I think something wrong with tests.
For n=311 m=10131 the test says
Expected
: 71692423655005205742475058887780204076478173193756056534361211129546043664445431944499667343853437837654574420941236308628252496657306440547150042542033422966836724604589618585313406081996653652790266390363056344043348948460554622622321171105487547727180837279888801878208802638642014343289117270679561876255479945479493366274871820692161157345919355451766369038588713612753294660349103505913526811646787927664100720765220490895831907659845589011856751027720648370221163404996407536536129106286633176735546895953041399202973489205488615661260572453354171008663345444479871804393330314581222773072596927
to equal
: 3

Yes I think something wrong with tests.
For n=311 m=10131 the test say
Expected
: 71692423655005205742475058887780204076478173193756056534361211129546043664445431944499667343853437837654574420941236308628252496657306440547150042542033422966836724604589618585313406081996653652790266390363056344043348948460554622622321171105487547727180837279888801878208802638642014343289117270679561876255479945479493366274871820692161157345919355451766369038588713612753294660349103505913526811646787927664100720765220490895831907659845589011856751027720648370221163404996407536536129106286633176735546895953041399202973489205488615661260572453354171008663345444479871804393330314581222773072596927
to equal
: 3

No. At least two clues don't fit your solution.

[0,2,3,0,2,0,0
,5,0,4,5,0,4,0
,0,4,2,0,0,0,6
,5,2,2,2,2,4,1
]

      1  2  3  3  4  2  3
  1 [ 7, 6, 5, 4, 2, 1, 3 ] 5
  4 [ 3, 4, 2, 5, 1, 7, 6 ] 2
  2 [ 6, 5, 4, 7, 3, 2, 1 ] 4
  2 [ 5, 7, 6, 1, 4, 3, 2 ] 5
  2 [ 4, 3, 1, 2, 7, 6, 5 ] 3
  2 [ 2, 1, 7, 3, 6, 5, 4 ] 4
  5 [ 1, 2, 3, 6, 5, 4, 7 ] 1
      6  3  2  2  3  4  1   

Tests are not correct, there may exist more than one solution for a specific input!. Both solutions shown below are valid.

Input: [0,2,3,0,2,0,0,5,0,4,5,0,4,0,0,4,2,0,0,0,6,5,2,2,2,2,4,1]

Expected: [ [ 7, 6, 2, 1, 5, 4, 3 ], [ 1, 3, 5, 4, 2, 7, 6 ], [ 6, 5, 4, 7, 3, 2, 1 ], [ 5, 1, 7, 6, 4, 3, 2 ], [ 4, 2, 1, 3, 7, 6, 5 ], [ 3, 7, 6, 2, 1, 5, 4 ], [ 2, 4, 3, 5, 6, 1, 7 ] ]

Actual: [ [ 7, 6, 5, 4, 2, 1, 3 ], [ 3, 4, 2, 5, 1, 7, 6 ], [ 6, 5, 4, 7, 3, 2, 1 ], [ 5, 7, 6, 1, 4, 3, 2 ], [ 4, 3, 1, 2, 7, 6, 5 ], [ 2, 1, 7, 3, 6, 5, 4 ], [ 1, 2, 3, 6, 5, 4, 7 ] ]

for input {2,2,1,3,2,2,3,1,1,2,2,3,3,2,1,3} my algorithm produces valid solution {{1,3,4,2},{4,2,1,3},{3,4,2,1},{2,1,3,4}}
yet the test says it's wrong.