import choco.Problem;
import choco.integer.*;
import choco.Solver;
import choco.Solution;
import choco.search.*;

public class OldMagic {

    public static void main(String[] args) throws Exception {
	int n = Integer.parseInt(args[0]);
	int k = n*(n*n + 1)/2;   // what a row/col/diag sums to
	int q = 0;
	Problem pb = new Problem();

	IntDomainVar S[][]   = new IntDomainVar[n][n]; // the square
	IntDomainVar T[][]   = new IntDomainVar[n][n]; // transpose of S
	IntDomainVar v[]     = new IntDomainVar[n*n];  // to be allDiff
	IntDomainVar temp[]  = new IntDomainVar[n];

	for (int i=0;i<n;i++)
	    for (int j=0;j<n;j++){
		S[i][j] = pb.makeEnumIntVar("SQ[" + i + "," + j + "]",1,n*n);
		T[j][i] = S[i][j];
		v[q++] = S[i][j];
	    }

	pb.post(pb.allDifferent(v));

	for (int i=0;i<n;i++){
	    pb.post(pb.eq(pb.sum(S[i]),k));
	    pb.post(pb.eq(pb.sum(T[i]),k));
	}
	// rows an colum sums

	for (int i=0;i<n;i++) temp[i] = S[i][i];
	pb.post(pb.eq(pb.sum(temp),k));
	// diag \ sum

	for (int i=0;i<n;i++) temp[i] = S[i][n-1-i];
	pb.post(pb.eq(pb.sum(temp),k));
	// diag / sum

       	Solver s = pb.getSolver();       
	pb.solve(false);
	// get 1st solution

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

	System.out.println("sum: " + k);
	// row/col/diag sum


	AbstractGlobalSearchLimit GS = (AbstractGlobalSearchLimit)s.getSearchSolver().limits.get(1);
	int nds = GS.getNbTot();
	System.out.println("nodes: " + nds);
	// stats
    }


}