We have caught N sardines. The deliciousness and fragrantness of the i-th sardine is A_i and B_i, respectively.

We will choose one or more of these sardines and put them into a cooler. However, two sardines on bad terms cannot be chosen at the same time.

The i-th and j-th sardines (i \neq j) are on bad terms if and only if A_i \cdot A_j + B_i \cdot B_j = 0.

In how many ways can we choose the set of sardines to put into the cooler? Since the count can be enormous, print it modulo 1000000007.

Constraints

* All values in input are integers.
* 1 \leq N \leq 2 \times 10^5
* -10^{18} \leq A_i, B_i \leq 10^{18}

Input

Input is given from Standard Input in the following format:


N
A_1 B_1
:
A_N B_N


Output

Print the count modulo 1000000007.

Examples

Input

3
1 2
-1 1
2 -1


Output

5


Input

10
3 2
3 2
-1 1
2 -1
-3 -9
-8 12
7 7
8 1
8 2
8 4


Output

479
#include<bits/stdc++.h>
using namespace std;
 
#define INF 1234567890
#define ll long long
#define MOD 1000000007

int N;
ll res = 1;
map<pair<ll, ll>, int> m;

ll gcd(ll a, ll b)
{
	return a ? gcd(b%a, a) : b;
}

ll pw(ll a, ll n)
{
	ll ret = 1;
	while(n)
	{
		if (n&1) ret=ret*a%MOD;
		a=a*a%MOD;
		n>>=1;
	}
	return ret;
}

int main()
{
	scanf("%d", &N);
	ll zero = 0;
	for(int i=1; i<=N; i++)
	{
		ll a, b;
		scanf("%lld %lld", &a, &b);
		if (a == 0 && b == 0) //
		{
			zero++;
			continue;
		}
		ll g = gcd(a, b);
		a /= g; b /= g;
		if (b < 0) a=-a, b=-b;
		m[{a, b}]++;
	}
	while(!m.empty())
	{
		auto it = *m.begin();
		ll a = it.first.first, b = it.first.second;
		int cnt = it.second;
		m.erase(m.begin());

		ll na = b, nb = -a;
		if (nb < 0) na=-na, nb=-nb;
		
		if (m.find({na, nb}) == m.end())
		{
			//printf("%lld %lld (%d) deleted\n", a, b, cnt);
			res *= pw(2, cnt);
			res %= MOD;
		}
		else
		{
			int ncnt = m[{na, nb}];
			//printf("%lld %lld (%d) found %lld %lld (%d)\n", a, b, cnt, na, nb, ncnt);
			res *= (pw(2, cnt) + pw(2, ncnt) - 1) % MOD;
			res %= MOD;
			m.erase({na, nb});
		}
	}
	res--; // 공집합 제외
	res %= MOD; res += MOD; res %= MOD;

	res += zero; // 제로벡터도 하나만이라면 선택 가능하다.
	res %= MOD;

	printf("%lld", res);
	return 0;
}