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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;
import java.util.ArrayList;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyScan in = new MyScan(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        ArrayList<int[]> svd1 = new ArrayList<>();
        ArrayList<int[]> svd2 = new ArrayList<>();
        int[][] data;

        public void solve(int testNumber, MyScan in, PrintWriter out) {
            int n = in.nextInt();
            int d1 = in.nextInt();
            int d2 = in.nextInt();
            svd1 = fillSq(d1);
            svd2 = fillSq(d2);

            data = new int[n * 2][n * 2];
            boolean[][] vis = new boolean[n * 2][n * 2];
            vis[0][0] = true;
            fillf(vis, 0, 0, svd1, 1, 1);
            vis = new boolean[n * 2][n * 2];
            vis[0][0] = true;
            fillf(vis, 0, 0, svd2, 2, 2);
//        out.println(Arrays.deepToString(data));
            for (int s = 0; s < 4; s++) {
                int sum = 0;
                for (int l = 0; l < n * 2; l++) {
                    for (int l1 = 0; l1 < n * 2; l1++) {
                        if (data[l][l1] == s) {
                            sum++;
                        }
                    }
                }

                if (sum >= n * n) {
                    sum = 0;
                    for (int l = 0; l < n * 2; l++) {
                        for (int l1 = 0; l1 < n * 2; l1++) {
                            if (data[l][l1] == s) {
                                out.println(l + " " + l1);
                                sum++;
                            }
                            if (sum == n * n) return;
                        }
                    }
                }
            }

        }

        private ArrayList<int[]> fillSq(int d) {
            ArrayList<int[]> ans = new ArrayList<>();
            int mm = (int) Math.sqrt(d);
            for (int r = -mm; r <= mm; r++) {
                int off = d - r * r;
                int l = (int) Math.sqrt(off);
                if (l * l == off) {
                    if (l == 0) {
                        ans.add(new int[]{0, r});
                    } else {
                        ans.add(new int[]{-l, r});
                        ans.add(new int[]{l, r});
                    }
                }
            }
            return ans;
        }

        private void fillf(boolean[][] vis, int posx, int posy, ArrayList<int[]> svd, int point, int meta) {
            for (int[] p : svd) {
                int nx = posx + p[0];
                int ny = posy + p[1];
                if (nx >= vis.length || ny >= vis.length || nx < 0 || ny < 0 || vis[nx][ny]) {
                    continue;
                }
                vis[nx][ny] = true;
                data[nx][ny] += point;
                fillf(vis, nx, ny, svd, meta - point, meta);

            }
        }

    }

    static class MyScan {
        private final InputStream in;
        private byte[] inbuf = new byte[1024];
        public int lenbuf = 0;
        public int ptrbuf = 0;

        public MyScan(InputStream in) {
            this.in = in;
        }

        private int readByte() {
            if (lenbuf == -1) throw new InputMismatchException();
            if (ptrbuf >= lenbuf) {
                ptrbuf = 0;
                try {
                    lenbuf = in.read(inbuf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (lenbuf <= 0) return -1;
            }
            return inbuf[ptrbuf++];
        }

        public int nextInt() {
            int num = 0, b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }

            while (true) {
                if (b >= '0' && b <= '9') {
                    num = num * 10 + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

    }
}