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MiniZinc

include "all_different.mzn";
int: n; % size
array[1..n,1..n] of 0..n: s; % 0 = unfixed 1..n = fixed
array[1..n,1..n] of var 1..n: q; % qcp array;
constraint forall(i,j in 1..n where s[i,j] > 0)(
q[i,j] = s[i,j]
);
solve maximize sum(i in 1..n)(all_different([q[i,j] | j in 1..n]))
+ sum(j in 1..n)(all_different([q[i,j] | i in 1..n]));