Problem:
Score: 500 points

Problem Statement

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.

Sample Input 1

3
1 2
-1 1
2 -1

Sample Output 1

5

There are five ways to choose the set of sardines, as follows:

The 1-st

The 1-st and 2-nd

The 2-nd

The 2-nd and 3-rd

The 3-rd

Sample Input 2

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

Sample Output 2

479

Solution in PyPy3 (7.3.0) (judge verdict: Accepted)

#!/usr/bin/env python3
#E

import sys
import math
from bisect import bisect_right as br
from bisect import bisect_left as bl
sys.setrecursionlimit(2147483647)
from heapq import heappush, heappop,heappushpop
from collections import defaultdict
from itertools import accumulate
from collections import Counter
from collections import deque
from operator import itemgetter
from itertools import permutations
mod = 10**9 + 7
inf = float('inf')
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))

def comb(n, r):
    return fact[n]*pow(fact[n-r], mod-2, mod)*pow(fact[r], mod-2, mod) % mod
n = I()
ab = [LI() for _ in range(n)]

fact = [1]*(n+1)
for i in range(1, n+1):
    fact[i] = i * fact[i-1]
    fact[i] %= mod

x = defaultdict(lambda : 0)
y = defaultdict(lambda : 0)
z = defaultdict(lambda : 0)
tmp = 0
for a, b in ab:
    if a == 0 and b == 0:
        tmp += 1
    elif a == 0:
        x[0] += 1
        z[0] = 1
    elif b == 0:
        y[0] += 1
        z[0] = 1
    else:
        if a * b > 0:
            g = math.gcd(a, b)
            a //= g
            b //= g
            x[(abs(a), abs(b))] += 1
            z[(abs(a), abs(b))] = 1
        else:
            g = math.gcd(a, b)
            a //= g
            b //= g
            y[(abs(b), abs(a))] += 1
            z[(abs(b), abs(a))] = 1

ans = 1
for i in z.keys():
    ans *= (2**x[i] + 2**y[i] - 1)
    ans %= mod
ans -= 1
ans += tmp
ans %= mod
print(ans)