 0, 3, 0, 4, 0, 0, 7, 0], [0, 7, 0, 9, 6, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 7, 6, 0], [0, 0, 0, 8, 0, 1, 0, 0, 2], [0, 0, 8, 2, 9, 4, 0, 1, 6], [6, 0, 9, 1, 0, 8, 0, 2, 0], [0, 0, 0, 0, 0, 7, 0, 0, 3]]
[[8, 6, 7, 3, 1, 9, 2, 5, 4], [2, 4, 5, 7, 8, 6, 9, 3, 1], [9, 1, 3, 5, 4, 2, 6, 7, 8], [4, 7, 2, 9, 6, 3, 1, 8, 5], [3, 8, 1, 4, 2, 5, 7, 6, 9], [5, 9, 6, 8, 7, 1, 3, 4, 2], [7, 3, 8, 2, 9, 4, 5, 1, 6], [6, 5, 9, 1, 3, 8, 4, 2, 7], [1, 2, 4, 6, 5, 7, 8, 9, 3]]
47
34
0.419753
[4, 5, 3, 3, 3, 3, 6, 5, 2]
[2, 2, 5, 5, 5, 4, 2, 5, 4]
6
13
0.404255
false
0
47
medium
[[0, 0, 5, 3, 4, 6, 1, 7, 0], [0, 0, 0, 0, 0, 0, 0, 5, 0], [0, 0, 0, 8, 0, 0, 0, 0, 9], [5, 0, 2, 9, 3, 0, 7, 4, 1], [0, 7, 0, 0, 0, 0, 0, 0, 3], [0, 0, 0, 7, 0, 0, 0, 2, 0], [0, 9, 0, 0, 5, 0, 6, 3, 2], [2, 0, 7, 6, 0, 0, 4, 0, 0], [6, 0, 0, 4, 2, 0, 0, 0, 7]]
[[9, 2, 5, 3, 4, 6, 1, 7, 8], [7, 8, 6, 2, 9, 1, 3, 5, 4], [3, 4, 1, 8, 7, 5, 2, 6, 9], [5, 6, 2, 9, 3, 8, 7, 4, 1], [1, 7, 4, 5, 6, 2, 9, 8, 3], [8, 3, 9, 7, 1, 4, 5, 2, 6], [4, 9, 8, 1, 5, 7, 6, 3, 2], [2, 1, 7, 6, 8, 3, 4, 9, 5], [6, 5, 3, 4, 2, 9, 8, 1, 7]]
48
33
0.407407
[6, 1, 2, 7, 2, 2, 5, 4, 4]
[3, 2, 3, 6, 4, 1, 4, 5, 5]
4
7
0.229167
false
0
48
medium
[[3, 2, 0, 0, 9, 0, 4, 0, 0], [7, 0, 5, 0, 2, 1, 8, 0, 0], [0, 0, 1, 0, 6, 0, 3, 7, 2], [2, 1, 8, 0, 3, 7, 0, 0, 9], [5, 0, 0, 4, 8, 0, 7, 0, 0], [0, 0, 0, 0, 0, 5, 0, 0, 0], [6, 7, 0, 0, 0, 0, 2, 8, 0], [0, 0, 0, 8, 7, 3, 9, 0, 0], [8, 0, 4, 0, 0, 0, 1, 0, 7]]
[[3, 2, 6, 7, 9, 8, 4, 5, 1], [7, 4, 5, 3, 2, 1, 8, 9, 6], [9, 8, 1, 5, 6, 4, 3, 7, 2], [2, 1, 8, 6, 3, 7, 5, 4, 9], [5, 6, 9, 4, 8, 2, 7, 1, 3], [4, 3, 7, 9, 1, 5, 6, 2, 8], [6, 7, 3, 1, 4, 9, 2, 8, 5], [1, 5, 2, 8, 7, 3, 9, 6, 4], [8, 9, 4, 2, 5, 6, 1, 3, 7]]
44
37
0.45679
[4, 5, 5, 6, 4, 1, 4, 4, 4]
[6, 3, 4, 2, 6, 4, 7, 2, 3]
12
10
0.5
false
0
44
medium
[[0, 0, 0, 0, 3, 0, 0, 0, 7], [4, 8, 0, 9, 6, 0, 5, 0, 1], [0, 6, 3, 5, 7, 0, 8, 2, 0], [0, 0, 9, 6, 1, 0, 2, 0, 3], [3, 5, 0, 0, 9, 7, 0, 0, 6], [0, 0, 0, 0, 0, 5, 0, 9, 4], [0, 0, 0, 0, 0, 0, 0, 0, 5], [8, 0, 4, 7, 0, 6, 9, 1, 0], [0, 0, 1, 0, 4, 0, 0, 7, 0]]
[[9, 2, 5, 8, 3, 1, 4, 6, 7], [4, 8, 7, 9, 6, 2, 5, 3, 1], [1, 6, 3, 5, 7, 4, 8, 2, 9], [7, 4, 9, 6, 1, 8, 2, 5, 3], [3, 5, 2, 4, 9, 7, 1, 8, 6], [6, 1, 8, 3, 2, 5, 7, 9, 4], [2, 7, 6, 1, 8, 9, 3, 4, 5], [8, 3, 4, 7, 5, 6, 9, 1, 2], [5, 9, 1, 2, 4, 3, 6, 7, 8]]
44
37
0.45679
[2, 6, 6, 5, 5, 3, 1, 6, 3]
[3, 3, 4, 4, 6, 3, 4, 4, 6]
7
12
0.431818
false
0
44
medium
[[0, 8, 7, 0, 0, 2, 0, 1, 0], [2, 0, 4, 0, 1, 7, 0, 0, 3], [0, 0, 6, 8, 0, 0, 7, 0, 5], [5, 0, 8, 0, 0, 1, 0, 0, 0], [6, 4, 0, 0, 0, 8, 1, 0, 0], [0, 0, 2, 0, 5, 0, 6, 7, 0], [4, 3, 9, 1, 8, 0, 0, 0, 7], [0, 2, 0, 9, 0, 0, 0, 3, 0], [7, 0, 0, 0, 2, 3, 0, 9, 1]]
[[9, 8, 7, 5, 3, 2, 4, 1, 6], [2, 5, 4, 6, 1, 7, 9, 8, 3], [3, 1, 6, 8, 4, 9, 7, 2, 5], [5, 7, 8, 2, 6, 1, 3, 4, 9], [6, 4, 3, 7, 9, 8, 1, 5, 2], [1, 9, 2, 3, 5, 4, 6, 7, 8], [4, 3, 9, 1, 8, 5, 2, 6, 7], [8, 2, 1, 9, 7, 6, 5, 3, 4], [7, 6, 5, 4, 2, 3, 8, 9, 1]]
43
38
0.469136
[4, 5, 4, 3, 4, 4, 6, 3, 5]
[5, 4, 6, 3, 4, 5, 3, 4, 4]
2
13
0.348837
false
0
43
medium
[[0, 4, 0, 0, 0, 0, 0, 0, 8], [7, 6, 0, 0, 2, 0, 3, 4, 9], [0, 0, 0, 4, 7, 0, 5, 0, 0], [9, 0, 0, 0, 0, 0, 0, 3, 0], [0, 0, 0, 0, 3, 6, 7, 0, 2], [3, 0, 8, 9, 4, 7, 0, 0, 0], [0, 0, 0, 0, 0, 4, 0, 1, 0], [2, 0, 0, 7, 0, 0, 6, 0, 3], [6, 9, 0, 0, 0, 1, 0, 0, 0]]
[[1, 4, 9, 6, 5, 3, 2, 7, 8], [7, 6, 5, 1, 2, 8, 3, 4, 9], [8, 3, 2, 4, 7, 9, 5, 6, 1], [9, 7, 6, 5, 1, 2, 8, 3, 4], [4, 5, 1, 8, 3, 6, 7, 9, 2], [3, 2, 8, 9, 4, 7, 1, 5, 6], [5, 8, 3, 2, 6, 4, 9, 1, 7], [2, 1, 4, 7, 9, 5, 6, 8, 3], [6, 9, 7, 3, 8, 1, 4, 2, 5]]
50
31
0.382716
[2, 6, 3, 2, 4, 5, 2, 4, 3]
[5, 3, 1, 3, 4, 4, 4, 3, 4]
1
8
0.18
false
0
50
medium
[[0, 0, 7, 0, 0, 9, 0, 5, 0], [0, 4, 0, 0, 0, 0, 9, 3, 0], [0, 5, 9, 7, 4, 0, 0, 8, 0], [0, 0, 0, 0, 1, 6, 7, 9, 0], [0, 8, 3, 0, 0, 0, 0, 0, 2], [7, 1, 0, 0, 0, 0, 0, 0, 0], [8, 3, 0, 0, 6, 0, 0, 2, 0], [0, 0, 0, 3, 9, 5, 0, 1, 8], [6, 0, 5, 0, 2, 0, 0, 7, 0]]
[[3, 6, 7, 2, 8, 9, 4, 5, 1], [2, 4, 8, 6, 5, 1, 9, 3, 7], [1, 5, 9, 7, 4, 3, 2, 8, 6], [5, 2, 4, 8, 1, 6, 7, 9, 3], [9, 8, 3, 5, 7, 4, 1, 6, 2], [7, 1, 6, 9, 3, 2, 8, 4, 5], [8, 3, 1, 4, 6, 7, 5, 2, 9], [4, 7, 2, 3, 9, 5, 6, 1, 8], [6, 9, 5, 1, 2, 8, 3, 7, 4]]
48
33
0.407407
[3, 3, 5, 4, 3, 2, 4, 5, 4]
[3, 5, 4, 2, 5, 3, 2, 7, 2]
2
16
0.375
false
0
48
medium
[[6, 2, 0, 7, 4, 0, 1, 0, 0], [0, 7, 0, 1, 0, 0, 0, 5, 2], [5, 0, 8, 0, 0, 0, 3, 7, 0], [0, 6, 7, 3, 0, 0, 9, 0, 0], [0, 9, 0, 0, 0, 0, 0, 6, 0], [8, 0, 0, 9, 7, 0, 0, 3, 1], [0, 0, 2, 0, 0, 0, 0, 0, 6], [0, 0, 0, 8, 0, 0, 0, 0, 0], [4, 5, 0, 0, 0, 2, 0, 0, 3]]
[[6, 2, 3, 7, 4, 5, 1, 9, 8], [9, 7, 4, 1, 3, 8, 6, 5, 2], [5, 1, 8, 2, 6, 9, 3, 7, 4], [2, 6, 7, 3, 8, 1, 9, 4, 5], [3, 9, 1, 5, 2, 4, 8, 6, 7], [8, 4, 5, 9, 7, 6, 2, 3, 1], [7, 8, 2, 4, 9, 3, 5, 1, 6], [1, 3, 6, 8, 5, 7, 4, 2, 9], [4, 5, 9, 6, 1, 2, 7, 8, 3]]
50
31
0.382716
[5, 4, 4, 4, 2, 5, 2, 1, 4]
[4, 5, 3, 5, 2, 1, 3, 4, 4]
2
7
0.18
true
1
49
hard
[[6, 2, 7, 1, 4, 0, 5, 0, 3], [3, 4, 5, 2, 0, 6, 9, 7, 1], [0, 8, 9, 5, 0, 3, 6, 0, 2], [0, 0, 0, 7, 0, 0, 3, 6, 4], [7, 9, 3, 0, 5, 4, 0, 1, 8], [4, 6, 0, 0, 0, 8, 0, 5, 9], [0, 5, 6, 0, 3, 1, 0, 9, 7], [9, 7, 1, 0, 0, 5, 8, 3, 6], [8, 3, 4, 0, 6, 7, 1, 0, 5]]
[[6, 2, 7, 1, 4, 9, 5, 8, 3], [3, 4, 5, 2, 8, 6, 9, 7, 1], [1, 8, 9, 5, 7, 3, 6, 4, 2], [5, 1, 8, 7, 9, 2, 3, 6, 4], [7, 9, 3, 6, 5, 4, 2, 1, 8], [4, 6, 2, 3, 1, 8, 7, 5, 9], [2, 5, 6, 8, 3, 1, 4, 9, 7], [9, 7, 1, 4, 2, 5, 8, 3, 6], [8, 3, 4, 9, 6, 7, 1, 2, 5]]
24
57
0.703704
[7, 8, 6, 4, 7, 5, 6, 7, 7]
[6, 8, 7, 4, 4, 7, 6, 6, 9]
16
8
1
false
0
24
easy
[[7, 2, 0, 8, 9, 0, 5, 0, 0], [3, 9, 0, 4, 6, 0, 1, 0, 0], [0, 0, 0, 2, 1, 7, 8, 9, 0], [8, 0, 9, 0, 0, 2, 0, 0, 0], [2, 0, 4, 0, 0, 8, 0, 0, 0], [1, 0, 5, 0, 4, 9, 2, 8, 7], [6, 1, 0, 0, 0, 0, 0, 2, 8], [0, 8, 0, 0, 2, 0, 9, 1, 5], [9, 5, 0, 7, 0, 1, 0, 4, 0]]
[[7, 2, 1, 8, 9, 3, 5, 6, 4], [3, 9, 8, 4, 6, 5, 1, 7, 2], [5, 4, 6, 2, 1, 7, 8, 9, 3], [8, 6, 9, 5, 7, 2, 4, 3, 1], [2, 7, 4, 1, 3, 8, 6, 5, 9], [1, 3, 5, 6, 4, 9, 2, 8, 7], [6, 1, 3, 9, 5, 4, 7, 2, 8], [4, 8, 7, 3, 2, 6, 9, 1, 5], [9, 5, 2, 7, 8, 1, 3, 4, 6]]
39
42
0.518519
[5, 5, 5, 3, 3, 7, 4, 5, 5]
[7, 5, 3, 4, 5, 5, 5, 5, 3]
7
14
0.538462
false
0
39
medium
[[8, 0, 3, 7, 0, 0, 0, 0, 0], [0, 2, 6, 0, 0, 0, 0, 0, 4], [0, 9, 7, 1, 0, 0, 2, 0, 3], [7, 0, 5, 0, 0, 0, 9, 0, 8], [9, 0, 1, 0, 7, 0, 0, 4, 0], [0, 3, 8, 4, 0, 1, 5, 6, 7], [1, 7, 0, 9, 5, 0, 8, 0, 0], [6, 8, 0, 2, 1, 0, 4, 3, 5], [3, 5, 2, 8, 4, 6, 0, 0, 0]]
[[8, 1, 3, 7, 2, 4, 6, 5, 9], [5, 2, 6, 3, 8, 9, 1, 7, 4], [4, 9, 7, 1, 6, 5, 2, 8, 3], [7, 4, 5, 6, 3, 2, 9, 1, 8], [9, 6, 1, 5, 7, 8, 3, 4, 2], [2, 3, 8, 4, 9, 1, 5, 6, 7], [1, 7, 4, 9, 5, 3, 8, 2, 6], [6, 8, 9, 2, 1, 7, 4, 3, 5], [3, 5, 2, 8, 4, 6, 7, 9, 1]]
37
44
0.54321
[3, 3, 5, 4, 4, 7, 5, 7, 6]
[6, 6, 7, 6, 4, 2, 5, 3, 5]
10
9
0.513514
false
0
37
medium
[[2, 0, 6, 0, 0, 7, 9, 0, 5], [3, 4, 5, 0, 9, 2, 0, 1, 8], [0, 0, 0, 8, 5, 0, 0, 6, 0], [0, 0, 0, 5, 0, 9, 0, 0, 0], [7, 0, 8, 0, 0, 0, 4, 5, 0], [0, 0, 4, 0, 8, 3, 1, 2, 6], [4, 2, 0, 0, 6, 0, 5, 8, 0], [5, 7, 1, 2, 0, 0, 0, 9, 4], [8, 6, 0, 0, 0, 0, 2, 0, 0]]
[[2, 8, 6, 3, 1, 7, 9, 4, 5], [3, 4, 5, 6, 9, 2, 7, 1, 8], [1, 9, 7, 8, 5, 4, 3, 6, 2], [6, 1, 2, 5, 4, 9, 8, 7, 3], [7, 3, 8, 1, 2, 6, 4, 5, 9], [9, 5, 4, 7, 8, 3, 1, 2, 6], [4, 2, 3, 9, 6, 1, 5, 8, 7], [5, 7, 1, 2, 3, 8, 6, 9, 4], [8, 6, 9, 4, 7, 5, 2, 3, 1]]
40
41
0.506173
[5, 7, 3, 2, 4, 6, 5, 6, 3]
[6, 4, 5, 3, 4, 4, 5, 6, 4]
7
15
0.55
false
0
40
medium
[[7, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, 7, 0, 8, 0, 6, 1], [1, 0, 0, 2, 9, 6, 8, 4, 7], [0, 0, 0, 0, 0, 1, 4, 0, 0], [8, 0, 1, 0, 0, 0, 0, 3, 0], [0, 9, 0, 6, 0, 0, 0, 7, 5], [0, 8, 0, 0, 1, 0, 0, 0, 6], [0, 0, 7, 0, 5, 2, 3, 9, 4], [9, 3, 5, 4, 6, 7, 0, 1, 0]]
[[7, 6, 8, 1, 4, 5, 9, 2, 3], [4, 2, 9, 7, 3, 8, 5, 6, 1], [1, 5, 3, 2, 9, 6, 8, 4, 7], [5, 7, 6, 3, 2, 1, 4, 8, 9], [8, 4, 1, 5, 7, 9, 6, 3, 2], [3, 9, 2, 6, 8, 4, 1, 7, 5], [2, 8, 4, 9, 1, 3, 7, 5, 6], [6, 1, 7, 8, 5, 2, 3, 9, 4], [9, 3, 5, 4, 6, 7, 2, 1, 8]]
43
38
0.469136
[1, 5, 7, 2, 3, 4, 3, 6, 7]
[5, 3, 3, 4, 4, 5, 3, 6, 5]
7
13
0.465116
false
0
43
medium
[[9, 0, 0, 0, 0, 0, 0, 0, 2], [0, 1, 0, 0, 6, 0, 3, 9, 0], [0, 8, 3, 9, 0, 0, 1, 0, 0], [8, 0, 4, 0, 9, 5, 0, 0, 7], [1, 3, 0, 6, 7, 0, 0, 4, 9], [0, 6, 0, 0, 4, 1, 0, 0, 0], [3, 0, 2, 0, 1, 0, 0, 5, 0], [0, 0, 0, 5, 0, 0, 0, 0, 0], [5, 4, 1, 0, 8, 0, 0, 3, 0]]
[[9, 5, 6, 1, 3, 4, 7, 8, 2], [4, 1, 7, 2, 6, 8, 3, 9, 5], [2, 8, 3, 9, 5, 7, 1, 6, 4], [8, 2, 4, 3, 9, 5, 6, 1, 7], [1, 3, 5, 6, 7, 2, 8, 4, 9], [7, 6, 9, 8, 4, 1, 5, 2, 3], [3, 7, 2, 4, 1, 6, 9, 5, 8], [6, 9, 8, 5, 2, 3, 4, 7, 1], [5, 4, 1, 7, 8, 9, 2, 3, 6]]
47
34
0.419753
[2, 4, 4, 5, 6, 3, 4, 1, 5]
[5, 5, 4, 3, 6, 2, 2, 4, 3]
3
8
0.234043
false
0
47
medium
[[0, 0, 5, 0, 0, 0, 0, 6, 0], [0, 0, 0, 0, 0, 6, 3, 0, 2], [0, 4, 0, 0, 8, 1, 5, 9, 7], [0, 1, 2, 0, 3, 8, 7, 5, 4], [0, 0, 0, 2, 0, 0, 8, 1, 0], [0, 8, 7, 0, 1, 4, 0, 0, 0], [1, 2, 0, 0, 0, 7, 6, 8, 0], [0, 0, 0, 0, 9, 2, 0, 3, 0], [9, 5, 4, 8, 6, 0, 2, 0, 0]]
[[3, 7, 5, 4, 2, 9, 1, 6, 8], [8, 9, 1, 7, 5, 6, 3, 4, 2], [2, 4, 6, 3, 8, 1, 5, 9, 7], [6, 1, 2, 9, 3, 8, 7, 5, 4], [4, 3, 9, 2, 7, 5, 8, 1, 6], [5, 8, 7, 6, 1, 4, 9, 2, 3], [1, 2, 3, 5, 4, 7, 6, 8, 9], [7, 6, 8, 1, 9, 2, 4, 3, 5], [9, 5, 4, 8, 6, 3, 2, 7, 1]]
42
39
0.481481
[2, 3, 6, 7, 3, 4, 5, 3, 6]
[2, 5, 4, 2, 5, 6, 6, 6, 3]
9
11
0.47619
false
0
42
medium
[[7, 0, 9, 0, 0, 0, 1, 0, 0], [4, 2, 1, 0, 0, 0, 0, 5, 0], [3, 0, 0, 7, 0, 0, 0, 0, 8], [1, 0, 0, 0, 0, 0, 3, 0, 2], [9, 0, 8, 3, 2, 0, 0, 0, 0], [0, 0, 2, 0, 7, 0, 8, 0, 9], [0, 7, 0, 5, 3, 0, 4, 0, 0], [0, 9, 0, 0, 0, 0, 6, 7, 5], [0, 0, 0, 6, 0, 0, 0, 9, 3]]
[[7, 8, 9, 2, 5, 6, 1, 3, 4], [4, 2, 1, 8, 9, 3, 7, 5, 6], [3, 6, 5, 7, 1, 4, 9, 2, 8], [1, 5, 7, 9, 6, 8, 3, 4, 2], [9, 4, 8, 3, 2, 1, 5, 6, 7], [6, 3, 2, 4, 7, 5, 8, 1, 9], [2, 7, 6, 5, 3, 9, 4, 8, 1], [8, 9, 3, 1, 4, 2, 6, 7, 5], [5, 1, 4, 6, 8, 7, 2, 9, 3]]
49
32
0.395062
[3, 4, 3, 3, 4, 4, 4, 4, 3]
[5, 3, 4, 4, 3, 0, 5, 3, 5]
3
11
0.285714
true
1
48
hard
[[0, 0, 1, 3, 0, 0, 0, 0, 2], [0, 7, 9, 0, 0, 0, 0, 0, 0], [0, 2, 0, 6, 7, 0, 9, 0, 3], [0, 0, 0, 9, 6, 7, 3, 0, 0], [7, 5, 0, 0, 0, 1, 0, 4, 9], [0, 8, 0, 5, 0, 3, 1, 0, 0], [0, 4, 0, 7, 0, 2, 5, 3, 0], [2, 0, 5, 8, 0, 6, 7, 0, 0], [1, 0, 7, 4, 0, 5, 0, 6, 0]]
[[8, 6, 1, 3, 5, 9, 4, 7, 2], [3, 7, 9, 1, 2, 4, 8, 5, 6], [5, 2, 4, 6, 7, 8, 9, 1, 3], [4, 1, 2, 9, 6, 7, 3, 8, 5], [7, 5, 3, 2, 8, 1, 6, 4, 9], [9, 8, 6, 5, 4, 3, 1, 2, 7], [6, 4, 8, 7, 9, 2, 5, 3, 1], [2, 3, 5, 8, 1, 6, 7, 9, 4], [1, 9, 7, 4, 3, 5, 2, 6, 8]]
43
38
0.469136
[3, 2, 5, 4, 5, 4, 5, 5, 5]
[3, 5, 4, 7, 2, 6, 5, 3, 3]
5
13
0.418605
false
0
43
medium
[[6, 0, 0, 0, 1, 7, 4, 0, 0], [4, 0, 1, 0, 0, 3, 0, 0, 8], [0, 5, 9, 8, 0, 0, 7, 2, 1], [1, 2, 0, 0, 0, 0, 0, 5, 0], [0, 0, 0, 0, 4, 0, 8, 0, 0], [0, 0, 8, 0, 2, 0, 1, 0, 0], [0, 0, 4, 5, 3, 0, 0, 0, 7], [7, 0, 0, 0, 9, 0, 0, 8, 6], [2, 6, 3, 1, 7, 0, 0, 0, 0]]
[[6, 8, 2, 9, 1, 7, 4, 3, 5], [4, 7, 1, 2, 5, 3, 9, 6, 8], [3, 5, 9, 8, 6, 4, 7, 2, 1], [1, 2, 7, 3, 8, 9, 6, 5, 4], [5, 3, 6, 7, 4, 1, 8, 9, 2], [9, 4, 8, 6, 2, 5, 1, 7, 3], [8, 9, 4, 5, 3, 6, 2, 1, 7], [7, 1, 5, 4, 9, 2, 3, 8, 6], [2, 6, 3, 1, 7, 8, 5, 4, 9]]
46
35
0.432099
[4, 4, 6, 3, 2, 3, 4, 4, 5]
[5, 3, 5, 3, 6, 2, 4, 3, 4]
6
16
0.478261
false
0
46
medium
[[8, 0, 0, 0, 0, 5, 0, 4, 7], [0, 4, 0, 0, 0, 8, 5, 0, 0], [0, 0, 0, 0, 0, 0, 6, 3, 0], [0, 0, 0, 0, 0, 0, 4, 9, 0], [5, 9, 0, 0, 4, 0, 0, 0, 2], [0, 7, 2, 0, 0, 6, 3, 0, 5], [9, 8, 0, 0, 0, 0, 2, 7, 3], [0, 6, 7, 8, 0, 4, 0, 5, 1], [0, 3, 0, 0, 7, 0, 0, 0, 0]]
[[8, 2, 9, 3, 6, 5, 1, 4, 7], [6, 4, 3, 7, 1, 8, 5, 2, 9], [7, 5, 1, 4, 9, 2, 6, 3, 8], [3, 1, 8, 5, 2, 7, 4, 9, 6], [5, 9, 6, 1, 4, 3, 7, 8, 2], [4, 7, 2, 9, 8, 6, 3, 1, 5], [9, 8, 4, 6, 5, 1, 2, 7, 3], [2, 6, 7, 8, 3, 4, 9, 5, 1], [1, 3, 5, 2, 7, 9, 8, 6, 4]]
48
33
0.407407
[4, 3, 2, 2, 4, 5, 5, 6, 2]
[3, 6, 2, 1, 2, 4, 5, 5, 5]
5
9
0.291667
false
0
48
medium
[[4, 0, 0, 0, 0, 0, 0, 7, 0], [0, 6, 0, 8, 5, 0, 2, 4, 0], [0, 0, 0, 3, 0, 1, 0, 6, 5], [0, 4, 9, 0, 7, 8, 5, 0, 0], [0, 0, 7, 0, 3, 2, 0, 0, 8], [2, 8, 0, 0, 0, 9, 4, 3, 0], [1, 2, 0, 7, 0, 3, 0, 0, 4], [7, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 6, 2, 0, 0, 0, 0, 9]]
[[4, 1, 5, 9, 2, 6, 8, 7, 3], [9, 6, 3, 8, 5, 7, 2, 4, 1], [8, 7, 2, 3, 4, 1, 9, 6, 5], [3, 4, 9, 1, 7, 8, 5, 2, 6], [6, 5, 7, 4, 3, 2, 1, 9, 8], [2, 8, 1, 5, 6, 9, 4, 3, 7], [1, 2, 8, 7, 9, 3, 6, 5, 4], [7, 9, 4, 6, 1, 5, 3, 8, 2], [5, 3, 6, 2, 8, 4, 7, 1, 9]]
46
35
0.432099
[2, 5, 4, 5, 4, 5, 5, 2, 3]
[4, 4, 3, 4, 4, 5, 3, 4, 4]
3
11
0.304348
false
0
46
medium
[[5, 0, 0, 0, 0, 0, 2, 6, 0], [0, 2, 4, 0, 8, 6, 0, 0, 0], [8, 0, 7, 1, 5, 2, 3, 0, 0], [0, 0, 0, 6, 0, 0, 7, 0, 3], [0, 0, 3, 4, 0, 0, 0, 0, 6], [7, 0, 0, 0, 9, 8, 1, 2, 0], [0, 3, 0, 8, 0, 0, 6, 0, 0], [0, 7, 2, 0, 0, 0, 4, 8, 1], [0, 0, 0, 0, 7, 0, 0, 0, 0]]
[[5, 1, 9, 7, 3, 4, 2, 6, 8], [3, 2, 4, 9, 8, 6, 5, 1, 7], [8, 6, 7, 1, 5, 2, 3, 4, 9], [4, 8, 1, 6, 2, 5, 7, 9, 3], [2, 9, 3, 4, 1, 7, 8, 5, 6], [7, 5, 6, 3, 9, 8, 1, 2, 4], [1, 3, 5, 8, 4, 9, 6, 7, 2], [9, 7, 2, 5, 6, 3, 4, 8, 1], [6, 4, 8, 2, 7, 1, 9, 3, 5]]
48
33
0.407407
[3, 4, 6, 3, 3, 5, 3, 5, 1]
[3, 3, 4, 4, 4, 3, 6, 3, 3]
0
10
0.208333
true
5
66
hard
[[6, 0, 4, 0, 0, 1, 0, 3, 5], [0, 0, 3, 4, 5, 0, 0, 0, 1], [5, 2, 1, 9, 0, 0, 0, 0, 0], [0, 6, 9, 8, 0, 7, 1, 0, 4], [2, 5, 0, 0, 1, 4, 0, 0, 7], [4, 1, 0, 0, 9, 0, 0, 0, 6], [0, 0, 0, 0, 6, 0, 0, 1, 0], [0, 0, 0, 0, 3, 9, 0, 7, 0], [0, 7, 0, 1, 4, 0, 5, 0, 3]]
[[6, 9, 4, 2, 8, 1, 7, 3, 5], [7, 8, 3, 4, 5, 6, 9, 2, 1], [5, 2, 1, 9, 7, 3, 6, 4, 8], [3, 6, 9, 8, 2, 7, 1, 5, 4], [2, 5, 8, 6, 1, 4, 3, 9, 7], [4, 1, 7, 3, 9, 5, 2, 8, 6], [8, 3, 5, 7, 6, 2, 4, 1, 9], [1, 4, 6, 5, 3, 9, 8, 7, 2], [9, 7, 2, 1, 4, 8, 5, 6, 3]]
43
38
0.469136
[5, 4, 4, 6, 5, 4, 2, 3, 5]
[4, 5, 4, 4, 6, 4, 2, 3, 6]
4
10
0.325581
false
0
43
medium
[[4, 2, 0, 7, 9, 6, 0, 5, 0], [3, 0, 0, 2, 8, 0, 4, 9, 7], [8, 7, 9, 0, 0, 4, 6, 1, 2], [6, 9, 0, 0, 0, 5, 2, 0, 1], [5, 3, 8, 4, 0, 0, 0, 0, 9], [0, 1, 0, 3, 6, 9, 0, 0, 4], [9, 8, 3, 6, 4, 7, 0, 2, 5], [0, 0, 6, 1, 5, 0, 0, 0, 0], [1, 0, 0, 0, 2, 0, 3, 4, 6]]
[[4, 2, 1, 7, 9, 6, 8, 5, 3], [3, 6, 5, 2, 8, 1, 4, 9, 7], [8, 7, 9, 5, 3, 4, 6, 1, 2], [6, 9, 4, 8, 7, 5, 2, 3, 1], [5, 3, 8, 4, 1, 2, 7, 6, 9], [7, 1, 2, 3, 6, 9, 5, 8, 4], [9, 8, 3, 6, 4, 7, 1, 2, 5], [2, 4, 6, 1, 5, 3, 9, 7, 8], [1, 5, 7, 9, 2, 8, 3, 4, 6]]
31
50
0.617284
[6, 6, 7, 5, 5, 5, 8, 3, 5]
[7, 6, 4, 6, 6, 5, 4, 5, 7]
13
14
0.870968
false
0
31
easy
[[0, 8, 0, 0, 0, 0, 0, 9, 0], [0, 9, 0, 5, 0, 2, 0, 0, 0], [0, 0, 3, 0, 0, 1, 4, 0, 8], [0, 0, 7, 0, 9, 0, 6, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1], [6, 5, 0, 0, 2, 0, 0, 0, 0], [9, 0, 0, 3, 0, 0, 0, 8, 0], [3, 1, 0, 0, 4, 0, 9, 7, 0], [0, 0, 2, 8, 7, 9, 0, 1, 3]]
[[5, 8, 6, 4, 3, 7, 1, 9, 2], [1, 9, 4, 5, 8, 2, 3, 6, 7], [7, 2, 3, 9, 6, 1, 4, 5, 8], [2, 4, 7, 1, 9, 8, 6, 3, 5], [8, 3, 9, 6, 5, 4, 7, 2, 1], [6, 5, 1, 7, 2, 3, 8, 4, 9], [9, 7, 5, 3, 1, 6, 2, 8, 4], [3, 1, 8, 2, 4, 5, 9, 7, 6], [4, 6, 2, 8, 7, 9, 5, 1, 3]]
50
31
0.382716
[2, 3, 4, 4, 1, 3, 3, 5, 6]
[3, 4, 3, 3, 4, 3, 3, 5, 3]
4
12
0.32
false
0
50
medium
[[0, 0, 5, 0, 2, 0, 0, 4, 0], [0, 0, 7, 0, 9, 0, 3, 1, 8], [1, 0, 6, 8, 4, 0, 0, 7, 0], [5, 1, 0, 0, 0, 0, 6, 9, 3], [3, 0, 0, 0, 0, 0, 7, 0, 0], [0, 7, 4, 2, 3, 0, 0, 0, 1], [0, 5, 0, 7, 6, 4, 1, 8, 9], [0, 4, 0, 0, 0, 1, 0, 0, 2], [0, 8, 1, 9, 0, 2, 0, 3, 0]]
[[8, 3, 5, 1, 2, 7, 9, 4, 6], [4, 2, 7, 6, 9, 5, 3, 1, 8], [1, 9, 6, 8, 4, 3, 2, 7, 5], [5, 1, 2, 4, 7, 8, 6, 9, 3], [3, 6, 8, 5, 1, 9, 7, 2, 4], [9, 7, 4, 2, 3, 6, 8, 5, 1], [2, 5, 3, 7, 6, 4, 1, 8, 9], [7, 4, 9, 3, 8, 1, 5, 6, 2], [6, 8, 1, 9, 5, 2, 4, 3, 7]]
41
40
0.493827
[3, 5, 5, 5, 2, 5, 7, 3, 5]
[3, 5, 5, 4, 5, 3, 4, 6, 5]
9
19
0.682927
false
0
41
medium
[[0, 0, 0, 0, 0, 0, 0, 6, 5], [0, 0, 4, 0, 5, 6, 7, 0, 1], [0, 7, 0, 8, 1, 3, 9, 4, 0], [0, 0, 6, 0, 0, 5, 4, 9, 0], [5, 0, 0, 6, 9, 0, 0, 0, 0], [0, 0, 9, 0, 4, 2, 0, 0, 0], [0, 6, 2, 5, 0, 4, 1, 7, 9], [0, 0, 0, 0, 0, 0, 0, 3, 0], [0, 0, 0, 0, 0, 0, 6, 2, 8]]
[[1, 9, 8, 4, 2, 7, 3, 6, 5], [2, 3, 4, 9, 5, 6, 7, 8, 1], [6, 7, 5, 8, 1, 3, 9, 4, 2], [8, 2, 6, 1, 7, 5, 4, 9, 3], [5, 4, 3, 6, 9, 8, 2, 1, 7], [7, 1, 9, 3, 4, 2, 8, 5, 6], [3, 6, 2, 5, 8, 4, 1, 7, 9], [9, 8, 7, 2, 6, 1, 5, 3, 4], [4, 5, 1, 7, 3, 9, 6, 2, 8]]
47
34
0.419753
[2, 5, 6, 4, 3, 3, 7, 1, 3]
[1, 2, 4, 3, 4, 5, 5, 6, 4]
5
7
0.255319
true
5
84
hard
[[7, 9, 0, 0, 4, 8, 0, 6, 0], [1, 2, 5, 9, 7, 6, 3, 0, 0], [0, 4, 0, 3, 0, 5, 7, 2, 0], [9, 8, 0, 6, 5, 7, 4, 1, 3], [0, 0, 7, 1, 0, 0, 8, 5, 6], [0, 0, 1, 0, 0, 0, 0, 0, 7], [0, 0, 6, 0, 0, 2, 1, 3, 5], [0, 0, 9, 7, 0, 1, 0, 0, 0], [0, 1, 0, 5, 0, 0, 0, 0, 0]]
[[7, 9, 3, 2, 4, 8, 5, 6, 1], [1, 2, 5, 9, 7, 6, 3, 8, 4], [6, 4, 8, 3, 1, 5, 7, 2, 9], [9, 8, 2, 6, 5, 7, 4, 1, 3], [4, 3, 7, 1, 2, 9, 8, 5, 6], [5, 6, 1, 8, 3, 4, 2, 9, 7], [8, 7, 6, 4, 9, 2, 1, 3, 5], [3, 5, 9, 7, 8, 1, 6, 4, 2], [2, 1, 4, 5, 6, 3, 9, 7, 8]]
39
42
0.518519
[5, 7, 5, 8, 5, 2, 5, 3, 2]
[3, 5, 5, 6, 3, 6, 5, 5, 4]
10
7
0.435897
false
0
39
medium
[[2, 9, 0, 8, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 6], [7, 8, 6, 5, 0, 0, 2, 0, 0], [0, 2, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 9, 4, 8, 2], [6, 4, 7, 0, 0, 0, 9, 0, 3], [8, 7, 5, 2, 0, 0, 0, 0, 4], [3, 1, 0, 6, 4, 5, 7, 0, 0], [0, 0, 9, 0, 0, 8, 0, 0, 0]]
[[2, 9, 4, 8, 1, 6, 3, 7, 5], [5, 3, 1, 9, 2, 7, 8, 4, 6], [7, 8, 6, 5, 3, 4, 2, 1, 9], [9, 2, 8, 4, 5, 3, 1, 6, 7], [1, 5, 3, 7, 6, 9, 4, 8, 2], [6, 4, 7, 1, 8, 2, 9, 5, 3], [8, 7, 5, 2, 9, 1, 6, 3, 4], [3, 1, 2, 6, 4, 5, 7, 9, 8], [4, 6, 9, 3, 7, 8, 5, 2, 1]]
45
36
0.444444
[4, 2, 5, 2, 5, 5, 5, 6, 2]
[6, 6, 4, 4, 1, 3, 6, 2, 4]
8
13
0.466667
false
0
45
medium
[[1, 8, 0, 0, 2, 3, 0, 0, 0], [9, 4, 2, 5, 0, 0, 0, 0, 8], [0, 6, 0, 0, 1, 0, 0, 9, 2], [2, 0, 9, 8, 4, 0, 0, 0, 0], [6, 0, 8, 3, 9, 5, 0, 4, 0], [3, 0, 0, 0, 6, 7, 8, 5, 0], [8, 0, 6, 0, 0, 0, 0, 2, 7], [4, 0, 7, 0, 0, 2, 9, 0, 0], [0, 0, 1, 7, 0, 0, 0, 0, 4]]
[[1, 8, 5, 9, 2, 3, 4, 7, 6], [9, 4, 2, 5, 7, 6, 1, 3, 8], [7, 6, 3, 4, 1, 8, 5, 9, 2], [2, 5, 9, 8, 4, 1, 7, 6, 3], [6, 7, 8, 3, 9, 5, 2, 4, 1], [3, 1, 4, 2, 6, 7, 8, 5, 9], [8, 9, 6, 1, 5, 4, 3, 2, 7], [4, 3, 7, 6, 8, 2, 9, 1, 5], [5, 2, 1, 7, 3, 9, 6, 8, 4]]
42
39
0.481481
[4, 5, 4, 4, 6, 5, 4, 4, 3]
[7, 3, 6, 4, 5, 4, 2, 4, 4]
9
9
0.428571
false
0
42
medium
[[9, 0, 8, 2, 6, 0, 3, 5, 1], [5, 0, 0, 0, 9, 4, 8, 7, 2], [0, 0, 2, 0, 1, 0, 4, 0, 9], [0, 0, 3, 0, 0, 0, 0, 8, 4], [1, 5, 4, 0, 8, 3, 0, 0, 7], [0, 2, 0, 0, 0, 0, 9, 0, 5], [7, 6, 0, 1, 0, 0, 0, 4, 0], [0, 0, 9, 0, 0, 6, 0, 0, 0], [0, 0, 1, 0, 0, 5, 0, 9, 0]]
[[9, 4, 8, 2, 6, 7, 3, 5, 1], [5, 1, 6, 3, 9, 4, 8, 7, 2], [3, 7, 2, 5, 1, 8, 4, 6, 9], [6, 9, 3, 7, 5, 2, 1, 8, 4], [1, 5, 4, 9, 8, 3, 6, 2, 7], [8, 2, 7, 6, 4, 1, 9, 3, 5], [7, 6, 5, 1, 3, 9, 2, 4, 8], [2, 8, 9, 4, 7, 6, 5, 1, 3], [4, 3, 1, 8, 2, 5, 7, 9, 6]]
43
38
0.469136
[7, 6, 4, 3, 6, 3, 4, 2, 3]
[4, 3, 6, 2, 4, 4, 4, 5, 6]
6
12
0.418605
false
0
43
medium
[[9, 5, 0, 0, 6, 4, 0, 3, 7], [0, 4, 6, 0, 8, 1, 0, 5, 9], [0, 0, 1, 5, 3, 9, 0, 8, 0], [0, 3, 4, 1, 0, 6, 0, 7, 0], [8, 6, 5, 0, 0, 0, 0, 2, 0], [0, 9, 0, 0, 2, 8, 0, 0, 0], [5, 0, 0, 6, 1, 2, 0, 0, 0], [6, 1, 3, 4, 7, 0, 0, 9, 0], [0, 0, 0, 8, 9, 0, 0, 0, 5]]
[[9, 5, 8, 2, 6, 4, 1, 3, 7], [3, 4, 6, 7, 8, 1, 2, 5, 9], [7, 2, 1, 5, 3, 9, 4, 8, 6], [2, 3, 4, 1, 5, 6, 9, 7, 8], [8, 6, 5, 9, 4, 7, 3, 2, 1], [1, 9, 7, 3, 2, 8, 5, 6, 4], [5, 8, 9, 6, 1, 2, 7, 4, 3], [6, 1, 3, 4, 7, 5, 8, 9, 2], [4, 7, 2, 8, 9, 3, 6, 1, 5]]
39
42
0.518519
[6, 6, 5, 5, 4, 3, 4, 6, 3]
[4, 6, 5, 5, 7, 6, 0, 6, 3]
10
12
0.564103
false
0
39
medium
[[0, 7, 0, 6, 2, 0, 5, 0, 9], [0, 2, 9, 4, 0, 0, 0, 0, 0], [6, 8, 0, 5, 7, 0, 0, 0, 0], [3, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 6, 7, 5, 0, 0, 9, 3], [0, 0, 0, 0, 8, 6, 0, 0, 5], [0, 0, 0, 0, 0, 0, 1, 7, 0], [0, 6, 4, 0, 3, 0, 0, 0, 0], [0, 0, 5, 0, 0, 4, 0, 3, 2]]
[[4, 7, 1, 6, 2, 3, 5, 8, 9], [5, 2, 9, 4, 1, 8, 3, 6, 7], [6, 8, 3, 5, 7, 9, 4, 2, 1], [3, 5, 7, 9, 4, 2, 8, 1, 6], [8, 4, 6, 7, 5, 1, 2, 9, 3], [1, 9, 2, 3, 8, 6, 7, 4, 5], [9, 3, 8, 2, 6, 5, 1, 7, 4], [2, 6, 4, 1, 3, 7, 9, 5, 8], [7, 1, 5, 8, 9, 4, 6, 3, 2]]
50
31
0.382716
[5, 3, 4, 1, 6, 3, 2, 3, 4]
[3, 4, 4, 4, 5, 2, 2, 3, 4]
2
13
0.3
false
0
50
medium
[[7, 9, 0, 4, 0, 0, 8, 0, 1], [1, 0, 0, 7, 8, 0, 0, 9, 0], [0, 0, 0, 9, 1, 0, 4, 0, 2], [9, 7, 5, 8, 2, 1, 0, 4, 6], [0, 0, 0, 0, 0, 0, 7, 8, 5], [0, 0, 6, 5, 0, 4, 0, 0, 0], [2, 0, 7, 0, 9, 0, 0, 3, 4], [3, 0, 0, 2, 0, 0, 9, 0, 8], [0, 0, 9, 1, 0, 0, 6, 2, 7]]
[[7, 9, 3, 4, 5, 2, 8, 6, 1], [1, 2, 4, 7, 8, 6, 5, 9, 3], [6, 5, 8, 9, 1, 3, 4, 7, 2], [9, 7, 5, 8, 2, 1, 3, 4, 6], [4, 1, 2, 3, 6, 9, 7, 8, 5], [8, 3, 6, 5, 7, 4, 2, 1, 9], [2, 8, 7, 6, 9, 5, 1, 3, 4], [3, 6, 1, 2, 4, 7, 9, 5, 8], [5, 4, 9, 1, 3, 8, 6, 2, 7]]
40
41
0.506173
[5, 4, 4, 8, 3, 3, 5, 4, 5]
[5, 2, 4, 7, 4, 2, 5, 5, 7]
6
9
0.375
false
0
40
medium
[[6, 0, 0, 5, 0, 2, 0, 0, 0], [4, 5, 0, 0, 9, 3, 7, 0, 0], [0, 3, 0, 6, 8, 4, 0, 9, 0], [2, 0, 3, 8, 0, 0, 5, 6, 0], [0, 0, 1, 0, 0, 0, 0, 0, 2], [0, 0, 7, 0, 2, 5, 0, 1, 0], [0, 0, 5, 0, 3, 6, 4, 0, 0], [3, 2, 0, 7, 5, 0, 6, 0, 1], [9, 7, 6, 4, 1, 8, 0, 5, 3]]
[[6, 1, 9, 5, 7, 2, 3, 4, 8], [4, 5, 8, 1, 9, 3, 7, 2, 6], [7, 3, 2, 6, 8, 4, 1, 9, 5], [2, 9, 3, 8, 4, 1, 5, 6, 7], [5, 4, 1, 9, 6, 7, 8, 3, 2], [8, 6, 7, 3, 2, 5, 9, 1, 4], [1, 8, 5, 2, 3, 6, 4, 7, 9], [3, 2, 4, 7, 5, 9, 6, 8, 1], [9, 7, 6, 4, 1, 8, 2, 5, 3]]
39
42
0.518519
[3, 5, 5, 5, 2, 4, 4, 6, 8]
[5, 4, 5, 5, 6, 6, 4, 4, 3]
8
10
0.461538
false
0
39
medium
[[8, 7, 0, 5, 0, 0, 0, 6, 0], [0, 1, 0, 0, 0, 0, 2, 0, 7], [6, 4, 0, 1, 8, 0, 5, 0, 9], [0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 2, 0, 0, 0, 6, 0, 7, 5], [0, 0, 8, 0, 7, 2, 0, 0, 6], [0, 0, 0, 6, 0, 5, 0, 0, 8], [0, 0, 0, 0, 0, 4, 0, 0, 0], [9, 0, 4, 0, 0, 8, 6, 2, 1]]
[[8, 7, 9, 5, 2, 3, 1, 6, 4], [3, 1, 5, 4, 6, 9, 2, 8, 7], [6, 4, 2, 1, 8, 7, 5, 3, 9], [4, 6, 7, 8, 5, 1, 3, 9, 2], [1, 2, 3, 9, 4, 6, 8, 7, 5], [5, 9, 8, 3, 7, 2, 4, 1, 6], [2, 3, 1, 6, 9, 5, 7, 4, 8], [7, 8, 6, 2, 1, 4, 9, 5, 3], [9, 5, 4, 7, 3, 8, 6, 2, 1]]
48
33
0.407407
[4, 3, 6, 1, 5, 4, 3, 1, 6]
[4, 4, 2, 3, 2, 6, 3, 3, 6]
4
14
0.375
false
0
48
medium
[[0, 3, 2, 1, 0, 4, 0, 7, 0], [5, 0, 0, 3, 0, 0, 0, 0, 2], [0, 0, 0, 6, 2, 5, 0, 0, 0], [0, 8, 0, 0, 6, 1, 0, 2, 0], [0, 0, 7, 4, 0, 2, 6, 0, 8], [2, 0, 1, 7, 8, 0, 0, 5, 4], [6, 4, 0, 0, 0, 0, 0, 3, 0], [0, 9, 8, 0, 0, 3, 7, 0, 0], [7, 2, 3, 0, 5, 6, 0, 0, 1]]
[[8, 3, 2, 1, 9, 4, 5, 7, 6], [5, 1, 6, 3, 7, 8, 4, 9, 2], [4, 7, 9, 6, 2, 5, 1, 8, 3], [3, 8, 4, 5, 6, 1, 9, 2, 7], [9, 5, 7, 4, 3, 2, 6, 1, 8], [2, 6, 1, 7, 8, 9, 3, 5, 4], [6, 4, 5, 8, 1, 7, 2, 3, 9], [1, 9, 8, 2, 4, 3, 7, 6, 5], [7, 2, 3, 9, 5, 6, 8, 4, 1]]
42
39
0.481481
[5, 3, 3, 4, 5, 6, 3, 4, 6]
[4, 5, 5, 5, 4, 6, 2, 4, 4]
7
13
0.47619
false
0
42
medium
[[4, 8, 0, 0, 6, 0, 0, 0, 1], [1, 0, 3, 0, 0, 8, 5, 2, 6], [0, 6, 5, 7, 0, 0, 0, 8, 0], [0, 5, 8, 2, 0, 0, 0, 1, 0], [0, 0, 4, 0, 8, 0, 3, 0, 0], [0, 2, 1, 6, 7, 9, 0, 0, 5], [0, 0, 6, 0, 2, 3, 9, 0, 7], [5, 1, 0, 9, 4, 6, 0, 0, 8], [0, 0, 9, 8, 0, 0, 0, 0, 0]]
[[4, 8, 2, 3, 6, 5, 7, 9, 1], [1, 7, 3, 4, 9, 8, 5, 2, 6], [9, 6, 5, 7, 1, 2, 4, 8, 3], [7, 5, 8, 2, 3, 4, 6, 1, 9], [6, 9, 4, 5, 8, 1, 3, 7, 2], [3, 2, 1, 6, 7, 9, 8, 4, 5], [8, 4, 6, 1, 2, 3, 9, 5, 7], [5, 1, 7, 9, 4, 6, 2, 3, 8], [2, 3, 9, 8, 5, 7, 1, 6, 4]]
41
40
0.493827
[4, 6, 4, 4, 3, 6, 5, 6, 2]
[3, 5, 7, 5, 5, 4, 3, 3, 5]
12
11
0.560976
false
0
41
medium
[[0, 3, 0, 0, 7, 4, 0, 9, 6], [6, 0, 0, 3, 9, 8, 7, 0, 0], [0, 0, 8, 0, 6, 1, 3, 4, 0], [0, 5, 3, 0, 0, 7, 0, 0, 9], [4, 0, 0, 0, 5, 9, 0, 7, 0], [0, 9, 6, 0, 0, 2, 0, 8, 4], [0, 0, 0, 0, 2, 3, 6, 0, 0], [3, 1, 0, 0, 4, 0, 0, 0, 0], [8, 6, 2, 0, 0, 0, 4, 3, 7]]
[[1, 3, 5, 2, 7, 4, 8, 9, 6], [6, 2, 4, 3, 9, 8, 7, 5, 1], [9, 7, 8, 5, 6, 1, 3, 4, 2], [2, 5, 3, 4, 8, 7, 1, 6, 9], [4, 8, 1, 6, 5, 9, 2, 7, 3], [7, 9, 6, 1, 3, 2, 5, 8, 4], [5, 4, 9, 7, 2, 3, 6, 1, 8], [3, 1, 7, 8, 4, 6, 9, 2, 5], [8, 6, 2, 9, 1, 5, 4, 3, 7]]
41
40
0.493827
[5, 5, 5, 4, 4, 5, 3, 3, 6]
[4, 5, 4, 1, 6, 7, 4, 5, 4]
4
14
0.439024
false
0
41
medium
[[0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 3, 0, 0, 6, 0, 9, 7], [0, 6, 1, 0, 3, 7, 5, 0, 0], [0, 0, 0, 7, 0, 9, 8, 0, 0], [8, 3, 0, 0, 4, 0, 0, 0, 1], [0, 0, 0, 0, 2, 0, 0, 0, 6], [7, 4, 0, 0, 0, 8, 6, 1, 0], [3, 0, 0, 0, 6, 0, 0, 5, 2], [0, 0, 0, 9, 0, 0, 0, 0, 3]]
[[2, 8, 7, 5, 9, 1, 3, 6, 4], [4, 5, 3, 2, 8, 6, 1, 9, 7], [9, 6, 1, 4, 3, 7, 5, 2, 8], [6, 2, 4, 7, 1, 9, 8, 3, 5], [8, 3, 9, 6, 4, 5, 2, 7, 1], [1, 7, 5, 8, 2, 3, 9, 4, 6], [7, 4, 2, 3, 5, 8, 6, 1, 9], [3, 9, 8, 1, 6, 4, 7, 5, 2], [5, 1, 6, 9, 7, 2, 4, 8, 3]]
51
30
0.37037
[1, 4, 5, 3, 4, 2, 5, 4, 2]
[3, 3, 2, 2, 4, 5, 3, 3, 5]
4
14
0.352941
false
0
51
medium
[[0, 0, 1, 0, 0, 2, 0, 0, 3], [0, 0, 4, 0, 0, 0, 9, 0, 0], [2, 9, 6, 0, 1, 5, 0, 4, 8], [5, 6, 0, 0, 0, 8, 1, 9, 7], [0, 0, 9, 0, 0, 0, 0, 5, 4], [7, 0, 0, 9, 5, 0, 3, 0, 0], [4, 0, 0, 1, 8, 7, 6, 0, 0], [0, 1, 0, 5, 0, 0, 4, 0, 2], [9, 0, 0, 0, 2, 0, 0, 0, 5]]
[[8, 7, 1, 4, 9, 2, 5, 6, 3], [3, 5, 4, 8, 7, 6, 9, 2, 1], [2, 9, 6, 3, 1, 5, 7, 4, 8], [5, 6, 3, 2, 4, 8, 1, 9, 7], [1, 8, 9, 7, 6, 3, 2, 5, 4], [7, 4, 2, 9, 5, 1, 3, 8, 6], [4, 2, 5, 1, 8, 7, 6, 3, 9], [6, 1, 8, 5, 3, 9, 4, 7, 2], [9, 3, 7, 6, 2, 4, 8, 1, 5]]
44
37
0.45679
[3, 2, 7, 6, 3, 4, 5, 4, 3]
[5, 3, 4, 3, 4, 4, 5, 3, 6]
5
14
0.431818
false
0
44
medium
[[0, 0, 3, 0, 6, 0, 0, 0, 5], [7, 9, 2, 0, 5, 1, 4, 0, 0], [0, 0, 6, 2, 0, 0, 0, 0, 9], [2, 6, 8, 7, 1, 9, 0, 5, 4], [0, 3, 0, 0, 2, 6, 9, 7, 8], [0, 0, 0, 0, 0, 0, 6, 0, 1], [0, 5, 0, 1, 0, 3, 0, 9, 0], [0, 2, 9, 0, 0, 4, 0, 0, 0], [8, 0, 0, 0, 0, 2, 0, 0, 3]]
[[4, 8, 3, 9, 6, 7, 2, 1, 5], [7, 9, 2, 3, 5, 1, 4, 8, 6], [5, 1, 6, 2, 4, 8, 7, 3, 9], [2, 6, 8, 7, 1, 9, 3, 5, 4], [1, 3, 5, 4, 2, 6, 9, 7, 8], [9, 4, 7, 8, 3, 5, 6, 2, 1], [6, 5, 4, 1, 7, 3, 8, 9, 2], [3, 2, 9, 5, 8, 4, 1, 6, 7], [8, 7, 1, 6, 9, 2, 5, 4, 3]]
43
38
0.469136
[3, 6, 3, 8, 6, 2, 4, 3, 3]
[3, 5, 5, 3, 4, 6, 3, 3, 6]
2
9
0.255814
true
2
54
hard
[[0, 4, 9, 0, 0, 3, 8, 2, 5], [5, 0, 0, 7, 0, 9, 1, 0, 6], [3, 6, 1, 0, 2, 5, 0, 0, 7], [6, 0, 0, 5, 9, 0, 0, 8, 4], [8, 0, 0, 0, 0, 4, 3, 0, 9], [1, 9, 0, 3, 7, 0, 5, 6, 2], [0, 0, 8, 0, 0, 0, 6, 9, 1], [4, 1, 5, 9, 8, 6, 2, 7, 3], [9, 7, 0, 1, 3, 0, 4, 5, 0]]
[[7, 4, 9, 6, 1, 3, 8, 2, 5], [5, 8, 2, 7, 4, 9, 1, 3, 6], [3, 6, 1, 8, 2, 5, 9, 4, 7], [6, 2, 3, 5, 9, 1, 7, 8, 4], [8, 5, 7, 2, 6, 4, 3, 1, 9], [1, 9, 4, 3, 7, 8, 5, 6, 2], [2, 3, 8, 4, 5, 7, 6, 9, 1], [4, 1, 5, 9, 8, 6, 2, 7, 3], [9, 7, 6, 1, 3, 2, 4, 5, 8]]
29
52
0.641975
[6, 5, 6, 5, 4, 7, 4, 9, 6]
[7, 5, 4, 5, 5, 5, 7, 6, 8]
13
12
0.862069
false
0
29
easy
[[0, 2, 6, 8, 5, 3, 7, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 3, 0, 4, 0, 0, 9, 6], [2, 4, 0, 0, 7, 6, 8, 1, 0], [3, 1, 9, 0, 0, 5, 4, 6, 0], [6, 0, 0, 1, 3, 4, 0, 2, 0], [0, 6, 4, 3, 9, 7, 1, 8, 0], [7, 0, 8, 5, 0, 2, 6, 0, 4], [0, 0, 2, 0, 6, 0, 0, 7, 9]]
[[9, 2, 6, 8, 5, 3, 7, 4, 1], [4, 7, 1, 6, 2, 9, 3, 5, 8], [8, 5, 3, 7, 4, 1, 2, 9, 6], [2, 4, 5, 9, 7, 6, 8, 1, 3], [3, 1, 9, 2, 8, 5, 4, 6, 7], [6, 8, 7, 1, 3, 4, 9, 2, 5], [5, 6, 4, 3, 9, 7, 1, 8, 2], [7, 9, 8, 5, 1, 2, 6, 3, 4], [1, 3, 2, 4, 6, 8, 5, 7, 9]]
36
45
0.555556
[6, 0, 5, 6, 6, 5, 7, 6, 4]
[4, 5, 6, 4, 6, 6, 5, 6, 3]
13
16
0.805556
false
0
36
easy
[[4, 6, 8, 0, 5, 0, 7, 0, 2], [2, 7, 3, 1, 4, 0, 5, 0, 9], [0, 0, 9, 0, 0, 2, 4, 6, 3], [0, 0, 1, 8, 6, 0, 0, 0, 0], [0, 9, 0, 0, 3, 0, 0, 0, 1], [0, 3, 0, 0, 0, 0, 6, 0, 0], [9, 8, 0, 5, 0, 1, 2, 0, 0], [3, 2, 7, 6, 0, 0, 1, 0, 4], [0, 1, 6, 3, 2, 4, 9, 0, 8]]
[[4, 6, 8, 9, 5, 3, 7, 1, 2], [2, 7, 3, 1, 4, 6, 5, 8, 9], [1, 5, 9, 7, 8, 2, 4, 6, 3], [7, 4, 1, 8, 6, 9, 3, 2, 5], [6, 9, 5, 2, 3, 7, 8, 4, 1], [8, 3, 2, 4, 1, 5, 6, 9, 7], [9, 8, 4, 5, 7, 1, 2, 3, 6], [3, 2, 7, 6, 9, 8, 1, 5, 4], [5, 1, 6, 3, 2, 4, 9, 7, 8]]
37
44
0.54321
[6, 7, 5, 3, 3, 2, 5, 6, 7]
[4, 7, 6, 5, 5, 3, 7, 1, 6]
11
11
0.594595
false
0
37
medium
[[0, 0, 0, 0, 0, 9, 0, 3, 8], [0, 0, 0, 0, 0, 5, 0, 0, 4], [3, 5, 0, 7, 0, 0, 0, 9, 1], [0, 0, 0, 4, 0, 0, 0, 0, 0], [4, 0, 7, 5, 0, 0, 0, 2, 0], [0, 6, 0, 0, 2, 0, 8, 0, 5], [5, 0, 0, 9, 0, 0, 0, 0, 6], [8, 4, 0, 0, 0, 1, 0, 7, 0], [0, 3, 6, 0, 4, 0, 0, 0, 9]]
[[6, 7, 4, 2, 1, 9, 5, 3, 8], [1, 9, 2, 3, 8, 5, 7, 6, 4], [3, 5, 8, 7, 6, 4, 2, 9, 1], [2, 8, 5, 4, 3, 6, 9, 1, 7], [4, 1, 7, 5, 9, 8, 6, 2, 3], [9, 6, 3, 1, 2, 7, 8, 4, 5], [5, 2, 1, 9, 7, 3, 4, 8, 6], [8, 4, 9, 6, 5, 1, 3, 7, 2], [7, 3, 6, 8, 4, 2, 1, 5, 9]]
51
30
0.37037
[3, 2, 5, 1, 4, 4, 3, 4, 4]
[4, 4, 2, 4, 2, 3, 1, 4, 6]
2
12
0.27451
true
3
60
hard
[[6, 0, 4, 3, 0, 0, 0, 9, 0], [2, 1, 0, 0, 7, 9, 0, 6, 4], [9, 0, 5, 0, 1, 4, 2, 7, 0], [4, 5, 0, 0, 0, 3, 9, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 3, 2, 7, 0, 0, 0, 8, 0], [8, 9, 0, 2, 0, 6, 0, 1, 0], [5, 0, 6, 0, 0, 0, 0, 0, 0]]
[[6, 7, 4, 3, 8, 2, 5, 9, 1], [2, 1, 3, 5, 7, 9, 8, 6, 4], [9, 8, 5, 6, 1, 4, 2, 7, 3], [4, 5, 1, 8, 6, 3, 9, 2, 7], [7, 6, 9, 4, 2, 1, 3, 5, 8], [3, 2, 8, 9, 5, 7, 1, 4, 6], [1, 3, 2, 7, 4, 5, 6, 8, 9], [8, 9, 7, 2, 3, 6, 4, 1, 5], [5, 4, 6, 1, 9, 8, 7, 3, 2]]
48
33
0.407407
[4, 6, 6, 4, 1, 1, 4, 5, 2]
[6, 4, 5, 3, 2, 5, 2, 5, 1]
7
8
0.3125
false
0
48
medium
[[5, 9, 1, 3, 0, 0, 2, 0, 0], [0, 0, 4, 0, 6, 2, 0, 3, 1], [0, 0, 0, 9, 1, 7, 5, 0, 8], [0, 6, 3, 0, 0, 5, 0, 8, 0], [1, 0, 0, 4, 8, 0, 0, 0, 3], [0, 5, 7, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 9, 0, 6, 1, 0], [0, 4, 8, 2, 7, 0, 3, 9, 5], [0, 0, 0, 0, 5, 0, 8, 7, 0]]
[[5, 9, 1, 3, 4, 8, 2, 6, 7], [7, 8, 4, 5, 6, 2, 9, 3, 1], [2, 3, 6, 9, 1, 7, 5, 4, 8], [4, 6, 3, 7, 2, 5, 1, 8, 9], [1, 2, 9, 4, 8, 6, 7, 5, 3], [8, 5, 7, 1, 3, 9, 4, 2, 6], [3, 7, 5, 8, 9, 4, 6, 1, 2], [6, 4, 8, 2, 7, 1, 3, 9, 5], [9, 1, 2, 6, 5, 3, 8, 7, 4]]
43
38
0.469136
[5, 5, 5, 4, 4, 2, 3, 7, 3]
[2, 4, 5, 4, 6, 3, 5, 5, 4]
5
14
0.44186
false
0
43
medium
[[3, 0, 9, 0, 0, 0, 0, 5, 0], [0, 0, 7, 0, 0, 3, 0, 6, 0], [0, 8, 1, 4, 0, 7, 2, 0, 0], [1, 0, 8, 9, 0, 0, 0, 2, 0], [7, 0, 0, 3, 4, 0, 9, 1, 0], [9, 3, 2, 0, 6, 8, 0, 0, 0], [0, 0, 4, 0, 8, 0, 0, 9, 0], [5, 0, 6, 7, 0, 4, 0, 0, 0], [0, 0, 3, 0, 2, 0, 6, 0, 7]]
[[3, 2, 9, 8, 1, 6, 7, 5, 4], [4, 5, 7, 2, 9, 3, 8, 6, 1], [6, 8, 1, 4, 5, 7, 2, 3, 9], [1, 4, 8, 9, 7, 5, 3, 2, 6], [7, 6, 5, 3, 4, 2, 9, 1, 8], [9, 3, 2, 1, 6, 8, 4, 7, 5], [2, 7, 4, 6, 8, 1, 5, 9, 3], [5, 9, 6, 7, 3, 4, 1, 8, 2], [8, 1, 3, 5, 2, 9, 6, 4, 7]]
45
36
0.444444
[3, 3, 5, 4, 5, 5, 3, 4, 4]
[5, 2, 8, 4, 4, 4, 3, 5, 1]
7
14
0.466667
false
0
45
medium
[[4, 0, 6, 1, 5, 0, 0, 8, 3], [7, 0, 3, 2, 0, 0, 0, 0, 0], [5, 0, 8, 0, 0, 3, 2, 0, 0], [6, 3, 0, 7, 0, 0, 5, 0, 0], [1, 5, 7, 0, 0, 9, 0, 2, 4], [9, 8, 2, 5, 0, 0, 3, 0, 7], [0, 4, 9, 6, 8, 0, 7, 0, 2], [0, 0, 0, 9, 0, 0, 0, 3, 0], [0, 7, 1, 3, 0, 0, 0, 0, 9]]
[[4, 2, 6, 1, 5, 7, 9, 8, 3], [7, 9, 3, 2, 6, 8, 1, 4, 5], [5, 1, 8, 4, 9, 3, 2, 7, 6], [6, 3, 4, 7, 1, 2, 5, 9, 8], [1, 5, 7, 8, 3, 9, 6, 2, 4], [9, 8, 2, 5, 4, 6, 3, 1, 7], [3, 4, 9, 6, 8, 1, 7, 5, 2], [2, 6, 5, 9, 7, 4, 8, 3, 1], [8, 7, 1, 3, 2, 5, 4, 6, 9]]
40
41
0.506173
[6, 3, 4, 4, 6, 6, 6, 2, 4]
[6, 5, 7, 7, 2, 2, 4, 3, 5]
7
6
0.325
false
0
40
medium
[[1, 0, 0, 0, 0, 0, 8, 0, 9], [9, 5, 0, 0, 1, 8, 0, 0, 0], [3, 0, 0, 0, 0, 0, 0, 7, 6], [5, 8, 0, 9, 0, 6, 0, 0, 0], [0, 0, 3, 5, 0, 0, 0, 0, 0], [2, 0, 4, 7, 0, 0, 5, 6, 0], [0, 0, 0, 0, 0, 0, 0, 8, 1], [6, 0, 0, 0, 0, 4, 0, 0, 3], [8, 3, 0, 1, 6, 9, 0, 4, 5]]
[[1, 4, 6, 3, 2, 7, 8, 5, 9], [9, 5, 7, 6, 1, 8, 4, 3, 2], [3, 2, 8, 4, 9, 5, 1, 7, 6], [5, 8, 1, 9, 4, 6, 3, 2, 7], [7, 6, 3, 5, 8, 2, 9, 1, 4], [2, 9, 4, 7, 3, 1, 5, 6, 8], [4, 7, 9, 2, 5, 3, 6, 8, 1], [6, 1, 5, 8, 7, 4, 2, 9, 3], [8, 3, 2, 1, 6, 9, 7, 4, 5]]
48
33
0.407407
[3, 4, 3, 4, 2, 5, 2, 3, 7]
[7, 3, 2, 4, 2, 4, 2, 4, 5]
2
10
0.25
false
0
48
medium
[[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 4, 5, 0, 0, 9, 7, 0], [2, 9, 1, 0, 0, 0, 0, 0, 8], [8, 0, 9, 1, 0, 0, 5, 0, 0], [7, 5, 3, 9, 4, 2, 0, 6, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 7, 1, 4, 0, 0, 0], [3, 7, 0, 0, 8, 0, 4, 0, 0], [1, 0, 0, 0, 3, 5, 7, 0, 0]]
[[5, 3, 7, 8, 9, 6, 1, 4, 2], [6, 8, 4, 5, 2, 1, 9, 7, 3], [2, 9, 1, 4, 7, 3, 6, 5, 8], [8, 2, 9, 1, 6, 7, 5, 3, 4], [7, 5, 3, 9, 4, 2, 8, 6, 1], [4, 1, 6, 3, 5, 8, 2, 9, 7], [9, 6, 2, 7, 1, 4, 3, 8, 5], [3, 7, 5, 2, 8, 9, 4, 1, 6], [1, 4, 8, 6, 3, 5, 7, 2, 9]]
48
33
0.407407
[0, 5, 4, 4, 7, 1, 4, 4, 4]
[5, 5, 5, 4, 4, 3, 4, 2, 1]
4
12
0.333333
false
0
48
medium
[[2, 4, 3, 6, 0, 0, 9, 5, 0], [0, 0, 5, 2, 0, 1, 0, 0, 0], [7, 0, 6, 9, 5, 3, 8, 0, 2], [6, 5, 7, 0, 0, 9, 0, 8, 0], [8, 0, 4, 5, 0, 7, 0, 2, 9], [0, 0, 9, 0, 3, 0, 0, 6, 0], [5, 0, 1, 4, 0, 2, 7, 0, 0], [0, 0, 8, 0, 1, 6, 0, 0, 5], [0, 9, 2, 7, 8, 5, 0, 0, 4]]
[[2, 4, 3, 6, 7, 8, 9, 5, 1], [9, 8, 5, 2, 4, 1, 3, 7, 6], [7, 1, 6, 9, 5, 3, 8, 4, 2], [6, 5, 7, 1, 2, 9, 4, 8, 3], [8, 3, 4, 5, 6, 7, 1, 2, 9], [1, 2, 9, 8, 3, 4, 5, 6, 7], [5, 6, 1, 4, 9, 2, 7, 3, 8], [4, 7, 8, 3, 1, 6, 2, 9, 5], [3, 9, 2, 7, 8, 5, 6, 1, 4]]
36
45
0.555556
[6, 3, 7, 5, 6, 3, 5, 4, 6]
[5, 3, 9, 6, 4, 7, 3, 4, 4]
11
18
0.805556
false
0
36
easy
[[0, 0, 1, 0, 9, 0, 0, 0, 0], [0, 0, 9, 0, 8, 0, 0, 5, 4], [0, 8, 0, 5, 7, 6, 9, 0, 0], [0, 7, 6, 9, 2, 5, 3, 0, 1], [1, 3, 0, 0, 0, 0, 0, 0, 7], [4, 9, 5, 7, 0, 0, 0, 8, 0], [6, 0, 8, 2, 5, 0, 0, 7, 0], [0, 0, 0, 0, 0, 0, 0, 0, 6], [9, 4, 3, 6, 0, 7, 0, 2, 0]]
[[7, 5, 1, 3, 9, 4, 2, 6, 8], [3, 6, 9, 1, 8, 2, 7, 5, 4], [2, 8, 4, 5, 7, 6, 9, 1, 3], [8, 7, 6, 9, 2, 5, 3, 4, 1], [1, 3, 2, 4, 6, 8, 5, 9, 7], [4, 9, 5, 7, 3, 1, 6, 8, 2], [6, 1, 8, 2, 5, 3, 4, 7, 9], [5, 2, 7, 8, 4, 9, 1, 3, 6], [9, 4, 3, 6, 1, 7, 8, 2, 5]]
43
38
0.469136
[2, 4, 5, 7, 3, 5, 5, 1, 6]
[4, 5, 6, 5, 5, 3, 2, 4, 4]
6
7
0.302326
false
0
43
medium
[[0, 3, 0, 8, 1, 0, 0, 7, 0], [0, 0, 0, 0, 6, 7, 1, 0, 5], [7, 1, 0, 0, 0, 3, 0, 8, 4], [0, 0, 2, 0, 8, 5, 7, 9, 0], [8, 0, 7, 4, 3, 6, 0, 0, 0], [6, 0, 0, 7, 9, 2, 0, 4, 0], [1, 6, 0, 3, 2, 9, 0, 0, 0], [9, 2, 0, 5, 7, 1, 8, 6, 0], [5, 7, 3, 0, 4, 8, 9, 1, 0]]
[[2, 3, 5, 8, 1, 4, 6, 7, 9], [4, 8, 9, 2, 6, 7, 1, 3, 5], [7, 1, 6, 9, 5, 3, 2, 8, 4], [3, 4, 2, 1, 8, 5, 7, 9, 6], [8, 9, 7, 4, 3, 6, 5, 2, 1], [6, 5, 1, 7, 9, 2, 3, 4, 8], [1, 6, 8, 3, 2, 9, 4, 5, 7], [9, 2, 4, 5, 7, 1, 8, 6, 3], [5, 7, 3, 6, 4, 8, 9, 1, 2]]
34
47
0.580247
[4, 4, 5, 5, 5, 5, 5, 7, 7]
[6, 5, 3, 5, 8, 8, 4, 6, 2]
11
13
0.705882
false
0
34
easy
[[6, 9, 0, 5, 3, 8, 0, 7, 2], [0, 8, 0, 0, 0, 0, 6, 0, 0], [0, 3, 0, 9, 0, 7, 0, 8, 5], [0, 4, 0, 0, 0, 0, 9, 0, 0], [0, 0, 6, 0, 2, 9, 0, 5, 1], [0, 0, 0, 7, 5, 1, 8, 0, 0], [9, 0, 4, 0, 0, 0, 0, 1, 0], [0, 0, 8, 6, 1, 0, 0, 9, 0], [0, 0, 3, 0, 0, 0, 7, 4, 0]]
[[6, 9, 1, 5, 3, 8, 4, 7, 2], [5, 8, 7, 1, 4, 2, 6, 3, 9], [4, 3, 2, 9, 6, 7, 1, 8, 5], [1, 4, 5, 3, 8, 6, 9, 2, 7], [8, 7, 6, 4, 2, 9, 3, 5, 1], [3, 2, 9, 7, 5, 1, 8, 6, 4], [9, 6, 4, 2, 7, 3, 5, 1, 8], [7, 5, 8, 6, 1, 4, 2, 9, 3], [2, 1, 3, 8, 9, 5, 7, 4, 6]]
46
35
0.432099
[7, 2, 5, 2, 5, 4, 3, 4, 3]
[2, 4, 4, 4, 4, 4, 4, 6, 3]
6
13
0.413043
false
0
46
medium
[[1, 0, 0, 5, 0, 0, 0, 0, 7], [0, 9, 0, 8, 3, 0, 0, 0, 4], [8, 0, 0, 2, 0, 0, 1, 0, 0], [4, 0, 0, 0, 1, 0, 0, 7, 2], [0, 0, 0, 0, 4, 8, 3, 5, 1], [0, 0, 1, 3, 0, 2, 0, 0, 6], [2, 0, 4, 9, 0, 0, 7, 1, 5], [3, 1, 5, 0, 0, 7, 6, 9, 0], [0, 0, 0, 0, 0, 0, 0, 2, 3]]
[[1, 4, 3, 5, 6, 9, 2, 8, 7], [7, 9, 2, 8, 3, 1, 5, 6, 4], [8, 5, 6, 2, 7, 4, 1, 3, 9], [4, 3, 8, 6, 1, 5, 9, 7, 2], [6, 2, 9, 7, 4, 8, 3, 5, 1], [5, 7, 1, 3, 9, 2, 8, 4, 6], [2, 6, 4, 9, 8, 3, 7, 1, 5], [3, 1, 5, 4, 2, 7, 6, 9, 8], [9, 8, 7, 1, 5, 6, 4, 2, 3]]
44
37
0.45679
[3, 4, 3, 4, 5, 4, 6, 6, 2]
[5, 2, 3, 5, 3, 3, 4, 5, 7]
5
10
0.340909
false
0
44
medium
[[0, 7, 2, 8, 3, 4, 0, 6, 9], [0, 4, 5, 0, 2, 0, 0, 0, 8], [0, 0, 0, 0, 7, 5, 0, 2, 0], [0, 1, 4, 0, 8, 0, 0, 0, 0], [8, 6, 7, 0, 4, 0, 0, 0, 3], [2, 0, 0, 3, 0, 0, 8, 0, 0], [5, 2, 3, 4, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 3, 0, 8, 0], [4, 8, 6, 0, 0, 7, 3, 1, 0]]
[[1, 7, 2, 8, 3, 4, 5, 6, 9], [9, 4, 5, 1, 2, 6, 7, 3, 8], [6, 3, 8, 9, 7, 5, 4, 2, 1], [3, 1, 4, 7, 8, 9, 6, 5, 2], [8, 6, 7, 5, 4, 2, 1, 9, 3], [2, 5, 9, 3, 6, 1, 8, 4, 7], [5, 2, 3, 4, 1, 8, 9, 7, 6], [7, 9, 1, 6, 5, 3, 2, 8, 4], [4, 8, 6, 2, 9, 7, 3, 1, 5]]
43
38
0.469136
[7, 4, 3, 3, 5, 3, 5, 2, 6]
[4, 6, 6, 3, 5, 5, 2, 4, 3]
3
10
0.302326
true
4
82
hard
[[9, 0, 7, 2, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 6], [0, 1, 0, 0, 7, 0, 2, 5, 0], [8, 2, 5, 0, 1, 9, 0, 6, 4], [7, 4, 9, 0, 3, 2, 8, 0, 0], [0, 0, 3, 5, 0, 8, 0, 9, 0], [3, 0, 2, 0, 0, 0, 5, 0, 1], [6, 8, 0, 3, 0, 0, 9, 0, 7], [5, 0, 0, 0, 2, 7, 6, 3, 8]]
[[9, 5, 7, 2, 6, 1, 4, 8, 3], [2, 3, 8, 4, 9, 5, 1, 7, 6], [4, 1, 6, 8, 7, 3, 2, 5, 9], [8, 2, 5, 7, 1, 9, 3, 6, 4], [7, 4, 9, 6, 3, 2, 8, 1, 5], [1, 6, 3, 5, 4, 8, 7, 9, 2], [3, 7, 2, 9, 8, 6, 5, 4, 1], [6, 8, 1, 3, 5, 4, 9, 2, 7], [5, 9, 4, 1, 2, 7, 6, 3, 8]]
40
41
0.506173
[4, 1, 4, 7, 6, 4, 4, 5, 6]
[6, 4, 5, 3, 4, 5, 5, 4, 5]
11
11
0.55
false
0
40
medium
[[0, 0, 8, 0, 5, 2, 0, 7, 0], [0, 9, 1, 0, 4, 0, 0, 0, 6], [7, 0, 5, 8, 0, 0, 4, 0, 0], [5, 7, 0, 0, 8, 3, 2, 0, 4], [6, 0, 0, 0, 0, 0, 0, 1, 7], [8, 1, 0, 7, 6, 4, 0, 3, 5], [1, 5, 6, 4, 0, 0, 3, 2, 0], [0, 2, 4, 0, 3, 0, 7, 0, 0], [3, 8, 7, 0, 9, 5, 6, 4, 1]]
[[4, 6, 8, 9, 5, 2, 1, 7, 3], [2, 9, 1, 3, 4, 7, 5, 8, 6], [7, 3, 5, 8, 1, 6, 4, 9, 2], [5, 7, 9, 1, 8, 3, 2, 6, 4], [6, 4, 3, 5, 2, 9, 8, 1, 7], [8, 1, 2, 7, 6, 4, 9, 3, 5], [1, 5, 6, 4, 7, 8, 3, 2, 9], [9, 2, 4, 6, 3, 1, 7, 5, 8], [3, 8, 7, 2, 9, 5, 6, 4, 1]]
35
46
0.567901
[4, 4, 4, 6, 3, 7, 6, 4, 8]
[6, 6, 6, 3, 6, 4, 5, 5, 5]
13
12
0.714286
false
0
35
easy
[[0, 3, 7, 6, 0, 4, 2, 5, 0], [2, 0, 0, 3, 0, 0, 1, 0, 0], [0, 0, 9, 2, 5, 0, 0, 0, 8], [0, 0, 0, 7, 0, 0, 0, 9, 0], [9, 0, 2, 0, 0, 5, 0, 3, 1], [7, 4, 0, 1, 3, 0, 0, 0, 6], [0, 9, 0, 0, 7, 0, 6, 0, 4], [0, 0, 1, 0, 6, 0, 0, 0, 0], [5, 2, 6, 8, 0, 0, 9, 0, 3]]
[[8, 3, 7, 6, 1, 4, 2, 5, 9], [2, 5, 4, 3, 9, 8, 1, 6, 7], [6, 1, 9, 2, 5, 7, 3, 4, 8], [1, 8, 3, 7, 2, 6, 4, 9, 5], [9, 6, 2, 4, 8, 5, 7, 3, 1], [7, 4, 5, 1, 3, 9, 8, 2, 6], [3, 9, 8, 5, 7, 2, 6, 1, 4], [4, 7, 1, 9, 6, 3, 5, 8, 2], [5, 2, 6, 8, 4, 1, 9, 7, 3]]
44
37
0.45679
[6, 3, 4, 2, 5, 5, 4, 2, 6]
[4, 4, 5, 6, 4, 2, 4, 3, 5]
4
12
0.363636
false
0
44
medium
[[0, 0, 6, 0, 0, 7, 2, 0, 8], [3, 1, 0, 0, 8, 2, 0, 7, 6], [7, 0, 0, 0, 6, 1, 4, 3, 0], [0, 0, 9, 0, 1, 8, 5, 0, 0], [1, 0, 5, 4, 7, 0, 0, 6, 0], [8, 0, 0, 2, 0, 3, 0, 0, 4], [0, 0, 0, 0, 3, 0, 6, 8, 0], [6, 7, 8, 0, 9, 5, 3, 0, 0], [0, 0, 0, 8, 2, 0, 7, 5, 0]]
[[5, 9, 6, 3, 4, 7, 2, 1, 8], [3, 1, 4, 5, 8, 2, 9, 7, 6], [7, 8, 2, 9, 6, 1, 4, 3, 5], [4, 3, 9, 6, 1, 8, 5, 2, 7], [1, 2, 5, 4, 7, 9, 8, 6, 3], [8, 6, 7, 2, 5, 3, 1, 9, 4], [2, 5, 1, 7, 3, 4, 6, 8, 9], [6, 7, 8, 1, 9, 5, 3, 4, 2], [9, 4, 3, 8, 2, 6, 7, 5, 1]]
40
41
0.506173
[4, 6, 5, 4, 5, 4, 3, 6, 4]
[5, 2, 4, 3, 7, 6, 6, 5, 3]
11
13
0.6
false
0
40
medium
[[0, 0, 0, 0, 0, 0, 8, 4, 0], [0, 9, 0, 2, 0, 7, 1, 0, 0], [0, 1, 7, 5, 6, 8, 9, 0, 3], [7, 0, 0, 0, 0, 0, 6, 0, 0], [0, 4, 0, 6, 0, 2, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 0, 2], [0, 3, 0, 8, 5, 0, 2, 7, 1], [9, 0, 0, 0, 3, 6, 5, 0, 0], [0, 0, 1, 7, 0, 0, 0, 0, 6]]
[[2, 5, 6, 3, 9, 1, 8, 4, 7], [3, 9, 8, 2, 4, 7, 1, 6, 5], [4, 1, 7, 5, 6, 8, 9, 2, 3], [7, 2, 9, 4, 1, 3, 6, 5, 8], [1, 4, 5, 6, 8, 2, 7, 3, 9], [8, 6, 3, 9, 7, 5, 4, 1, 2], [6, 3, 4, 8, 5, 9, 2, 7, 1], [9, 7, 2, 1, 3, 6, 5, 8, 4], [5, 8, 1, 7, 2, 4, 3, 9, 6]]
48
33
0.407407
[2, 4, 7, 2, 3, 2, 6, 4, 3]
[2, 4, 3, 5, 3, 4, 6, 2, 4]
4
9
0.270833
false
0
48
medium
[[0, 0, 0, 0, 0, 0, 0, 4, 8], [3, 0, 0, 1, 0, 0, 7, 2, 0], [8, 4, 0, 0, 0, 0, 0, 0, 3], [0, 0, 3, 0, 0, 2, 0, 0, 6], [0, 1, 7, 0, 6, 0, 2, 0, 0], [6, 2, 0, 5, 8, 0, 3, 0, 4], [0, 0, 0, 0, 1, 3, 4, 0, 2], [1, 0, 0, 6, 0, 0, 8, 9, 0], [0, 0, 4, 8, 5, 7, 0, 0, 1]]
[[9, 7, 1, 2, 3, 6, 5, 4, 8], [3, 5, 6, 1, 4, 8, 7, 2, 9], [8, 4, 2, 7, 9, 5, 1, 6, 3], [5, 8, 3, 4, 7, 2, 9, 1, 6], [4, 1, 7, 3, 6, 9, 2, 8, 5], [6, 2, 9, 5, 8, 1, 3, 7, 4], [7, 6, 8, 9, 1, 3, 4, 5, 2], [1, 3, 5, 6, 2, 4, 8, 9, 7], [2, 9, 4, 8, 5, 7, 6, 3, 1]]
46
35
0.432099
[2, 4, 3, 3, 4, 6, 4, 4, 5]
[4, 3, 3, 4, 4, 3, 5, 3, 6]
4
13
0.369565
false
0
46
medium
[[7, 6, 0, 0, 0, 9, 0, 0, 1], [0, 2, 4, 8, 1, 0, 0, 7, 6], [0, 0, 1, 7, 0, 6, 9, 0, 2], [6, 0, 0, 9, 0, 5, 0, 1, 8], [0, 0, 5, 0, 3, 0, 6, 0, 7], [8, 0, 0, 0, 6, 0, 2, 9, 5], [2, 0, 0, 6, 0, 0, 7, 0, 0], [4, 0, 0, 3, 5, 7, 0, 0, 9], [5, 3, 0, 0, 9, 0, 8, 0, 0]]
[[7, 6, 8, 5, 2, 9, 4, 3, 1], [9, 2, 4, 8, 1, 3, 5, 7, 6], [3, 5, 1, 7, 4, 6, 9, 8, 2], [6, 4, 2, 9, 7, 5, 3, 1, 8], [1, 9, 5, 2, 3, 8, 6, 4, 7], [8, 7, 3, 4, 6, 1, 2, 9, 5], [2, 1, 9, 6, 8, 4, 7, 5, 3], [4, 8, 6, 3, 5, 7, 1, 2, 9], [5, 3, 7, 1, 9, 2, 8, 6, 4]]
40
41
0.506173
[4, 6, 5, 5, 4, 5, 3, 5, 4]
[6, 3, 3, 5, 5, 4, 5, 3, 7]
6
16
0.55
false
0
40
medium
[[2, 1, 0, 0, 8, 9, 3, 5, 7], [0, 9, 0, 0, 0, 2, 8, 0, 0], [0, 0, 4, 7, 0, 0, 9, 1, 2], [3, 4, 1, 5, 0, 6, 2, 0, 0], [5, 0, 9, 0, 0, 4, 0, 0, 1], [6, 0, 0, 8, 0, 0, 4, 3, 0], [0, 7, 0, 3, 2, 5, 0, 6, 0], [1, 0, 0, 0, 0, 7, 5, 8, 9], [0, 6, 5, 9, 1, 0, 0, 2, 0]]
[[2, 1, 6, 4, 8, 9, 3, 5, 7], [7, 9, 3, 1, 5, 2, 8, 4, 6], [8, 5, 4, 7, 6, 3, 9, 1, 2], [3, 4, 1, 5, 7, 6, 2, 9, 8], [5, 8, 9, 2, 3, 4, 6, 7, 1], [6, 2, 7, 8, 9, 1, 4, 3, 5], [9, 7, 8, 3, 2, 5, 1, 6, 4], [1, 3, 2, 6, 4, 7, 5, 8, 9], [4, 6, 5, 9, 1, 8, 7, 2, 3]]
37
44
0.54321
[7, 3, 5, 6, 4, 4, 5, 5, 5]
[5, 5, 4, 5, 3, 6, 6, 6, 4]
16
14
0.810811
false
0
37
easy
[[5, 8, 0, 0, 6, 2, 0, 4, 1], [0, 6, 0, 9, 0, 1, 0, 0, 0], [0, 0, 9, 0, 0, 0, 6, 0, 0], [0, 0, 6, 1, 0, 7, 8, 3, 9], [7, 2, 0, 0, 0, 8, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 6], [0, 0, 0, 7, 0, 5, 0, 0, 0], [0, 7, 5, 4, 0, 6, 0, 0, 3], [6, 4, 8, 0, 3, 9, 1, 5, 0]]
[[5, 8, 7, 3, 6, 2, 9, 4, 1], [2, 6, 4, 9, 7, 1, 3, 8, 5], [3, 1, 9, 8, 5, 4, 6, 7, 2], [4, 5, 6, 1, 2, 7, 8, 3, 9], [7, 2, 3, 6, 9, 8, 5, 1, 4], [8, 9, 1, 5, 4, 3, 7, 2, 6], [9, 3, 2, 7, 1, 5, 4, 6, 8], [1, 7, 5, 4, 8, 6, 2, 9, 3], [6, 4, 8, 2, 3, 9, 1, 5, 7]]
44
37
0.45679
[6, 3, 2, 6, 4, 2, 2, 5, 7]
[3, 5, 5, 4, 2, 7, 3, 4, 4]
4
8
0.272727
false
0
44
medium
[[1, 4, 0, 0, 0, 0, 2, 7, 0], [0, 7, 0, 0, 5, 4, 3, 1, 9], [5, 0, 0, 2, 0, 7, 0, 4, 8], [0, 0, 0, 0, 6, 8, 0, 2, 4], [0, 8, 0, 4, 0, 0, 1, 0, 7], [0, 2, 4, 7, 3, 0, 0, 0, 0], [0, 0, 7, 0, 0, 0, 8, 0, 2], [8, 0, 2, 0, 0, 3, 4, 0, 0], [4, 9, 1, 8, 0, 6, 0, 0, 0]]
[[1, 4, 6, 3, 8, 9, 2, 7, 5], [2, 7, 8, 6, 5, 4, 3, 1, 9], [5, 3, 9, 2, 1, 7, 6, 4, 8], [7, 1, 3, 5, 6, 8, 9, 2, 4], [6, 8, 5, 4, 9, 2, 1, 3, 7], [9, 2, 4, 7, 3, 1, 5, 8, 6], [3, 6, 7, 1, 4, 5, 8, 9, 2], [8, 5, 2, 9, 7, 3, 4, 6, 1], [4, 9, 1, 8, 2, 6, 7, 5, 3]]
42
39
0.481481
[4, 6, 5, 4, 4, 4, 3, 4, 5]
[4, 5, 4, 4, 3, 5, 5, 4, 5]
3
18
0.5
false
0
42
medium
[[0, 1, 0, 0, 0, 0, 6, 0, 8], [9, 0, 0, 0, 0, 0, 1, 0, 0], [7, 0, 6, 3, 0, 0, 0, 0, 0], [5, 0, 0, 7, 4, 3, 0, 0, 0], [0, 0, 0, 0, 0, 5, 4, 0, 0], [3, 4, 0, 0, 9, 1, 0, 7, 5], [0, 0, 3, 2, 0, 0, 0, 9, 1], [1, 0, 4, 0, 0, 0, 3, 0, 0], [0, 6, 9, 0, 0, 0, 0, 5, 0]]
[[4, 1, 2, 5, 7, 9, 6, 3, 8], [9, 3, 5, 4, 8, 6, 1, 2, 7], [7, 8, 6, 3, 1, 2, 5, 4, 9], [5, 2, 1, 7, 4, 3, 9, 8, 6], [6, 9, 7, 8, 2, 5, 4, 1, 3], [3, 4, 8, 6, 9, 1, 2, 7, 5], [8, 5, 3, 2, 6, 4, 7, 9, 1], [1, 7, 4, 9, 5, 8, 3, 6, 2], [2, 6, 9, 1, 3, 7, 8, 5, 4]]
51
30
0.37037
[3, 2, 3, 4, 2, 6, 4, 3, 3]
[5, 3, 4, 3, 2, 3, 4, 3, 3]
1
14
0.294118
false
0
51
medium
[[3, 8, 0, 5, 0, 0, 0, 9, 1], [6, 9, 7, 0, 1, 0, 0, 0, 5], [0, 0, 5, 0, 8, 0, 7, 0, 0], [4, 6, 0, 2, 0, 0, 0, 0, 3], [0, 7, 3, 0, 9, 8, 1, 4, 0], [8, 0, 0, 7, 4, 3, 0, 0, 0], [1, 4, 0, 0, 0, 0, 9, 0, 7], [7, 3, 0, 9, 0, 4, 0, 0, 0], [9, 5, 0, 0, 7, 0, 0, 3, 0]]
[[3, 8, 4, 5, 6, 7, 2, 9, 1], [6, 9, 7, 4, 1, 2, 3, 8, 5], [2, 1, 5, 3, 8, 9, 7, 6, 4], [4, 6, 9, 2, 5, 1, 8, 7, 3], [5, 7, 3, 6, 9, 8, 1, 4, 2], [8, 2, 1, 7, 4, 3, 6, 5, 9], [1, 4, 6, 8, 3, 5, 9, 2, 7], [7, 3, 8, 9, 2, 4, 5, 1, 6], [9, 5, 2, 1, 7, 6, 4, 3, 8]]
42
39
0.481481
[5, 5, 3, 4, 6, 4, 4, 4, 4]
[7, 7, 3, 4, 5, 3, 3, 3, 4]
4
14
0.428571
false
0
42
medium
[[0, 9, 0, 1, 4, 3, 8, 0, 2], [6, 0, 0, 5, 9, 0, 0, 0, 7], [4, 8, 0, 6, 7, 2, 5, 9, 3], [5, 4, 7, 2, 6, 1, 0, 0, 9], [3, 6, 8, 4, 5, 9, 7, 2, 1], [0, 1, 9, 8, 3, 7, 6, 5, 4], [9, 0, 6, 3, 8, 4, 2, 1, 5], [1, 5, 4, 7, 0, 6, 9, 3, 0], [0, 3, 0, 9, 1, 5, 0, 0, 6]]
[[7, 9, 5, 1, 4, 3, 8, 6, 2], [6, 2, 3, 5, 9, 8, 1, 4, 7], [4, 8, 1, 6, 7, 2, 5, 9, 3], [5, 4, 7, 2, 6, 1, 3, 8, 9], [3, 6, 8, 4, 5, 9, 7, 2, 1], [2, 1, 9, 8, 3, 7, 6, 5, 4], [9, 7, 6, 3, 8, 4, 2, 1, 5], [1, 5, 4, 7, 2, 6, 9, 3, 8], [8, 3, 2, 9, 1, 5, 4, 7, 6]]
19
62
0.765432
[6, 4, 8, 7, 9, 8, 8, 7, 5]
[6, 7, 5, 9, 8, 8, 6, 5, 8]
15
4
1
false
0
19
easy
[[0, 0, 0, 0, 5, 0, 7, 8, 0], [0, 0, 0, 6, 0, 0, 0, 1, 0], [0, 9, 0, 0, 2, 0, 6, 0, 3], [1, 0, 0, 4, 0, 0, 0, 0, 0], [0, 5, 4, 2, 6, 0, 0, 9, 0], [0, 0, 7, 0, 3, 0, 0, 0, 1], [5, 8, 2, 9, 1, 0, 3, 7, 0], [0, 0, 0, 0, 0, 2, 5, 0, 0], [0, 0, 3, 0, 0, 0, 1, 2, 9]]
[[2, 3, 6, 1, 5, 9, 7, 8, 4], [8, 7, 5, 6, 4, 3, 9, 1, 2], [4, 9, 1, 7, 2, 8, 6, 5, 3], [1, 6, 8, 4, 9, 7, 2, 3, 5], [3, 5, 4, 2, 6, 1, 8, 9, 7], [9, 2, 7, 8, 3, 5, 4, 6, 1], [5, 8, 2, 9, 1, 4, 3, 7, 6], [6, 1, 9, 3, 7, 2, 5, 4, 8], [7, 4, 3, 5, 8, 6, 1, 2, 9]]
49
32
0.395062
[3, 2, 4, 2, 5, 3, 7, 2, 4]
[2, 3, 4, 4, 5, 1, 5, 5, 3]
1
7
0.163265
false
0
49
medium
[[0, 4, 0, 3, 0, 1, 0, 0, 0], [0, 0, 0, 4, 2, 7, 0, 6, 0], [2, 7, 0, 5, 6, 0, 0, 4, 8], [5, 0, 0, 0, 9, 4, 6, 0, 0], [9, 0, 4, 0, 0, 6, 8, 5, 2], [7, 0, 6, 0, 0, 5, 0, 9, 0], [0, 0, 1, 9, 5, 0, 7, 8, 0], [0, 9, 0, 0, 1, 3, 0, 0, 0], [3, 2, 5, 7, 0, 0, 9, 0, 6]]
[[6, 4, 9, 3, 8, 1, 2, 7, 5], [1, 5, 8, 4, 2, 7, 3, 6, 9], [2, 7, 3, 5, 6, 9, 1, 4, 8], [5, 1, 2, 8, 9, 4, 6, 3, 7], [9, 3, 4, 1, 7, 6, 8, 5, 2], [7, 8, 6, 2, 3, 5, 4, 9, 1], [4, 6, 1, 9, 5, 2, 7, 8, 3], [8, 9, 7, 6, 1, 3, 5, 2, 4], [3, 2, 5, 7, 4, 8, 9, 1, 6]]
40
41
0.506173
[3, 4, 6, 4, 6, 4, 5, 3, 6]
[5, 4, 4, 5, 5, 6, 4, 5, 3]
8
12
0.5
false
0
40
medium
[[7, 5, 0, 3, 1, 4, 6, 0, 0], [8, 3, 0, 0, 0, 6, 0, 0, 1], [0, 1, 0, 0, 0, 0, 4, 0, 7], [5, 0, 7, 2, 0, 8, 0, 0, 0], [4, 0, 0, 0, 0, 0, 0, 5, 9], [0, 0, 0, 9, 5, 0, 0, 8, 4], [3, 0, 0, 0, 0, 0, 0, 7, 0], [0, 8, 1, 0, 0, 0, 0, 0, 3], [0, 0, 2, 0, 0, 1, 8, 0, 0]]
[[7, 5, 9, 3, 1, 4, 6, 2, 8], [8, 3, 4, 7, 2, 6, 5, 9, 1], [2, 1, 6, 8, 9, 5, 4, 3, 7], [5, 9, 7, 2, 4, 8, 3, 1, 6], [4, 2, 8, 1, 6, 3, 7, 5, 9], [1, 6, 3, 9, 5, 7, 2, 8, 4], [3, 4, 5, 6, 8, 9, 1, 7, 2], [6, 8, 1, 5, 7, 2, 9, 4, 3], [9, 7, 2, 4, 3, 1, 8, 6, 5]]
49
32
0.395062
[6, 4, 3, 4, 3, 4, 2, 3, 3]
[5, 4, 3, 3, 2, 4, 3, 3, 5]
2
15
0.346939
false
0
49
medium
[[0, 0, 0, 0, 0, 3, 6, 4, 8], [6, 0, 5, 7, 0, 0, 9, 2, 3], [0, 0, 3, 6, 8, 0, 0, 1, 5], [1, 0, 9, 4, 0, 8, 2, 0, 7], [0, 0, 0, 0, 0, 9, 0, 5, 0], [5, 0, 0, 0, 7, 0, 0, 0, 0], [8, 0, 7, 9, 0, 5, 0, 0, 0], [3, 0, 6, 8, 0, 4, 0, 7, 0], [2, 5, 0, 3, 0, 0, 1, 8, 9]]
[[7, 2, 1, 5, 9, 3, 6, 4, 8], [6, 8, 5, 7, 4, 1, 9, 2, 3], [9, 4, 3, 6, 8, 2, 7, 1, 5], [1, 6, 9, 4, 5, 8, 2, 3, 7], [4, 7, 2, 1, 3, 9, 8, 5, 6], [5, 3, 8, 2, 7, 6, 4, 9, 1], [8, 1, 7, 9, 2, 5, 3, 6, 4], [3, 9, 6, 8, 1, 4, 5, 7, 2], [2, 5, 4, 3, 6, 7, 1, 8, 9]]
41
40
0.493827
[4, 6, 5, 6, 2, 2, 4, 5, 6]
[6, 1, 5, 6, 2, 5, 4, 6, 5]
7
9
0.390244
false
0
41
medium
[[0, 0, 7, 3, 1, 0, 9, 0, 2], [3, 8, 0, 0, 5, 0, 0, 0, 6], [0, 2, 5, 0, 0, 0, 0, 3, 1], [0, 7, 3, 0, 0, 9, 1, 0, 4], [1, 4, 0, 8, 3, 0, 0, 0, 7], [6, 5, 0, 7, 0, 1, 3, 2, 8], [0, 3, 4, 0, 8, 0, 6, 0, 0], [5, 0, 0, 2, 0, 7, 0, 1, 0], [7, 1, 6, 4, 9, 3, 2, 8, 5]]
[[4, 6, 7, 3, 1, 8, 9, 5, 2], [3, 8, 1, 9, 5, 2, 7, 4, 6], [9, 2, 5, 6, 7, 4, 8, 3, 1], [8, 7, 3, 5, 2, 9, 1, 6, 4], [1, 4, 2, 8, 3, 6, 5, 9, 7], [6, 5, 9, 7, 4, 1, 3, 2, 8], [2, 3, 4, 1, 8, 5, 6, 7, 9], [5, 9, 8, 2, 6, 7, 4, 1, 3], [7, 1, 6, 4, 9, 3, 2, 8, 5]]
34
47
0.580247
[5, 4, 4, 5, 5, 7, 4, 4, 9]
[5, 7, 5, 5, 5, 4, 5, 4, 7]
11
15
0.764706
false
0
34
easy
[[1, 0, 8, 6, 0, 0, 0, 0, 3], [0, 0, 0, 0, 8, 0, 6, 0, 2], [0, 6, 0, 0, 5, 4, 8, 1, 9], [9, 0, 0, 0, 4, 5, 2, 3, 1], [0, 5, 0, 9, 6, 0, 0, 0, 0], [4, 8, 1, 7, 0, 0, 0, 9, 0], [0, 0, 0, 0, 9, 7, 0, 6, 5], [0, 1, 9, 0, 0, 0, 3, 8, 0], [6, 0, 5, 4, 1, 0, 9, 0, 0]]
[[1, 2, 8, 6, 7, 9, 4, 5, 3], [5, 9, 4, 1, 8, 3, 6, 7, 2], [3, 6, 7, 2, 5, 4, 8, 1, 9], [9, 7, 6, 8, 4, 5, 2, 3, 1], [2, 5, 3, 9, 6, 1, 7, 4, 8], [4, 8, 1, 7, 3, 2, 5, 9, 6], [8, 4, 2, 3, 9, 7, 1, 6, 5], [7, 1, 9, 5, 2, 6, 3, 8, 4], [6, 3, 5, 4, 1, 8, 9, 2, 7]]
41
40
0.493827
[4, 3, 6, 6, 3, 5, 4, 4, 5]
[4, 4, 4, 4, 6, 3, 5, 5, 5]
6
14
0.487805
false
0
41
medium
[[0, 0, 0, 0, 7, 0, 0, 6, 0], [2, 0, 0, 4, 8, 6, 0, 1, 0], [0, 8, 0, 0, 3, 2, 0, 0, 0], [4, 0, 0, 8, 0, 0, 0, 3, 0], [0, 0, 0, 0, 4, 7, 0, 0, 2], [6, 0, 0, 2, 1, 3, 7, 4, 0], [8, 3, 1, 0, 5, 4, 0, 0, 0], [5, 2, 7, 0, 0, 0, 0, 0, 0], [9, 6, 0, 0, 2, 0, 5, 7, 0]]
[[1, 4, 3, 5, 7, 9, 2, 6, 8], [2, 5, 9, 4, 8, 6, 3, 1, 7], [7, 8, 6, 1, 3, 2, 9, 5, 4], [4, 7, 2, 8, 9, 5, 1, 3, 6], [3, 1, 5, 6, 4, 7, 8, 9, 2], [6, 9, 8, 2, 1, 3, 7, 4, 5], [8, 3, 1, 7, 5, 4, 6, 2, 9], [5, 2, 7, 9, 6, 1, 4, 8, 3], [9, 6, 4, 3, 2, 8, 5, 7, 1]]
46
35
0.432099
[2, 5, 3, 3, 3, 6, 5, 3, 5]
[6, 4, 2, 3, 7, 5, 2, 5, 1]
1
8
0.195652
true
4
45
hard
[[3, 7, 0, 0, 0, 6, 9, 0, 5], [0, 4, 0, 3, 0, 0, 0, 0, 0], [9, 0, 6, 1, 0, 2, 0, 0, 4], [1, 6, 4, 0, 5, 9, 2, 0, 0], [8, 0, 0, 0, 3, 0, 0, 4, 7], [7, 3, 5, 2, 4, 8, 6, 0, 0], [5, 2, 0, 0, 6, 7, 0, 1, 0], [0, 1, 0, 0, 0, 3, 8, 0, 9], [0, 8, 3, 9, 0, 0, 7, 5, 2]]
[[3, 7, 1, 4, 8, 6, 9, 2, 5], [2, 4, 8, 3, 9, 5, 1, 7, 6], [9, 5, 6, 1, 7, 2, 3, 8, 4], [1, 6, 4, 7, 5, 9, 2, 3, 8], [8, 9, 2, 6, 3, 1, 5, 4, 7], [7, 3, 5, 2, 4, 8, 6, 9, 1], [5, 2, 9, 8, 6, 7, 4, 1, 3], [4, 1, 7, 5, 2, 3, 8, 6, 9], [6, 8, 3, 9, 1, 4, 7, 5, 2]]
37
44
0.54321
[5, 2, 5, 6, 4, 7, 5, 4, 6]
[6, 7, 4, 4, 4, 6, 5, 3, 5]
18
11
0.783784
false
0
37
easy
[[0, 0, 0, 5, 3, 4, 0, 0, 7], [0, 0, 0, 2, 9, 7, 5, 0, 0], [0, 2, 0, 0, 1, 6, 0, 0, 4], [0, 0, 0, 0, 0, 8, 0, 0, 0], [0, 5, 8, 4, 0, 9, 0, 7, 0], [0, 0, 0, 0, 0, 0, 6, 0, 0], [5, 0, 0, 0, 0, 0, 0, 1, 0], [9, 0, 0, 6, 4, 1, 8, 5, 0], [1, 8, 3, 7, 0, 0, 9, 4, 6]]
[[8, 6, 9, 5, 3, 4, 1, 2, 7], [4, 3, 1, 2, 9, 7, 5, 6, 8], [7, 2, 5, 8, 1, 6, 3, 9, 4], [6, 9, 7, 1, 2, 8, 4, 3, 5], [3, 5, 8, 4, 6, 9, 2, 7, 1], [2, 1, 4, 3, 7, 5, 6, 8, 9], [5, 4, 6, 9, 8, 3, 7, 1, 2], [9, 7, 2, 6, 4, 1, 8, 5, 3], [1, 8, 3, 7, 5, 2, 9, 4, 6]]
47
34
0.419753
[4, 4, 4, 1, 5, 1, 2, 6, 7]
[3, 3, 2, 5, 4, 6, 4, 4, 3]
3
6
0.191489
false
0
47
medium
[[7, 0, 9, 0, 0, 0, 0, 4, 0], [0, 3, 2, 6, 4, 0, 0, 5, 9], [0, 8, 0, 2, 7, 9, 1, 0, 6], [0, 0, 0, 3, 2, 0, 0, 0, 0], [2, 9, 0, 0, 0, 1, 3, 0, 8], [0, 1, 3, 0, 0, 0, 0, 2, 0], [0, 7, 6, 1, 0, 0, 2, 0, 0], [0, 0, 0, 8, 0, 4, 0, 0, 3], [5, 0, 0, 0, 0, 2, 0, 9, 1]]
[[7, 6, 9, 5, 1, 3, 8, 4, 2], [1, 3, 2, 6, 4, 8, 7, 5, 9], [4, 8, 5, 2, 7, 9, 1, 3, 6], [8, 5, 4, 3, 2, 6, 9, 1, 7], [2, 9, 7, 4, 5, 1, 3, 6, 8], [6, 1, 3, 9, 8, 7, 4, 2, 5], [3, 7, 6, 1, 9, 5, 2, 8, 4], [9, 2, 1, 8, 6, 4, 5, 7, 3], [5, 4, 8, 7, 3, 2, 6, 9, 1]]
45
36
0.444444
[3, 6, 6, 2, 5, 3, 4, 3, 4]
[3, 5, 4, 5, 3, 4, 3, 4, 5]
12
9
0.466667
false
0
45
medium
[[0, 0, 0, 9, 6, 3, 0, 0, 0], [3, 0, 1, 5, 2, 0, 4, 9, 0], [0, 6, 0, 0, 0, 1, 3, 2, 5], [8, 1, 0, 2, 9, 0, 5, 7, 4], [0, 9, 6, 0, 0, 0, 1, 3, 0], [0, 7, 2, 0, 0, 4, 0, 8, 0], [9, 3, 0, 0, 4, 8, 0, 6, 0], [1, 0, 8, 6, 5, 9, 7, 4, 0], [6, 4, 7, 1, 3, 0, 0, 5, 8]]
[[2, 5, 4, 9, 6, 3, 8, 1, 7], [3, 8, 1, 5, 2, 7, 4, 9, 6], [7, 6, 9, 4, 8, 1, 3, 2, 5], [8, 1, 3, 2, 9, 6, 5, 7, 4], [4, 9, 6, 8, 7, 5, 1, 3, 2], [5, 7, 2, 3, 1, 4, 6, 8, 9], [9, 3, 5, 7, 4, 8, 2, 6, 1], [1, 2, 8, 6, 5, 9, 7, 4, 3], [6, 4, 7, 1, 3, 2, 9, 5, 8]]
33
48
0.592593
[3, 6, 5, 7, 4, 4, 5, 7, 7]
[5, 6, 5, 5, 6, 5, 5, 8, 3]
15
12
0.818182
false
0
33
easy
[[0, 5, 0, 6, 0, 0, 0, 4, 1], [0, 0, 3, 0, 4, 5, 6, 0, 0], [9, 6, 0, 8, 0, 0, 3, 0, 0], [6, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 7, 0, 0, 8, 2, 0, 4], [4, 0, 2, 0, 0, 0, 0, 0, 3], [0, 2, 9, 5, 0, 0, 0, 3, 6], [0, 0, 6, 0, 2, 4, 5, 1, 0], [0, 0, 0, 0, 0, 0, 8, 0, 2]]
[[2, 5, 8, 6, 9, 3, 7, 4, 1], [1, 7, 3, 2, 4, 5, 6, 9, 8], [9, 6, 4, 8, 1, 7, 3, 2, 5], [6, 9, 5, 4, 3, 2, 1, 8, 7], [3, 1, 7, 9, 5, 8, 2, 6, 4], [4, 8, 2, 1, 7, 6, 9, 5, 3], [7, 2, 9, 5, 8, 1, 4, 3, 6], [8, 3, 6, 7, 2, 4, 5, 1, 9], [5, 4, 1, 3, 6, 9, 8, 7, 2]]
48
33
0.407407
[4, 4, 4, 2, 4, 3, 5, 5, 2]
[3, 3, 5, 3, 2, 3, 6, 3, 5]
1
5
0.125
true
5
79
hard
[[7, 6, 3, 5, 4, 1, 2, 8, 9], [0, 4, 8, 0, 0, 9, 0, 5, 0], [0, 0, 9, 8, 6, 0, 0, 7, 0], [4, 7, 6, 0, 0, 3, 0, 9, 5], [5, 3, 0, 0, 9, 6, 0, 0, 2], [0, 0, 2, 1, 5, 0, 7, 3, 0], [0, 0, 5, 0, 0, 0, 4, 0, 0], [0, 2, 7, 0, 0, 5, 0, 6, 0], [0, 8, 0, 6, 2, 7, 5, 1, 0]]
[[7, 6, 3, 5, 4, 1, 2, 8, 9], [2, 4, 8, 3, 7, 9, 6, 5, 1], [1, 5, 9, 8, 6, 2, 3, 7, 4], [4, 7, 6, 2, 8, 3, 1, 9, 5], [5, 3, 1, 7, 9, 6, 8, 4, 2], [8, 9, 2, 1, 5, 4, 7, 3, 6], [6, 1, 5, 9, 3, 8, 4, 2, 7], [3, 2, 7, 4, 1, 5, 9, 6, 8], [9, 8, 4, 6, 2, 7, 5, 1, 3]]
36
45
0.555556
[9, 4, 4, 6, 5, 5, 2, 4, 6]
[3, 6, 7, 4, 5, 6, 4, 7, 3]
10
15
0.694444
false
0
36
medium
[[6, 0, 0, 0, 5, 3, 9, 0, 4], [0, 0, 0, 6, 0, 0, 0, 8, 2], [0, 9, 8, 7, 1, 2, 3, 0, 5], [7, 8, 0, 3, 0, 4, 5, 2, 0], [1, 0, 9, 2, 0, 0, 7, 0, 6], [5, 2, 0, 1, 7, 6, 8, 3, 9], [0, 0, 0, 4, 3, 1, 2, 5, 8], [8, 4, 0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 6, 8, 0, 0, 7]]
[[6, 1, 2, 8, 5, 3, 9, 7, 4], [3, 7, 5, 6, 4, 9, 1, 8, 2], [4, 9, 8, 7, 1, 2, 3, 6, 5], [7, 8, 6, 3, 9, 4, 5, 2, 1], [1, 3, 9, 2, 8, 5, 7, 4, 6], [5, 2, 4, 1, 7, 6, 8, 3, 9], [9, 6, 7, 4, 3, 1, 2, 5, 8], [8, 4, 1, 5, 2, 7, 6, 9, 3], [2, 5, 3, 9, 6, 8, 4, 1, 7]]
35
46
0.567901
[5, 3, 7, 6, 5, 8, 6, 3, 3]
[5, 4, 2, 6, 5, 6, 7, 4, 7]
14
9
0.657143
false
0
35
medium
[[4, 0, 7, 8, 5, 1, 0, 3, 0], [0, 0, 0, 4, 7, 0, 8, 0, 5], [0, 0, 1, 0, 3, 2, 6, 4, 0], [0, 1, 8, 7, 2, 3, 4, 0, 0], [6, 7, 0, 0, 8, 9, 0, 2, 0], [9, 3, 0, 6, 0, 4, 7, 0, 8], [3, 4, 9, 2, 0, 8, 0, 0, 0], [0, 0, 0, 3, 0, 0, 2, 6, 9], [7, 2, 0, 0, 9, 0, 3, 8, 4]]
[[4, 6, 7, 8, 5, 1, 9, 3, 2], [2, 9, 3, 4, 7, 6, 8, 1, 5], [8, 5, 1, 9, 3, 2, 6, 4, 7], [5, 1, 8, 7, 2, 3, 4, 9, 6], [6, 7, 4, 5, 8, 9, 1, 2, 3], [9, 3, 2, 6, 1, 4, 7, 5, 8], [3, 4, 9, 2, 6, 8, 5, 7, 1], [1, 8, 5, 3, 4, 7, 2, 6, 9], [7, 2, 6, 1, 9, 5, 3, 8, 4]]
34
47
0.580247
[6, 4, 5, 6, 5, 6, 5, 4, 6]
[5, 5, 4, 6, 6, 6, 6, 5, 4]
10
15
0.735294
false
0
34
easy
[[0, 0, 0, 0, 9, 0, 0, 1, 5], [0, 0, 0, 1, 0, 0, 8, 4, 0], [0, 5, 0, 3, 8, 0, 2, 0, 7], [0, 0, 0, 5, 3, 0, 0, 0, 0], [0, 0, 0, 6, 0, 2, 4, 3, 1], [0, 1, 2, 0, 0, 9, 5, 0, 0], [0, 2, 8, 0, 0, 3, 0, 0, 4], [0, 3, 7, 0, 0, 0, 0, 0, 2], [4, 0, 0, 0, 5, 0, 0, 8, 3]]
[[2, 8, 4, 7, 9, 6, 3, 1, 5], [6, 7, 3, 1, 2, 5, 8, 4, 9], [9, 5, 1, 3, 8, 4, 2, 6, 7], [7, 4, 6, 5, 3, 1, 9, 2, 8], [8, 9, 5, 6, 7, 2, 4, 3, 1], [3, 1, 2, 8, 4, 9, 5, 7, 6], [1, 2, 8, 9, 6, 3, 7, 5, 4], [5, 3, 7, 4, 1, 8, 6, 9, 2], [4, 6, 9, 2, 5, 7, 1, 8, 3]]
48
33
0.407407
[3, 3, 5, 2, 5, 4, 4, 3, 4]
[1, 4, 3, 4, 4, 3, 4, 4, 6]
1
8
0.1875
true
2
52
hard