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.StringTokenizer;
import java.io.IOException;
import java.util.InputMismatchException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * 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;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DChoosingPoints solver = new DChoosingPoints();
        solver.solve(1, in, out);
        out.close();
    }

    static class DChoosingPoints {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int d1 = in.nextInt();
            int d2 = in.nextInt();

            int cnt = 0;
            for (int i = 0; i < 2 * n; i++) {
                for (int j = 0; j < 2 * n; j++) {
                    int tmpI = i;
                    int tmpJ = j;
                    int tmpD1 = d1;
                    while (tmpD1 % 4 == 0) {
                        tmpI /= 2;
                        tmpJ /= 2;
                        tmpD1 /= 4;
                    }

                    boolean flg1;
                    if (tmpD1 % 2 == 1) {
                        flg1 = (tmpI + tmpJ) % 2 == 0;
                    } else {
                        flg1 = tmpI % 2 == 0;
                    }

                    tmpI = i;
                    tmpJ = j;
                    int tmpD2 = d2;
                    while (tmpD2 % 4 == 0) {
                        tmpI /= 2;
                        tmpJ /= 2;
                        tmpD2 /= 4;
                    }

                    boolean flg2;
                    if (tmpD1 % 2 == 1) {
                        flg2 = (tmpI + tmpJ) % 2 == 0;
                    } else {
                        flg2 = tmpI % 2 == 0;
                    }

                    if (flg1 && flg2) {
                        out.println(i + " " + j);
                        cnt++;
                        if (cnt == n * n) return;
                    }
                }
            }
        }

    }

    static class InputReader {
        private BufferedReader br;
        private StringTokenizer st;

        public InputReader(InputStream inputStream) {
            br = new BufferedReader(new InputStreamReader(inputStream));
            st = new StringTokenizer("");
        }

        public String nextString() {
            while (!st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine(), " ");
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(nextString());
        }

    }
}