include "globals.mzn";

int: n;
array[1..n, 1..n] of var 1..n*n: square;
var 1..n*n*n: sum;

constraint
  alldifferent([square[j, i] | j, i in 1..n])

  /\
  forall (i in 1..n)
    (sum(j in 1..n)(square[i, j]) = sum)

  /\
  forall (i in 1..n)
    (sum(j in 1..n)(square[j, i]) = sum)

  /\
  sum(i in 1..n)(square[i, i]) = sum

  /\
  sum(i in 1..n)(square[i, n-i+1]) = sum
;

solve satisfy;

output [
  "\ns: ", show(sum)
] ++
[
 if  j = 1 then "\n" else " " endif ++
   show(square[i, j])
 | i, j in 1..n
] ++ ["\n"];