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



Sample input:
3
1 2
-1 1
2 -1


Sample output:
5

Submission status: Wrong Answer

Solution code:
from math import gcd
from bisect import bisect_left, bisect_right

MOD = 10 ** 9 + 7
pow2 = [1] * (2 * 10 ** 5 + 1)
for i in range(1, 2 * 10 ** 5 + 1):
	pow2[i] = (pow2[i - 1] * 2) % MOD

N = int(input())

iwasies = []
for i in range(N):
	A, B = map(int, input().split())
	if A == 0 and B == 0:
		continue
	elif A == 0:
		iwasies.append((0, 1))
	elif B == 0:
		iwasies.append((1, 0))
	else:
		g = gcd(A, B)
		A //= g
		B //= g
		if A < 0:
			iwasies.append((-A, -B))
		else:
			iwasies.append((A, B))

numiwasi = len(iwasies)
iwasies.sort()
badpairs = set()
for i in range(numiwasi):
	A, B = iwasies[i]
	abcount = bisect_right(iwasies, (A, B)) - bisect_left(iwasies, (A, B))
	
	Ao, Bo = B, -A
	if Ao < 0:
		Ao, Bo = -Ao, -Bo
	
	aobocount = bisect_right(iwasies, (Ao, Bo)) - bisect_left(iwasies, (Ao, Bo))
	
	if aobocount > 0:
		if (A, B) < (Ao, Bo):
			badpairs.add(((A, B, abcount), (Ao, Bo, aobocount)))
		else:
			badpairs.add(((Ao, Bo, aobocount), (A, B, abcount)))

sociable = numiwasi
ans = 1

for bp in badpairs:
	count1 = bp[0][2]
	count2 = bp[1][2]
	sociable -= (count1 + count2)
	ans = (ans * (pow2[count1] + pow2[count2] - 1)) % MOD
ans = (ans * pow2[sociable]) % MOD

print(ans - 1)

Submission status: Wrong Answer

Solution code:
from math import gcd
from bisect import bisect_left, bisect_right

MOD = 10 ** 9 + 7
pow2 = [1] * (2 * 10 ** 5 + 1)
for i in range(1, 2 * 10 ** 5 + 1):
	pow2[i] = (pow2[i - 1] * 2) % MOD
print(pow2[3])
N = int(input())

iwasies = []
for i in range(N):
	A, B = map(int, input().split())
	if A == 0 and B == 0:
		continue
	elif A == 0:
		iwasies.append((0, 1))
	elif B == 0:
		iwasies.append((1, 0))
	else:
		g = gcd(A, B)
		A //= g
		B //= g
		if A < 0:
			iwasies.append((-A, -B))
		else:
			iwasies.append((A, B))

numiwasi = len(iwasies)
iwasies.sort()
badpairs = set()
for i in range(numiwasi):
	A, B = iwasies[i]
	abcount = bisect_right(iwasies, (A, B)) - bisect_left(iwasies, (A, B))
	
	Ao, Bo = B, -A
	if Ao < 0:
		Ao, Bo = -Ao, -Bo
	
	aobocount = bisect_right(iwasies, (Ao, Bo)) - bisect_left(iwasies, (Ao, Bo))
	
	if aobocount > 0:
		if (A, B) < (Ao, Bo):
			badpairs.add(((A, B, abcount), (Ao, Bo, aobocount)))
		else:
			badpairs.add(((Ao, Bo, aobocount), (A, B, abcount)))

sociable = numiwasi
ans = 1

for bp in badpairs:
	count1 = bp[0][2]
	count2 = bp[1][2]
	sociable -= (count1 + count2)
	ans = (ans * (pow2[count1] + pow2[count2] - 1)) % MOD
ans = (ans * pow2[sociable]) % MOD

print(ans - 1)

Submission status: Wrong Answer

Solution code:
from collections import defaultdict
from math import gcd
N = int(input())
MOD = 10**9 + 7
L = defaultdict(lambda: [0,0])
zero = 0
for _ in range(N):
    A, B = map(int, input().split())
    if A==0: d=B
    elif B==0: d=A
    else: d=gcd(A,B)
    if d != 0:
        A, B = A//d, B//d
        if A<0: A, B = -A, -B
        if B>0: L[(A,B)][0] += 1
        else: L[(-B,A)][1] += 1
    else: zero += 1
print(L)
res = 1

for x,y in L.values():
    res *= pow(2,x,MOD) + pow(2,y,MOD) -1
    res %= MOD
print((res+zero-1)%MOD)

Submission status: Wrong Answer

Solution code:
N = int(input())
mod = 10 **9 + 7

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
bit = [1]
for k in range(N):
    bit.append(bit[-1]*2%mod)


AB = []
BA = []
zero = 0
from bisect import insort
for _ in range(N):
    A, B = map(int, input().split())
    if A*B == 0:
        if A == 0 and B == 0:
            zero += 1
        elif A == 0 and B != 0:
            AB = [0] + AB
        else:
            BA = [0] + BA
    elif A*B > 0:
        insort(AB, A/B)
    else:
        insort(BA, -B/A)
def make_count(list):
    k = 0
    lis = []
    while k < len(list):
        cnt = 1
        while k+1 < len(list):
            if equal(list[k], list[k+1]):
                cnt += 1
                k += 1
                continue
            else:
                break
        lis.append([list[k], cnt])
        k += 1
    return lis

AB = make_count(AB)
BA = make_count(BA)
from collections import deque
AB = deque(AB)
BA = deque(BA)
ans = 1 #all pattern
flag = True
pair = []
if len(AB) == 0:
    print(bit[N-zero]+zero-1)
    exit()
if len(BA) == 0:
    print(bit[N-zero]+ zero -1)
    exit()


while True:
    if flag:
        a = AB.popleft()
        b = BA.popleft()
    flag = False
    if equal(a[0], b[0]):
        pair.append([a[1], b[1]])
        if AB:
            a = AB.popleft()
        if BA:
            b = BA.popleft()
    elif bigger(a[0], b[0]):
        pair.append([0,b[1]])
        if BA:
            b = BA.popleft()
            continue
        elif AB:
            a = AB.popleft()
            continue
        else:
            break
    else:
        pair.append([a[1], 0])
        if AB:
            a = AB.popleft()
            continue
        elif BA:
            b = BA.popleft()
        else:
            break
ans = 1
for item in pair:
    ans *= bit[item[0]] + bit[item[1]] -1
    ans %= mod
ans += zero-1
ans %= mod
print(ans)

Submission status: Wrong Answer

Solution code:
N = int(input())
mod = 10 **9 + 7

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
bitlist = [1]
for k in range(N):
    bitlist.append(bitlist[-1]*2%mod)


liABplus = []
liBAplus = []
zero = 0
from bisect import insort
for _ in range(N):
    A, B = map(int, input().split())
    if A*B == 0:
        if A == 0 and B == 0:
            zero += 1
        elif A == 0 and B != 0:
            liABplus = [0] + liABplus
        else:
            liBAplus = [0] + liBAplus
    elif A*B > 0:
        insort(liABplus, A/B)
    else:
        insort(liBAplus, -B/A)
def make_count(list):
    k = 0
    lis = []
    while k < len(list):
        cnt = 1
        while k+1 < len(list):
            if equal(list[k], list[k+1]):
                cnt += 1
                k += 1
                continue
            else:
                break
        lis.append([list[k], cnt])
        k += 1
    return lis

liABplus = make_count(liABplus)
liBAplus = make_count(liBAplus)
N -= zero
from collections import deque
liABplus = deque(liABplus)
liBAplus = deque(liBAplus)
ans = bitlist[N]-1 #all pattern
flag = True
eqpair = []
while liABplus and liBAplus:
    if flag:
        AB = liABplus.popleft()
        BA = liBAplus.popleft()
    if equal(AB[0], BA[0]):
        eqpair.append([AB[1], BA[1]])
        if liABplus and liBAplus:
            flag = True
            continue
        else:
            break
    elif bigger(AB[0], BA[0]):
        if liBAplus:
            BA = liBAplus.popleft()
            flag = False
            continue
        else:
            break
    else:
        if liABplus:
            AB = liABplus.popleft()
            flag = False
            continue
        else:
            break

from itertools import combinations
for k in range(1, len(eqpair)+1):
    for item in combinations(eqpair, k):
        sgn = (-1)**k
        ideal = 1
        cnt = 0
        for i in item:
            cnt += i[0] + i[1]
            ideal *= bitlist[i[0]]-1
            ideal %= mod
            ideal *= bitlist[i[1]]-1
            ideal %= mod
        ideal *= bitlist[N-cnt]
        ideal %= mod
        ans += sgn*ideal
        ans %= mod
ans += zero
ans %= mod
print(ans)

Submission status: Wrong Answer

Solution code:
N = int(input())
mod = 10 **9 + 7

def equal(item0, item1, delta = 10 ** (-19)):
    if abs(item0 - item1) < delta:
        return True
    else:
        return False
def bigger(item0, item1, delta = 10** (-19)):
    if item0 -item1 > delta:
        return True
    else:
        return False
bitlist = [1]
for k in range(N):
    bitlist.append(bitlist[-1]*2%mod)


liABplus = []
liBAplus = []
zero = 0
from bisect import insort
for _ in range(N):
    A, B = map(int, input().split())
    if A*B == 0:
        if A == 0 and B == 0:
            zero += 1
        elif A == 0 and B != 0:
            liABplus = [0] + liABplus
        else:
            liBAplus = [0] + liBAplus
    elif A*B > 0:
        insort(liABplus, A/B)
    else:
        insort(liBAplus, -B/A)
def make_count(list):
    k = 0
    lis = []
    while k < len(list):
        cnt = 1
        while k+1 < len(list):
            if equal(list[k], list[k+1]):
                cnt += 1
                k += 1
                continue
            else:
                break
        lis.append([list[k], cnt])
        k += 1
    return lis

liABplus = make_count(liABplus)
liBAplus = make_count(liBAplus)
N -= zero
from collections import deque
liABplus = deque(liABplus)
liBAplus = deque(liBAplus)
ans = bitlist[N]-1 #all pattern
flag = True
eqpair = []
while liABplus and liBAplus:
    if flag:
        AB = liABplus.popleft()
        BA = liBAplus.popleft()
    if equal(AB[0], BA[0]):
        eqpair.append([AB[1], BA[1]])
        if liABplus and liBAplus:
            flag = True
            continue
        else:
            break
    elif bigger(AB[0], BA[0]):
        if liBAplus:
            BA = liBAplus.popleft()
            flag = False
            continue
        else:
            break
    else:
        if liABplus:
            AB = liABplus.popleft()
            flag = False
            continue
        else:
            break

minus = 0
from itertools import combinations
for k in range(1, len(eqpair)+1):
    for item in combinations(eqpair, k):
        sgn = (-1)**k
        ideal = 1
        cnt = 0
        for i in item:
            cnt += i[0] + i[1]
            ideal *= bitlist[i[0]]-1
            ideal %= mod
            ideal *= bitlist[i[1]]-1
            ideal %= mod
        ideal *= bitlist[N-cnt]
        ideal %= mod
        ans += sgn*ideal
        ans %= mod
ans += zero
ans %= mod
print(ans)

Submission status: Wrong Answer

Solution code:
N = int(input())
mod = 10 **9 + 7

def equal(item0, item1, delta = 10 ** (-19)):
    if abs(item0 - item1) < delta:
        return True
    else:
        return False
def bigger(item0, item1, delta = 10** (-19)):
    if item0 -item1 > delta:
        return True
    else:
        return False
bitlist = [1]
for k in range(N):
    bitlist.append(bitlist[-1]*2%mod)


liABplus = []
liBAplus = []
zero = 0
from bisect import insort
for _ in range(N):
    A, B = map(int, input().split())
    if A*B == 0:
        if A == 0 and B == 0:
            zero += 1
            if N == 1:
                print(1)
                exit()
        elif A == 0 and B != 0:
            liABplus = [0] + liABplus
        else:
            liBAplus = [0] + liBAplus
    elif A*B > 0:
        insort(liABplus, A/B)
    else:
        insort(liBAplus, -B/A)
def make_count(list):
    k = 0
    lis = []
    while k < len(list):
        cnt = 1
        while k+1 < len(list):
            if equal(list[k], list[k+1]):
                cnt += 1
                k += 1
                continue
            else:
                break
        lis.append([list[k], cnt])
        k += 1
    return lis

liABplus = make_count(liABplus)
liBAplus = make_count(liBAplus)
N -= zero
from collections import deque
liABplus = deque(liABplus)
liBAplus = deque(liBAplus)
ans = bitlist[N]-1 #all pattern
flag = True
eqpair = []
while liABplus and liBAplus:
    if flag:
        AB = liABplus.popleft()
        BA = liBAplus.popleft()
    if equal(AB[0], BA[0]):
        eqpair.append([AB[1], BA[1]])
        if liABplus and liBAplus:
            flag = True
            continue
        else:
            break
    elif bigger(AB[0], BA[0]):
        if liBAplus:
            BA = liBAplus.popleft()
            flag = False
            continue
        else:
            break
    else:
        if liABplus:
            AB = liABplus.popleft()
            flag = False
            continue
        else:
            break

minus = 0
from itertools import combinations
for k in range(1, len(eqpair)+1):
    for item in combinations(eqpair, k):
        sgn = (-1)**k
        ideal = 1
        cnt = 0
        for i in item:
            cnt += i[0] + i[1]
            ideal *= bitlist[i[0]]-1
            ideal %= mod
            ideal *= bitlist[i[1]]-1
            ideal %= mod
        ideal *= bitlist[N-cnt]
        ideal %= mod
        ans += sgn*ideal
        ans %= mod
print(ans)

Submission status: Wrong Answer

Solution code:
N = int(input())
mod = 10 **9 + 7

def equal(item0, item1, delta = 10 ** (-19)):
    if abs(item0 - item1) < delta:
        return True
    else:
        return False
def bigger(item0, item1, delta = 10** (-19)):
    if item0 -item1 > delta:
        return True
    else:
        return False
bitlist = [1]
for k in range(N):
    bitlist.append(bitlist[-1]*2%mod)


liABplus = []
liBAplus = []
zero = 0
from bisect import insort
for _ in range(N):
    A, B = map(int, input().split())
    if A*B == 0:
        if A == 0 and B == 0:
            zero += 1
        elif A == 0 and B != 0:
            liABplus = [0] + liABplus
        else:
            liBAplus = [0] + liBAplus
    elif A*B > 0:
        insort(liABplus, A/B)
    else:
        insort(liBAplus, -B/A)
def make_count(list):
    k = 0
    lis = []
    while k < len(list):
        cnt = 1
        while k+1 < len(list):
            if equal(list[k], list[k+1]):
                cnt += 1
                k += 1
                continue
            else:
                break
        lis.append([list[k], cnt])
        k += 1
    return lis

liABplus = make_count(liABplus)
liBAplus = make_count(liBAplus)
N -= zero
from collections import deque
liABplus = deque(liABplus)
liBAplus = deque(liBAplus)
ans = bitlist[N]-1 #all pattern
flag = True
eqpair = []
while liABplus and liBAplus:
    if flag:
        AB = liABplus.popleft()
        BA = liBAplus.popleft()
    if equal(AB[0], BA[0]):
        eqpair.append([AB[1], BA[1]])
        if liABplus and liBAplus:
            flag = True
            continue
        else:
            break
    elif bigger(AB[0], BA[0]):
        if liBAplus:
            BA = liBAplus.popleft()
            flag = False
            continue
        else:
            break
    else:
        if liABplus:
            AB = liABplus.popleft()
            flag = False
            continue
        else:
            break

minus = 0
from itertools import combinations
for k in range(1, len(eqpair)+1):
    for item in combinations(eqpair, k):
        sgn = (-1)**k
        ideal = 1
        cnt = 0
        for i in item:
            cnt += i[0] + i[1]
            ideal *= bitlist[i[0]]-1
            ideal %= mod
            ideal *= bitlist[i[1]]-1
            ideal %= mod
        ideal *= bitlist[N-cnt]
        ideal %= mod
        ans += sgn*ideal
        ans %= mod
print(ans)

Submission status: Wrong Answer

Solution code:
N = int(input())
mod = 10 **9 + 7

def equal(item0, item1, delta = 10 ** (-18)):
    if abs(item0 - item1) < delta:
        return True
    else:
        return False
def bigger(item0, item1, delta = 10** (-18)):
    if item0 -item1 > delta:
        return True
    else:
        return False
bitlist = [1]
for k in range(N):
    bitlist.append(bitlist[-1]*2%mod)


liABplus = []
liBAplus = []
zero = 0
from bisect import insort
for _ in range(N):
    A, B = map(int, input().split())
    if A*B == 0:
        if A == 0 and B == 0:
            zero += 1
        elif A == 0 and B != 0:
            liABplus = [0] + liABplus
        else:
            liBAplus = [0] + liBAplus
    elif A*B > 0:
        insort(liABplus, A/B)
    else:
        insort(liBAplus, -B/A)
def make_count(list):
    k = 0
    lis = []
    while k < len(list):
        cnt = 1
        while k+1 < len(list):
            if equal(list[k], list[k+1]):
                cnt += 1
                k += 1
                continue
            else:
                break
        lis.append([list[k], cnt])
        k += 1
    return lis

liABplus = make_count(liABplus)
liBAplus = make_count(liBAplus)
N -= zero
from collections import deque
liABplus = deque(liABplus)
liBAplus = deque(liBAplus)
ans = bitlist[N]-1 #all pattern
flag = True
eqpair = []
while liABplus and liBAplus:
    if flag:
        AB = liABplus.popleft()
        BA = liBAplus.popleft()
    if equal(AB[0], BA[0]):
        eqpair.append([AB[1], BA[1]])
        if liABplus and liBAplus:
            flag = True
            continue
        else:
            break
    elif bigger(AB[0], BA[0]):
        if liBAplus:
            BA = liBAplus.popleft()
            flag = False
            continue
        else:
            break
    else:
        if liABplus:
            AB = liABplus.popleft()
            flag = False
            continue
        else:
            break

minus = 0
from itertools import combinations
for k in range(1, len(eqpair)+1):
    for item in combinations(eqpair, k):
        sgn = (-1)**k
        ideal = 1
        cnt = 0
        for i in item:
            cnt += i[0] + i[1]
            ideal *= bitlist[i[0]]-1
            ideal %= mod
            ideal *= bitlist[i[1]]-1
            ideal %= mod
        ideal *= bitlist[N-cnt]
        ideal %= mod
        ans += sgn*ideal
        ans %= mod
print(ans)

Submission status: Wrong Answer

Solution code:
import fractions
import sys
sys.setrecursionlimit(10**9)

MOD = 1000000007  # type: int
INF=10**20

class Counter:
    def __init__(self):
        self.dict = {}

    def add(self,x):
        if x in self.dict: self.dict[x] += 1
        else: self.dict[x] = 1

    def decrement(self,x):
        self.dict[x] -= 1
        if self.dict[x] <= 0:
            del self.dict[x]

    def get_dict(self):
        return self.dict



class Counting():
    def __init__(self,maxim,mod):
        maxim += 1

        self.mod = mod
        self.fact = [0]*maxim
        self.fact[0] = 1
        for i in range(1,maxim):
            self.fact[i] = self.fact[i-1] * i % mod

        self.invfact = [0]*maxim
        self.invfact[maxim-1] = pow(self.fact[maxim-1],mod-2,mod)
        for i in reversed(range(maxim-1)):
            self.invfact[i] = self.invfact[i+1] * (i+1) % mod


    def nCk(self,n,r):
        if n < 0 or n < r: return 0
        return self.fact[n] * self.invfact[r] * self.invfact[n-r] % self.mod

    def nPk(self,n,r):
        if n < 0 or n < r: return 0
        return self.fact[n] * self.invfact[n-r] % self.mod

        


def solve(N: int, A: "List[int]", B: "List[int]"):

    both_zero = 0
    a_zero = 0
    b_zero = 0
    
    counter = Counter()
    for i in range(N):
        a,b=A[i],B[i]   

        if a * b == 0:
            if a == 0 and b == 0:
                both_zero += 1
                continue
            elif a == 0:
                a,b = 0,1
            else:
                a,b = -1,0

        
        gcd = fractions.gcd(a,b)
        a //= gcd
        b //= gcd

        # (a,b): -はaの方に寄せる
        if a < 0 and b < 0:
            a *= -1
            b *= -1
        if a < 0 and b > 0:
            pass

        if a > 0 and b < 0:
            a *= -1
            b *= -1
        
        counter.add((a,b))

    
    seen = set()
    cannot = 0
    counter = counter.get_dict()

    ans = 1
    for e,count in counter.items():
        a,b = e
        if e in seen: continue
        # print(e)
    
        if a > 0:
            b *= -1
        else:
            a *= -1

        if (b,a) in seen: continue

        if (b,a) in counter:
            count2 = counter[(b,a)]

            ans *= pow(2,count,MOD) + pow(2,count2,MOD) - 1
        else:
            ans *= pow(2,count,MOD)
        
        ans %= MOD
        seen.add((b,a))
        # print(ans)
        
    # ans *= pow(2,a_zero,MOD) + pow(2,b_zero,MOD) - 1
    ans %= MOD

    ans += both_zero
    ans %= MOD

    ans -= 1
    print(ans)


    return

def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    A = [int()] * (N)  # type: "List[int]"
    B = [int()] * (N)  # type: "List[int]"
    for i in range(N):
        A[i] = int(next(tokens))
        B[i] = int(next(tokens))
    solve(N, A, B)



if __name__ == "__main__":
    main()

Submission status: Wrong Answer

Solution code:
import fractions
import sys
sys.setrecursionlimit(10**9)

MOD = 1000000007  # type: int
INF=10**20

class Counter:
    def __init__(self):
        self.dict = {}

    def add(self,x):
        if x in self.dict: self.dict[x] += 1
        else: self.dict[x] = 1

    def decrement(self,x):
        self.dict[x] -= 1
        if self.dict[x] <= 0:
            del self.dict[x]

    def get_dict(self):
        return self.dict



class Counting():
    def __init__(self,maxim,mod):
        maxim += 1

        self.mod = mod
        self.fact = [0]*maxim
        self.fact[0] = 1
        for i in range(1,maxim):
            self.fact[i] = self.fact[i-1] * i % mod

        self.invfact = [0]*maxim
        self.invfact[maxim-1] = pow(self.fact[maxim-1],mod-2,mod)
        for i in reversed(range(maxim-1)):
            self.invfact[i] = self.invfact[i+1] * (i+1) % mod


    def nCk(self,n,r):
        if n < 0 or n < r: return 0
        return self.fact[n] * self.invfact[r] * self.invfact[n-r] % self.mod

    def nPk(self,n,r):
        if n < 0 or n < r: return 0
        return self.fact[n] * self.invfact[n-r] % self.mod

        


def solve(N: int, A: "List[int]", B: "List[int]"):

    both_zero = 0
    a_zero = 0
    b_zero = 0
    
    counter = Counter()
    for i in range(N):
        a,b=A[i],B[i]   

        if a * b == 0:
            if a == 0 and b == 0:
                both_zero += 1
            elif a == 0:
                a_zero += 1
            else:
                b_zero += 1

            continue
        
        
        gcd = fractions.gcd(a,b)
        a //= gcd
        b //= gcd

        # (a,b): -はaの方に寄せる
        if a < 0 and b < 0:
            a *= -1
            b *= -1
        if a < 0 and b > 0:
            pass

        if a > 0 and b < 0:
            a *= -1
            b *= -1
        
        counter.add((a,b))

    
    seen = set()
    cannot = 0
    counter = counter.get_dict()

    ans = 1
    for e,count in counter.items():
        a,b = e
        if e in seen: continue
        # print(e)
    
        if a > 0:
            b *= -1
        else:
            a *= -1

        if (b,a) in seen: continue

        if (b,a) in counter:
            count2 = counter[(b,a)]

            ans *= pow(2,count,MOD) + pow(2,count2,MOD) - 1
        else:
            ans *= pow(2,count,MOD)
        
        ans %= MOD
        seen.add((b,a))
        # print(ans)
        
    ans *= pow(2,a_zero,MOD) + pow(2,b_zero,MOD) - 1
    ans %= MOD

    ans += both_zero
    ans %= MOD

    ans -= 1
    print(ans)


    return

def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    A = [int()] * (N)  # type: "List[int]"
    B = [int()] * (N)  # type: "List[int]"
    for i in range(N):
        A[i] = int(next(tokens))
        B[i] = int(next(tokens))
    solve(N, A, B)



if __name__ == "__main__":
    main()

Submission status: Wrong Answer

Solution code:
from collections import defaultdict
from math import gcd
N = int(input())
MOD = 10**9 + 7
L = defaultdict(lambda: [0,0])
zero = 0
for _ in range(N):
    A, B = map(int, input().split())
    if A==0: d=B
    elif B==0: d=A
    else: d=gcd(A,B)
    if d != 0:
        A, B = A//d, B//d
        if A<0: A, B = -A, -B
        if B>0: L[(A,B)][0] += 1
        else: L[(-B,A)][1] += 1
    else: zero += 1
res = 1
for x,y in L.values():
    res *= pow(2,x,MOD) + pow(2,y,MOD) -1
    res %= MOD
print(res + zero-1)

Submission status: Wrong Answer

Solution code:
from collections import defaultdict
from math import gcd
N = int(input())
MOD = 10**9 + 7
L = defaultdict(lambda: [0,0])
zero = 0
for _ in range(N):
    A, B = map(int, input().split())
    if A==0: d=B
    elif B==0: d=A
    else: d=gcd(A,B)
    if d != 0:
        A, B = A//d, B//d
        if A<0: A, B = -A, -B
        if B>0: L[(A,B)][0] += 1
        else: L[(-B,A)][1] += 1
    else: zero += 1
res = 1
print(L)
for x,y in L.values():
    res *= pow(2,x,MOD) + pow(2,y,MOD) -1
    res %= MOD
print(res + zero-1)

Submission status: Wrong Answer

Solution code:
from collections import defaultdict
from math import gcd
N = int(input())
MOD = 10**9 + 7
L = defaultdict(lambda: [0,0])
for _ in range(N):
    A, B = map(int, input().split())
    if A==0: d=B
    elif B==0: d=A
    else: d=gcd(A,B)
    if d != 0: A, B = A//d, B//d
    if A<0:
        A, B = -A, -B
    if B>0:
        L[(A,B)][0] += 1
    else:
        L[(-B,A)][1] += 1
res = 1
for x,y in L.values():
    res *= pow(2,x,MOD) + pow(2,y,MOD) -1
    res %= MOD
print(res-1)

Submission status: Wrong Answer

Solution code:
from collections import defaultdict
from math import gcd
N = int(input())
MOD = 10**9 + 7
L = defaultdict(lambda: [0,0])
for _ in range(N):
    A, B = map(int, input().split())
    if A==0: d=B
    elif B==0: d=A
    else: d=gcd(A,B)
    if d != 0: A, B = A//d, B//d
    if A<0:
        A, B = -A, -B
    if B>=0:
        L[(A,B)][0] += 1
    else:
        L[(-B,A)][1] += 1
res = 1
for x,y in L.values():
    res *= pow(2,x,MOD) + pow(2,y,MOD) -1
    res %= MOD
print(res-1)

Submission status: Wrong Answer

Solution code:
def numba_compile(numba_config):
    import os, sys
    if sys.argv[-1] == "ONLINE_JUDGE":
        from numba import njit
        from numba.pycc import CC
        cc = CC("my_module")
        for func, signature in numba_config:
            globals()[func.__name__] = njit(signature)(func)
            cc.export(func.__name__, signature)(func)
        cc.compile()
        exit()
    elif os.name == "posix":
        exec(f"from my_module import {','.join(func.__name__ for func, _ in numba_config)}")
        for func, _ in numba_config:
            globals()[func.__name__] = vars()[func.__name__]
    else:
        from numba import njit
        for func, signature in numba_config:
            globals()[func.__name__] = njit(signature, cache=True)(func)
        print("compiled!", file=sys.stderr)

import sys
import numpy as np
mod = 10**9+7
def pow_mod(base, exp):  # [pow_mod, "i8(i8,i8)"],
    # mod はグローバル変数を参照
    exp %= mod - 1
    res = 1
    while exp:
        if exp % 2:
            res = res * base % mod
        base = base * base % mod
        exp //= 2
    return res

def solve(N, AB):
    n = 0
    na = nb = nab = 0
    Cnt = {}
    for a, b in zip(AB[::2], AB[1::2]):
        if (a, b) == (0, 0):
            nab += 1
        elif a == 0:
            na += 1
        elif b == 0:
            nb += 1
        else:
            ab_fr = a * pow_mod(b, -1) % mod
            n += 1
            if ab_fr in Cnt:
                Cnt[ab_fr] += 1
            else:
                Cnt[ab_fr] = 1
            inv = -pow_mod(ab_fr, -1) % mod
            if inv not in Cnt:
                Cnt[inv] = 0
    ans = (pow_mod(2, na) + pow_mod(2, nb) - 1) % mod
    A = []
    for ab_fr, cnt in Cnt.items():
        cnt2 = Cnt[(-pow_mod(ab_fr, -1))%mod]
        p = pow_mod(2, cnt)
        p2 = pow_mod(2, cnt2)
        A.append((p + p2 - 1) % mod)
    A.sort()
    for a in A[::2]:
        ans = ans * a % mod
    ans += nab - 1
    return ans % mod

# numba_compile([
#     [pow_mod, "i8(i8,i8)"],
#     [solve, "i8(i8,i8[:])"],
# ])

def main():
    N = int(sys.stdin.buffer.readline())
    m = np.array(sys.stdin.buffer.read().split(), dtype=np.int64)
    ans = solve(N, m)
    print(ans)

main()

Submission status: Wrong Answer

Solution code:
def numba_compile(numba_config):
    import os, sys
    if sys.argv[-1] == "ONLINE_JUDGE":
        from numba import njit
        from numba.pycc import CC
        cc = CC("my_module")
        for func, signature in numba_config:
            globals()[func.__name__] = njit(signature)(func)
            cc.export(func.__name__, signature)(func)
        cc.compile()
        exit()
    elif os.name == "posix":
        exec(f"from my_module import {','.join(func.__name__ for func, _ in numba_config)}")
        for func, _ in numba_config:
            globals()[func.__name__] = vars()[func.__name__]
    else:
        from numba import njit
        for func, signature in numba_config:
            globals()[func.__name__] = njit(signature, cache=True)(func)
        print("compiled!", file=sys.stderr)

import sys
import numpy as np
mod = 10**9+7
def pow_mod(base, exp):  # [pow_mod, "i8(i8,i8)"],
    # mod はグローバル変数を参照
    exp %= mod - 1
    res = 1
    while exp:
        if exp % 2:
            res = res * base % mod
        base = base * base % mod
        exp //= 2
    return res

def solve(N, AB):
    n = 0
    na = nb = nab = 0
    Cnt = {}
    for a, b in zip(AB[::2], AB[1::2]):
        if (a, b) == (0, 0):
            nab += 1
        elif a == 0:
            na += 1
        elif b == 0:
            nb += 1
        else:
            ab_fr = a * pow_mod(b, -1) % mod
            n += 1
            if ab_fr in Cnt:
                Cnt[ab_fr] += 1
            else:
                Cnt[ab_fr] = 1
            inv = -pow_mod(ab_fr, -1) % mod
            if inv not in Cnt:
                Cnt[inv] = 0
    ans = (pow_mod(2, na) + pow_mod(2, nb) - 1) % mod
    A = []
    for ab_fr, cnt in Cnt.items():
        cnt2 = Cnt[(-pow_mod(ab_fr, -1))%mod]
        p = pow_mod(2, cnt)
        p2 = pow_mod(2, cnt2)
        A.append((p + p2 - 1) % mod)
    A.sort()
    for a in A[::2]:
        ans = ans * a % mod
    ans += nab - 1
    return ans % mod

numba_compile([
    [pow_mod, "i8(i8,i8)"],
    [solve, "i8(i8,i8[:])"],
])

def main():
    N = int(sys.stdin.buffer.readline())
    m = np.array(sys.stdin.buffer.read().split(), dtype=np.int64)
    ans = solve(N, m)
    print(ans)

main()