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;

using vi = vector<int>;
#define f(i,a,b) for (int i = a; i < b; i++)
#define IN(i,a,b) (a<=i&&i<=b)
#define pb push_back

int di[] = {1,-1,1,-1};
int dj[] = {1,1,-1,-1};

void color(int n, int d, vi &color) {
	bool vis[n*n];
	fill(vis,vis+n*n,0);
	vi dx,dy;
	for (int x = 0; x*x<=d; x++) {
		int y = int(sqrt(d-x*x));
		if (x*x+y*y==d)
			dx.pb(x),dy.pb(y);
	}
	function<void(int,int,int)> dfs = [&](int i, int j, int v) {
		color[i*n+j] = v; vis[i*n+j] = 1;
		f(z,0,dx.size()) {
			f(k,0,4) {
				int ni = i+di[k]*dx[z], nj = j+dj[k]*dy[z];
				if (IN(ni,0,n-1) && IN(nj,0,n-1) && !vis[ni*n+nj])
					dfs(ni,nj,v^1);
			}		
		}
	};
	f(i,0,n) f(j,0,n) if (!vis[i*n+j]) dfs(i,j,0);
}

int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
#ifdef LOCAL
	freopen("input.txt", "r", stdin);
	freopen("output.txt", "w", stdout);
	clock_t start = clock();
#endif

	int n; cin >> n;
	n*=2;
	int d1,d2; cin>>d1>>d2;
	vi c1(n*n),c2(n*n);
	color(n,d1,c1); color(n,d2,c2);
	stringstream ss;
	f(mask,0,4) {
		vi pos;
		f(i,0,n*n) if (c1[i]+(c2[i]<<1) == mask)
			pos.pb(i);
		if (pos.size() >= n*n/4) {
			f(i,0,n*n/4)
				ss << (pos[i]/n) << " " << (pos[i]%n) << endl;
			break;
		}
	}
	cout << ss.str();

#ifdef LOCAL
	cout << setprecision(12) << (long double)(clock()-start) / CLOCKS_PER_SEC << endl;
#endif
	
	return 0;
}

