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)

// package agc.agc025;

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

public class Main {
    public interface IJPredicator {
        boolean shouldSkip(int i, int j);
    }

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n = in.nextInt();
        int d1 = in.nextInt();
        int d2 = in.nextInt();

        char[][] map1 = doit(n*2, d1);
        char[][] map2 = doit(n*2, d2);

        int[][] d0 = new int[map1.length][map1[0].length];

        int[] cnt = new int[n*2];
        for (int i = 0; i < d0.length ; i++) {
            for (int j = 0; j < d0[0].length ; j++) {
                int a = map1[i][j] == '@' ? 1 : 0;
                int b = map2[i][j] == '@' ? 2 : 0;
                d0[i][j] = a+b;
                cnt[a+b]++;
            }
        }

        List<int[]> ans = new ArrayList<>();
        for (int k = 0; k < 4 ; k++) {
            if (cnt[k] >= n*n) {
                sch: for (int i = 0; i < d0.length ; i++) {
                    for (int j = 0; j < d0[0].length; j++) {
                        if (d0[i][j] == k) {
                            ans.add(new int[]{i, j});
                            if (ans.size() == n*n) {
                                break sch;
                            }
                        }
                    }
                }
                break;
            }
        }
        printAndFlush(out, ans);
    }

    static char[][] doit(int n, int d) {
        List<int[]> p = checkPair(n, d);
        char[][] map = new char[n][n];
        for (int i = 0; i < n ; i++) {
            for (int j = 0; j < n ; j++) {
                boolean isok = true;
                sch: for (int[] dd : p) {
                    int ti = i + dd[0];
                    int tj = j + dd[1];
                    if (ti < 0 || tj < 0 || ti >= map.length || tj >= map[0].length) {
                        continue;
                    }
                    if (map[ti][tj] == '@') {
                        isok = false;
                        break sch;
                    }
                }
                map[i][j] = isok ? '@' : '.';
            }
        }
//        System.out.println(String.format("d=%d", d));
//        for (int i = 0 ; i < n ; i++) {
//            System.out.println(String.valueOf(map[i]));
//        }
        return map;
    }

    static void printAndFlush(PrintWriter out, List<int[]> ans) {
        for (int[] a : ans) {
            out.println(String.format("%d %d", a[0], a[1]));
        }
        out.flush();
    }

    static List<int[]> checkPair(int n, int d) {
        List<int[]> wo = new ArrayList<>();
        for (int i = 0; i < 2*n ; i++) {
            for (int j = 0; j < 2*n; j++) {
                int ii = i*i;
                int jj = j*j;
                if (ii + jj == d) {
                    for (int dy = -1 ; dy <= 1 ; dy += 2) {
                        for (int dx = -1 ; dx <= 1 ; dx += 2) {
                            wo.add(new int[]{i * dy, j * dx});
                        }
                    }
                }
            }
        }
        return wo;
    }

    static int dist(int[] a, int[] b) {
        int dx = Math.abs(a[0]-b[0]);
        int dy = Math.abs(a[1]-b[1]);
        return dx*dx+dy*dy;
    }

    static List<List<int[]>> pairs;

    private static List<int[]> solve(int n, int d1, int d2, IJPredicator pred) {
        boolean[][] tbl = new boolean[2*n][2*n];
        List<int[]> selected = new ArrayList<>();
        sch: for (int i = 0; i < 2*n ; i++) {
            for (int j = 0; j < 2*n ; j++) {
                if (pred.shouldSkip(i, j)) {
                    continue;
                }
                if (canPlace(tbl, i, j, d1, d2)) {
                    tbl[i][j] = true;
                    selected.add(new int[]{i, j});
                    if (selected.size() == n*n) {
                        break sch;
                    }
                }
            }
        }
        return selected;
    }

    private static boolean canPlace(boolean[][] tbl, int y, int x, int d1, int d2) {
        int n = tbl.length;
        for (List<int[]> pa : pairs) {
            for (int[] f : pa) {
                int ty = y + f[0];
                int tx = x + f[1];
                if (ty < 0 || tx < 0 || ty >= n || tx >= n) {
                    continue;
                }
                if (tbl[ty][tx]) {
                    return false;
                }
            }
        }
        return true;
    }

    public static void debug(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }

    public static class InputReader {
        private static final int BUFFER_LENGTH = 1 << 12;
        private InputStream stream;
        private byte[] buf = new byte[BUFFER_LENGTH];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        private int next() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public char nextChar() {
            return (char) skipWhileSpace();
        }

        public String nextToken() {
            int c = skipWhileSpace();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char) c);
                c = next();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public int nextInt() {
            return (int) nextLong();
        }

        public long nextLong() {
            int c = skipWhileSpace();
            long sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = next();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble() {
            return Double.valueOf(nextToken());
        }

        int skipWhileSpace() {
            int c = next();
            while (isSpaceChar(c)) {
                c = next();
            }
            return c;
        }

        boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    }
}