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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>
#include<vector>
#include<algorithm>
#include<cstring>
#include<cstdio>
#include<cmath>

using namespace std;

#define pii pair<int,int>
#define fir first
#define sec second
#define makr(x,y) make_pair(x,y)

const int N=666;

int n,m,d1,d2,wt;

bool mp[N][N];

void check(int x,int y,int d)
{
	int b=-2*y,c,t,t2;
	for(int i=0;i<=m;++i)
	{
		c=y*y-d-2*i*x+i*i+x*x;
		t=b*b-4*c;
		if(t<0)
			continue;
		t2=sqrt(t);
		if(t2*t2!=t)
			continue;
		t=-b+t2;
		if(0<=t&&!(t&1)&&(t>>=1)<=m)
			mp[i][t]=false;
		t=-b-t2;
		if(0<=t&&!(t&1)&&(t>>=1)<=m)
			mp[i][t]=false;
	}
}

vector<pii> res;

int main()
{
	scanf("%d%d%d",&n,&d1,&d2);
	m=(n<<1)-1;
	wt=n*n;
	memset(mp,1,sizeof mp);
	bool fl=true;
	for(int i=0;i<=m&&fl;++i)
		for(int j=0;j<=m;++j)if(mp[i][j])
		{
			res.push_back(makr(i,j));
			if((int)res.size()==wt)
			{
				fl=false;
				break;
			}
			check(i,j,d1);
			check(i,j,d2);
		}
	if(fl)
	{
		res.clear();
		for(int i=0;i<=m&&fl;++i)
			for(int j=0;j<=m;++j)if(!mp[i][j])
			{
				memset(mp,1,sizeof 1);
				res.push_back(makr(i,j));
				check(i,j,d1);
				check(i,j,d2);
				mp[i][j]=false;
				fl=false;
				break;
			}
		fl=true;
		for(int i=0;i<=m&&fl;++i)
			for(int j=0;j<=m;++j)if(mp[i][j])
			{
				res.push_back(makr(i,j));
				if((int)res.size()==wt)
				{
					fl=false;
					break;
				}
				check(i,j,d1);
				check(i,j,d2);
			}
	}
	for(pii p:res)
		printf("%d %d\n",p.fir,p.sec);
	return 0;
}