import java.applet.*;
import java.awt.*;

public class FastChain9 extends Applet {

int[] digit;
int length = 9;
	
public void init() 
{
	digit = new int[length];
	PermutationGenerator permutationGenerator = new PermutationGenerator(length);
	int perms = permutationGenerator.factorial(length);
	digit = permutationGenerator.getThis();
	if (!redundant() && isMagichain9()) print9();
	for (int i = 1; i < perms; i++)
	{
		digit = permutationGenerator.getNext();
		if (!redundant() && isMagichain9()) print9();
	}
}

boolean redundant()
{
	return (digit[0] < digit[1] || digit[0] < digit[8] || digit[8] < digit[7]);
}

boolean isMagichain9()  // chain with same column and row sums
{
	int total  = digit[0] + digit[1] + digit[2];
	if (total != digit[2] + digit[3] + digit[4]) return false;
	if (total != digit[4] + digit[5] + digit[6]) return false;
	if (total != digit[6] + digit[7] + digit[8]) return false;
	return true;
}

void print9()  // prints sequence 
{
	String s = "";
	for (int i=length-1; i>= 0; i--) s += String.valueOf(digit[i] + 1);
	System.out.println(s);
}

public void paint(Graphics g)
{
	g.drawString("Results appear in the Java console", 20 , 25);
}
}  // END OF Class FastChain9



class PermutationGenerator {

int[] digit;
int length;
	
PermutationGenerator(int length)
{
	this.length = length;
	digit = new int[length];
	for (int i = 0; i < length; i++) digit[i] = i;
}

int[] getThis()
{
	return(digit);
}

int[] getNext()
{
	int i = length - 1;
	while (digit[i-1] > digit[i]) i--;
	int j = length;
	while (digit[j-1] <= digit[i-1]) j--;
	swap(i-1, j-1);
	i++; 
	j = length;
	while (i < j)
	{
		swap(i-1, j-1);
		i++;
		j--;
	}
	return(digit);
}

void swap(int first, int second)
{
	int temp = digit[first];
	digit[first] = digit[second];
	digit[second] = temp;
}

int factorial(int number) 
{
	int result = 1;
	for (int i = 1; i <= number; i++) result *= i;
	return result;
}
}  //  END OF Class PermutationGenerator