Input matrix M
Define X_1 = list of rows of M
Define X_2 = list of columns of M
Define X_3 = list of diagonals of M
Define X_4 = list of antidiagonals of M
For each {integer a in {1,2,3,4}}{               // X_a is the set of rows
   For each {integer b in {1,2,3,4} with b!=a}{  // X_b is the set of columns
      For each {permutation s in S_n}{           // s is an ordering of X_a
         For each {permutation t in S_n}{        // t is an ordering of X_b
            For each {integer k in {1,...,n^2}}{
               Define i such that k in X_a[s(i)]
               Define j such that k in X_b[t(j)]
               Define n_ij = k
            }
            Output matrix N_{a,b,s,t} = (n_ij).
         }
      }
   }
}