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: Wrong Answer)

N = int(input())
mod = 10 **9 + 7
from math import gcd
def equal(item0, item1, delta = 10 ** (-20)):
    if abs(item0 - item1) < delta:
        return True
    else:
        return False
def bigger(item0, item1, delta = 10** (-20)):
    if item0 -item1 > delta:
        return True
    else:
        return False

def binary_insert(list, item):
    low = 0
    high = len(list) - 1
    while low <= high:
        mid = (low + high) //2
        guess = list[mid][0]
        if equal(guess,item):
            list[mid][1] += 1
            return None
        if bigger(guess, item):
            high = mid -1
        else:
            low = mid + 1
    mid = (low + high) //2
    if list:
        if mid < len(list):
            if bigger(item, list[mid][0]):
                list.insert(mid+1, [item, 1])
                return None
        if mid > 0:
            if bigger(list[mid-1][0], item):
                list.insert(mid-1, [item, 1])
                return None
    list.insert(mid, [item, 1])
    return None


ab = []
ba = []
zero = 0
for _ in range(N):
    A, B = map(int, input().split())
    if A == 0:
        if B == 0:
            zero += 1
        else:
            binary_insert(ab, 0)
    elif B == 0:
        binary_insert(ba, 0)
    elif (A > 0 and B > 0) or (A < 0 and B < 0):
        d = gcd(A, B)
        A //= d
        B //= d
        binary_insert(ab, A/B)
    elif (A>0 and B <0) or (A<0 and B>0):
        d = gcd(A, B)
        A //= d
        B //= d
        binary_insert(ba, -B/A)

from collections import deque
ab = deque(ab)
ba = deque(ba)
ans = 1 #all pattern
pair = []
a = [-1, 0]
b = [-1, 0]
flaga = True
flagb = True

while True:
    if flaga:
        if ab:
            a = ab.popleft()
        else:
            a = [-1, 0]
            flaga = False
    if flagb:
        if ba:
            b = ba.popleft()
        else:
            b = [-1, 0]
            flagb = False
    if a[0] == b[0] == -1:
        break
    elif equal(a[0], b[0]):
        pair.append([a[1], b[1]])
        flaga = True
        flagb = True
        continue
    elif bigger(a[0], b[0]):
        if b[0] == -1:
            pair.append([a[1], 0])
            flaga = True
            continue
        else:
            pair.append([0, b[1]])
            if ba:
                flaga = False
                flagb = True
            continue
    else:
        if a[0] == -1:
            pair.append([0, b[1]])
            flagb = True
            continue
        else:
            pair.append([a[1], 0])
            if ab:
                flaga = True
                flagb = False

ans = 1
for item in pair:
    ans *= pow(2, item[0], mod) + pow(2, item[1], mod) -1
    ans %= mod
ans += zero-1
ans %= mod
print(ans)