//
// Why is this buggy?
//
import static choco.Choco.*;
import choco.cp.model.CPModel;
import choco.cp.solver.CPSolver;
import choco.kernel.model.Model;
import choco.cp.solver.search.integer.varselector.StaticVarOrder;
import choco.kernel.solver.Solver;
import choco.kernel.model.variables.integer.IntegerVariable;

public class Magic2 {

    public static void main(String[] args) throws Exception {
	int n = Integer.parseInt(args[0]);
	int k = n*(n*n + 1)/2;
	int q = 0;
	Model m = new CPModel();;

	IntegerVariable S[][]    = new IntegerVariable[n][n];
	IntegerVariable v[]      = new IntegerVariable[n*n];
	IntegerVariable col[]    = new IntegerVariable[n];
	IntegerVariable diag1[]  = new IntegerVariable[n];
	IntegerVariable diag2[]  = new IntegerVariable[n];

	for (int i=0;i<n;i++)
	    for (int j=0;j<n;j++){
		S[i][j]  = makeIntVar("S[" + i + "," + j + "]",1,n*n);
		v[q++]   = S[i][j];
	    }

	m.addConstraint(allDifferent(v));

	for (int i=0;i<n;i++)
	    m.addConstraint(eq(sum(S[i]),k));
	//
	// sum of each row is equal to k
	//

	for (int j=0;j<n;j++){
	    for (int i=0;i<n;i++)
		col[i] = S[i][j];
	    m.addConstraint(eq(sum(col),k));
	}
	//
	// sum of each colum is equal to k
	//

	for (int i=0;i<n;i++) diag1[i] = S[i][i];
	m.addConstraint(eq(sum(diag1),k));
	//
	// sum of diagonal top left to bottom right is k
	//

	for (int i=0;i<n;i++) diag2[i] = S[i][n-1-i];
	m.addConstraint(eq(sum(diag2),k));
	//
	// sum of diagonal bottom left to top right is k
	//

	Solver s = new CPSolver(); 
	s.read(m); 
	s.solve(false); 
	s.printRuntimeSatistics();
	System.out.println("feasible: " + s.isFeasible());
	System.out.println("k = " + k);

	for (int i=0;i<n;i++){
	    for (int j=0;j<n;j++)
		System.out.print(s.getVar(S[i][j]).getVal() + " ");
	    System.out.println();
	}
    }
}