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
#include<bits/stdc++.h>
using namespace std;

int n, d1, d2;
int co[666][666], cnt[4];

void gao(int d,int w){
    int b=1;
    while (d%4==0) d/=4, b*=2;
    for (int i=0;i<n;++i)
        for (int j=0;j<n;++j)
            if (d%4==1&&(i/b+j/b)%2||d%4==2&&i/b%2)
                co[i][j]|=w;
}

int main(){
    cin>>n>>d1>>d2; n*=2;
    gao(d1,1); gao(d2,2);
    for (int i=0;i<n;++i)
        for (int j=0;j<n;++j)
            ++cnt[co[i][j]];
    for (int aim=0;aim<4;++aim)
        if (cnt[aim]>=n*n/4){
            int las=n*n/4;
            for (int i=0;i<n;++i)
                for (int j=0;j<n;++j)
                    if (las&&co[i][j]==aim)
                        printf("%d %d\n",i,j), las--;
            return 0;
        }
}