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.

Examples

Input

2 1 2


Output

0 0
0 2
2 0
2 2


Input

3 1 5


Output

0 0
0 2
0 4
1 1
1 3
1 5
2 0
2 2
2 4
from itertools import product

N, D1, D2 = map(int, input().split())

# Dが「奇数」or「D%4=2」になるまで、4で割る
Ds = []
Ms = []
for D in [D1, D2]:
    M = 1
    while D % 4 == 0:
        D //= 4
        M *= 2

    Ds += [D]
    Ms += [M]

# 各点(i,j)に対して、処理を行う
num = 0
for i, j in product(range(2 * N), repeat=2):
    # 1/Mに縮小した平面で(0,0)と同じ色で塗るならば、出力する
    for D, M in zip(Ds, Ms):
        if D % 2:
            # Dが奇数→(x+y)の偶奇で塗り分ける
            if (i // M + j // M) % 2: break
        else:
            # D%4=2→xの偶奇で塗り分ける
            if (i // M) % 2: break
    else:
        print(i, j)
        num += 1
        if num == N * N: break
