% latin_squares.mzn
include "globals.mzn";

int: n = 3;
set of int: N = 1..n;
array[N, N] of var N: X;

constraint :: "ADRows"
    forall (i in N)
        (alldifferent(X[i,..])           :: "AD(row \(i))"
        );
constraint :: "ADCols"
    forall (j in N)
        (alldifferent(X[..,j])           :: "AD(col \(j))"
        );

constraint :: "LLRows"
    forall (i in 1..n-1)
        (lex_less(X[i,..], X[i+1,..])    :: "LL(rows \(i) \(i+1))"
        );
constraint :: "LGCols"
    forall (j in 1..n-1)
        (lex_greater(X[..,j], X[..,j+1]) :: "LG(cols \(j) \(j+1))"
        );

solve satisfy;

output [ show2d(X) ];