Problem: 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.

Submission attempts (in order):
import math


def main():

    mod = 1000000007
    N = int(input())

    A = [0]
    B = [0]

    for n in range(N):
        a, b = map(int, input().split())
        A.append(a)
        B.append(b)

    calc = dict()

    for i in range(1, N + 1):
        r = math.gcd(A[i], B[i])
        m = 1
        if A[i] * B[i] < 0:
            m = -1

        k1 = (m * abs(A[i] // r), abs(B[i] // r))
        k2 = (-m * abs(B[i] // r), abs(A[i] // r))
        if calc.get(k1):
            calc[k1][0] += 1
        elif not calc.get(k2):
            calc[k1] = [1, 0]

    for i in range(1, N + 1):
        r = math.gcd(A[i], B[i])
        m = 1
        if A[i] * B[i] < 0:
            m = -1

        k2 = (-m * abs(B[i] // r), abs(A[i] // r))
        if calc.get(k2):
            calc[k2][1] += 1

    count = 0
    for k, v in calc.items():
        if not v[0] * v[1] == 0:
            count += v[0] + v[1]

    ans = pow(2, N - count, mod)
    for k, v in calc.items():
        if not v[0] * v[1] == 0:
            comb = (pow(2, v[0]) + pow(2, v[1]) - 1)
            ans = (ans * comb) % mod

    for k, v in calc.items():
        print("{} {}".format(k, v))
    print(ans - 1)


if __name__ == '__main__':
    main()


import math


def main():

    mod = 1000000007
    N = int(input())

    A = [0]
    B = [0]

    for n in range(N):
        a, b = map(int, input().split())
        A.append(a)
        B.append(b)

    calc = dict()
    non_count = 0

    for i in range(1, N + 1):

        if A[i] == 0 and B[i] == 0:
            non_count += 1
        elif A[i] == 0:
            k = (0, 1)
            if calc.get(k):
                calc[k][0] += 1
            else:
                calc[k] = [1, 0]
        elif B[i] == 0:
            k = (0, 1)
            if calc.get(k):
                calc[k][1] += 1
            else:
                calc[k] = [0, 1]
        else:
            r = math.gcd(A[i], B[i])
            m = 1
            if A[i] * B[i] < 0:
                m = -1
            k1 = (m * abs(A[i] // r), abs(B[i] // r))
            k2 = (-m * abs(B[i] // r), abs(A[i] // r))
            if calc.get(k1):
                calc[k1][0] += 1
            elif not calc.get(k2):
                calc[k1] = [1, 0]
            else:
                calc[k2][1] += 1

    N = N - non_count

    count = 0
    for k, v in calc.items():
        if not v[0] * v[1] == 0:
            count += v[0] + v[1]

    ans = pow(2, N - count, mod)
    for k, v in calc.items():
        if not v[0] * v[1] == 0:
            comb = (pow(2, v[0]) + pow(2, v[1]) - 1)
            ans = (ans * comb) % mod

    print((ans - 1 + non_count) % mod)


if __name__ == '__main__':
    main()


Verdicts: Runtime Error

Accepted