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.Configuration;
using System.Linq;
using System.Runtime.CompilerServices;

namespace AGC025D
{
    internal class Program
    {
        public static void Main(string[] args)
        {
            long[] input = Array.ConvertAll(Console.ReadLine().Split(' '), long.Parse);
            long N = input[0];
            long n = N * 2;
            Distance d1 = new Distance(input[1]);
            Distance d2 = new Distance(input[2]);

            Point[] ps = new Point[n * n];
            for (long i = 0; i < n; i++)
            {
                for (long j = 0; j < n; j++)
                {
                    ps[i * n + j] = new Point(i, j);
                }
            }

            for (long i = 0; i < n; i++)
            {
                for (long j = 0; j < n; j++)
                {
                    if (!ps[i * n + j].Can)
                    {
                        continue;
                    }

                    long ii;
                    long jj;
                    if (d1.Can)
                    {
                        ii = i + d1.Max;
                        jj = j + d1.Min;
                        if (ii < n && jj < n) ps[ii * n + jj].Can = false;

                        ii = i + d1.Min;
                        jj = j + d1.Max;
                        if (ii < n && jj < n) ps[ii * n + jj].Can = false;
                        
                        ii = i + d1.Max;
                        jj = j - d1.Min;
                        if (ii < n && jj >= 0) ps[ii * n + jj].Can = false;

                        ii = i + d1.Min;
                        jj = j - d1.Max;
                        if (ii < n && jj >= 0) ps[ii * n + jj].Can = false;
                                                
                        ii = i - d1.Max;
                        jj = j + d1.Min;
                        if (ii >= 0 && jj < n) ps[ii * n + jj].Can = false;

                        ii = i - d1.Min;
                        jj = j + d1.Max;
                        if (ii >= 0 && jj < n) ps[ii * n + jj].Can = false;
                        
                        ii = i - d1.Max;
                        jj = j - d1.Min;
                        if (ii >= 0 && jj >= 0) ps[ii * n + jj].Can = false;

                        ii = i - d1.Min;
                        jj = j - d1.Max;
                        if (ii >= 0 && jj >= 0) ps[ii * n + jj].Can = false;
                    }

                    if (d2.Can)
                    {
                        ii = i + d2.Max;
                        jj = j + d2.Min;
                        if (ii < n && jj < n) ps[ii * n + jj].Can = false;

                        ii = i + d2.Min;
                        jj = j + d2.Max;
                        if (ii < n && jj < n) ps[ii * n + jj].Can = false;
                        
                        ii = i + d2.Max;
                        jj = j - d2.Min;
                        if (ii < n && jj >= 0) ps[ii * n + jj].Can = false;

                        ii = i + d2.Min;
                        jj = j - d2.Max;
                        if (ii < n && jj >= 0) ps[ii * n + jj].Can = false;
                        
                        ii = i - d2.Max;
                        jj = j + d2.Min;
                        if (ii >= 0 && jj < n) ps[ii * n + jj].Can = false;

                        ii = i - d2.Min;
                        jj = j + d2.Max;
                        if (ii >= 0 && jj < n) ps[ii * n + jj].Can = false;
                        
                        ii = i - d2.Max;
                        jj = j - d2.Min;
                        if (ii >= 0 && jj >= 0) ps[ii * n + jj].Can = false;

                        ii = i - d2.Min;
                        jj = j - d2.Max;
                        if (ii >= 0 && jj >= 0) ps[ii * n + jj].Can = false;
                    }
                }
            }

            Point[] ans = ps.Where(p => p.Can).ToArray();
            long nn = N * N;
            for (long i = 0; i < nn; i++)
            {
                ans[i].Show();
            }
        }
    }

    class Distance
    {
        public long D;
        public long Min;
        public long Max;
        public bool Can;

        public Distance(long d)
        {
            D = d;
            Search();
        }

        private void Search()
        {
            long droot = Convert.ToInt64(Math.Sqrt(D));
            for (long i = 0; i <= droot; i++)
            {
                for (long j = i; j <= droot; j++)
                {
                    long l = i * i + j * j;
                    if (l == D)
                    {
                        Min = Math.Min(i, j);
                        Max = Math.Max(i, j);
                        Can = true;
                        return;
                    }

                    if (l > D)
                    {
                        break;
                    }
                }
            }

            Can = false;
        }
    }

    class Point
    {
        public long X;
        public long Y;
        public bool Can;

        public Point(long i, long j)
        {
            Can = true;
            X = i;
            Y = j;
        }

        public void Show()
        {
            Console.WriteLine("" + X + " " + Y);
        }
    }
}