matrix11:= [
[ , ,6,1, ,2,8, , ],
[ ,2, ,7, ,6, ,9, ],
[ , , , ,4, , , , ],
[ , ,2,4, ,1,9, , ],
[ , , , , , , , , ],
[ ,5,7, , , ,1,2, ],
[1, , , , , , , ,8],
[ , ,3, ,2, ,6, , ],
[ , , , , , , , , ]
];

matrix12:= [
[6, , ,2, , , , ,9],
[ , , , , ,7,6, ,4],
[ , ,4,1,8, , , , ],
[3,5,2,8,6, ,4, ,1],
[ , ,1, ,2, ,8, , ],
[4, ,8, ,7,1,9,5,2],
[ , , , ,5,3,2, , ],
[5, ,3,4, , , , , ],
[1, , , , ,8, , ,5]
];


matrix13:= [
[8,4, , , , , ,9,7],
[ , , ,8, ,9, , , ],
[ , , ,6, ,5, , , ],
[ , , , ,1, , , , ],
[3,5, ,9, ,8, ,2,1],
[ ,2,6, , , ,9,7, ],
[ , , , , , , , , ],
[ , ,4, , , ,1, , ],
[ , ,9, , , ,7, , ]
];



matrix21:= [
[6, , ,2, ,9, ,7,3],
[ , , ,6,7, , , , ],
[9,7, , , , ,1, , ],
[8,9, , , , ,1, , ],
[ ,3, ,8,9,4, ,5, ],
[4,2, ,3, , , ,9,7],
[ , ,3, , , , ,8,4],
[ , , , ,6,8, , , ],
[5,6, ,4, ,7, , ,2]
];



matrix22:= [
[ , , , , , , , , ],
[ , , , , , , , , ],
[ ,5, ,3,2,7, ,6, ],
[ , ,3,9,8,4,7, , ],
[ , , ,7, ,1, , , ],
[ , ,7,2, ,5,1, , ],
[ ,2, , , , , ,3, ],
[5,7, , , , , ,8,6],
[ , , , , , , , , ]
];





matrix :=
[ [ 1, 2, 3, 4 ], [ 3, 4, 1, 2 ], [ 2, 1, [ 1 .. 4 ], [ 1 .. 4 ] ], [ 4, 3, [ 1 .. 4 ], [ 1 .. 4 ] ] ];


matrix := [ 
[ 1, 2, 3, 4 ],
[ 3, 4, 1, 2 ],
[ 2, 1, ,  ],
[ 4, 3, ,  ]
];

sudoku := function (matrix)
local parameter, parameter2,i, ii, matrix_bak, clean, positions, iii, iiii, temp, res
;


#parameter2:= DimensionsMat(matrix)[1];
#if parameter2 <> DimensionsMat(matrix)[2] then Error ("different dimensions");fi;
parameter2:=Length(matrix);

parameter := Sqrt(parameter2);

for i in [1..parameter2] do
for ii in [1..parameter2] do
if not IsBound(matrix[i][ii]) then 
matrix[i][ii] := [1..parameter2];
fi;
od;
od;


clean := function ( subset )
    local  i, ii;
    for i  in [ 1 .. parameter2 ]  do

        if IsInt( subset[i] )  then
            for ii  in [ 1 .. parameter2 ]  do
                if IsList( subset[ii] ) and subset[i] in subset[ii]  then
                    Unbind( subset[ii][Position( subset[ii], subset[i] )] );
                    subset[ii] := SortedList( subset[ii] );
                    if Length( subset[ii] ) = 1  then
                        subset[ii] := subset[ii][1];
                    fi;
                fi;
            od;

        elif IsList( subset[i] )  then
            for ii  in [ 1 .. Length( subset[i] ) ]  do
                if ForAll( Union( [ 1 .. i - 1 ], [ i + 1 .. parameter2 ] ), 
x-> (IsList(subset[x]) and not subset[i][ii] in subset[x]) or 
IsInt(subset[x]) and subset[i][ii] <> subset[x])  then
                    subset[i] := subset[i][ii];
                    break;
                fi;
            od;

        fi;
    od;
    return StructuralCopy( subset );
end;

matrix_bak:=fail;

repeat

Print("#\c");
matrix_bak := StructuralCopy(matrix);


#Print(matrix, "\n");

# orizontali

for i in [ 1 .. parameter2 ]  do
clean(matrix[i]);
od;

#Print(matrix, "\n");

# verticali

for i in [ 1 .. parameter2 ]  do
temp := StructuralCopy(List ( [ 1 .. parameter2 ], x -> matrix[x][i] ));
temp := clean(temp);
#if res<>temp then
for ii in [ 1 .. parameter2 ]  do
matrix[ii][i] := temp[ii];
od;
#fi;
od;


#Print(matrix, "\n");
# quadratini


for iii in [ 0 .. parameter-1 ]  do
for iiii in [ 0 .. parameter-1 ]  do

temp:=[];
for i in [ 1 .. parameter ]  do
Append (temp, StructuralCopy(matrix[iii*parameter+i]{[iiii*parameter+1..(iiii+1)*parameter]}));
od;

temp := clean(temp);
#if res<>temp then
for i in [ 1 .. parameter ]  do
matrix[iii*parameter+i]{[iiii*parameter+1..(iiii+1)*parameter]} := 
temp{[(i-1)*parameter+1..i*parameter]};
od;
#fi;

od;
od;

#Print(matrix, "\n");


until matrix_bak = matrix;

Print("\n");
return matrix;

end;