Problem:
Score : 800 points

Problem Statement

Takahashi is doing a research on sets of points in a plane.
Takahashi thinks a set S of points in a coordinate plane is a good set when S satisfies both of the following conditions:

The distance between any two points in S is not \sqrt{D_1}.

The distance between any two points in S is not \sqrt{D_2}.

Here, D_1 and D_2 are positive integer constants that Takahashi specified.

Let X be a set of points (i,j) on a coordinate plane where i and j are integers and satisfy 0 ≤ i,j < 2N.

Takahashi has proved that, for any choice of D_1 and D_2, there exists a way to choose N^2 points from X so that the chosen points form a good set.
However, he does not know the specific way to choose such points to form a good set.
Find a subset of X whose size is N^2 that forms a good set.

Constraints

1 ≤ N ≤ 300

1 ≤ D_1 ≤ 2×10^5

1 ≤ D_2 ≤ 2×10^5

All values in the input are integers.

Input

Input is given from Standard Input in the following format:

N D_1 D_2

Output

Print N^2 distinct points that satisfy the condition in the following format:

x_1 y_1
x_2 y_2
:
x_{N^2} y_{N^2}

Here, (x_i,y_i) represents the i-th chosen point.
0 ≤ x_i,y_i < 2N must hold, and they must be integers.
The chosen points may be printed in any order.
In case there are multiple possible solutions, you can output any.

Sample Input 1

2 1 2

Sample Output 1

0 0
0 2
2 0
2 2

Among these points, the distance between 2 points is either 2 or 2\sqrt{2}, thus it satisfies the condition.

Sample Input 2

3 1 5

Sample Output 2

0 0
0 2
0 4
1 1
1 3
1 5
2 0
2 2
2 4

Solution in C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.Globalization;
using System.Threading;
using System.Linq;

public static class ProblemD
{
    #region Common routines

    private static int _currentTokenNumber;

    private static string[] _tokens;

    private static void StartReading()
    {
        _currentTokenNumber = 0;

        Thread.CurrentThread.CurrentCulture = CultureInfo.InvariantCulture;

        _tokens = Console.In.ReadToEnd().Split(new[] { ' ', '\t', '\r', '\n' }, StringSplitOptions.RemoveEmptyEntries);
    }

    private static string NextString()
    {
        return _tokens[_currentTokenNumber++];
    }

    private static int NextInt()
    {
        return int.Parse(NextString());
    }

    private static long NextLong()
    {
        return long.Parse(NextString());
    }

    #endregion

    private static void Main(string[] args)
    {
        StartReading();

        int n = NextInt();
        var d1 = NextInt();
        var d2 = NextInt();



        var xp = new int[n * n];
        var yp = new int[n * n];

        var last = 0;
        for (int i = 0; i < 2*n && last < n*n; i++)
        {
            for (int j = 0; j < 2*n && last < n*n; j++)
            {
                bool canBeUsed = true;
                for (int k = last-1; k >=0; k--)
                {
                    var d = (xp[k] - i) * (xp[k] - i) + (yp[k] - j) * (yp[k] - j);
                    if (d == d1 || d == d2)
                    {
                        canBeUsed = false;
                        break;

                    }
                }

                if (canBeUsed)
                {

                    xp[last] = i;
                    yp[last] = j;
                    ++last;
                }
            }
        }

        for (int i = 0; i <= last; i++)
        {
            Console.WriteLine(xp[i] + " " + yp[i]);
        }
    }
}