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 Python (3.4.3) (judge verdict: Accepted)

import sys
input = sys.stdin.readline

import numpy as np

N,*D = map(int,input().split())

grid = np.zeros((2*N,2*N), dtype=np.int8)

for i,d in enumerate(D):
    width = 1
    while d % 4 == 0:
        d //= 4
        width *= 2
    if d%4 == 1:
        x = np.arange(2*N)
        bl = (x%(2*width) >= width)
        grid += (bl[:,None]^bl[None,:]) * (1<<i)
    elif d%4 == 2:
        x = np.arange(2*N)
        bl = (x%(2*width) >= width)
        grid += bl * (1<<i)

for i in range(4):
    X,Y = np.where(grid == i)
    if len(X) >= N*N:
        break

X,Y = X[:N*N], Y[:N*N]
for x,y in zip(X,Y):
    print(x,y)