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 (Python):
mod = 1000000007

N = int(input())

pos = []
neg = []
zer = []
inf = []
sol = 0


NG = []

for i in range(N):
    a,b = map(int,input().split())
    if a*b > 0:
        pos.append((abs(a),abs(b)))
    elif a*b < 0:
        neg.append((-abs(a),abs(b)))
    elif a == 0 and b != 0:
        inf.append((0,1))
    elif a != 0 and b == 0:
        zer.append((1,0))
    else:
        sol += 1

NG.append((len(inf),len(zer)))
free = len(pos)+len(neg)




pos.sort(key=lambda x:(x[1]/x[0]))
neg.sort(key=lambda x:(x[1]/x[0]))

x = 0
y = 0


while (x < len(pos) and y < len(neg)):
    if pos[x][0]*neg[y][0]+pos[x][1]*neg[y][1] == 0:
        s = 1
        t = 1
        while x+1 < len(pos) and pos[x+1][0]*neg[y][0]+pos[x+1][1]*neg[y][1] == 0:
            x += 1
            s += 1
        while y+1 < len(neg) and pos[x][0]*neg[y+1][0]+pos[x][1]*neg[y+1][1] == 0:
            y += 1
            t += 1
        NG.append((s,t))
        x += 1
        y += 1
        free -= (s+t)
        continue


    if x >= len(pos)-1 and y >= len(neg)-1:
        break

    elif y+1 < len(neg) and pos[x][0]*neg[y][0]+pos[x][1]*neg[y][1] > 0:
        y += 1
    elif x+1 < len(pos) and pos[x][0]*neg[y][0]+pos[x][1]*neg[y][1] < 0:
        x += 1
    elif x >= len(pos)-1:
        y += 1
    elif y >= len(neg)-1:
        x += 1

ans = pow(2,free,mod)

for s,t in NG:
    
    ans *= pow(2,s,mod)-1 +pow(2,t,mod)-1 +1
    ans %= mod





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

Solution (Python):
import sys
from math import gcd
from collections import defaultdict


def I(): return int(sys.stdin.readline().rstrip())
def MI(): return map(int,sys.stdin.readline().rstrip().split())


N = I()
mod = 10**9+7
plus = defaultdict(int)
minus = defaultdict(int)
flag = defaultdict(int)
A_zero,B_zero = 0,0
zero_zero = 0
for i in range(N):
    a,b = MI()
    if a == b == 0:
        zero_zero += 1
    elif a == 0:
        A_zero += 1
    elif b == 0:
        B_zero += 1
    else:
        if a < 0:
            a,b = -a,-b
        a,b = a//gcd(a,b),b//gcd(a,b)
        if b > 0:
            plus[(a,b)] += 1
        else:
            minus[(a,b)] += 1
            flag[(a,b)] = 0

ans = 1

for a,b in plus.keys():
    ans *= pow(2,plus[(a,b)],mod)+pow(2,minus[(b,-a)],mod)-1
    ans %= mod
    flag[(b,-a)] = 1

for key in minus.keys():
    if flag[key] == 0:
        ans *= pow(2,minus[key],mod)
        ans %= mod

ans *= pow(2,A_zero,mod)+pow(2,B_zero,mod)-1
ans %= mod

ans += zero_zero-1
ans %= mod

print(ans)

Solution (Python):
import sys
from math import gcd
from collections import defaultdict

sys.setrecursionlimit(10**7)
def I(): return int(sys.stdin.readline().rstrip())
def MI(): return map(int,sys.stdin.readline().rstrip().split())
def LI(): return list(map(int,sys.stdin.readline().rstrip().split()))  
def LI2(): return list(map(int,sys.stdin.readline().rstrip()))  
def S(): return sys.stdin.readline().rstrip()
def LS(): return list(sys.stdin.readline().rstrip().split())  
def LS2(): return list(sys.stdin.readline().rstrip())  


N = I()
mod = 10**9+7
plus = defaultdict(int)
minus = defaultdict(int)
flag = defaultdict(int)
A_zero,B_zero = 0,0
zero_zero = 0
for i in range(N):
    a,b = MI()
    if a == b == 0:
        zero_zero += 1
    elif a == 0:
        A_zero += 1
    elif b == 0:
        B_zero += 1
    else:
        if a < 0:
            a,b = -a,-b
        a,b = a//gcd(a,b),b//gcd(a,b)
        if b > 0:
            plus[(a,b)] += 1
        else:
            minus[(a,b)] += 1
            flag[(a,b)] = 1

ans = 1

for a,b in plus.keys():
    ans *= pow(2,plus[(a,b)],mod)+pow(2,minus[(b,-a)],mod)-1
    ans %= mod
    flag[(b,-a)] = 0

for key in minus.keys():
    if flag[key] == 1:
        ans *= pow(2,minus[key],mod)
        ans %= mod

ans *= pow(2,A_zero,mod)+pow(2,B_zero,mod)-1
ans %= mod

ans += zero_zero-1
ans %= mod

print(ans)

Solution (Python):
MOD = 10 ** 9 + 7
from math import gcd
from collections import defaultdict

n = int(input())
plus = defaultdict(int)
minus = defaultdict(int)
zero = [0, 0, 0]
for _ in range(n):
    a, b = map(int, input().split())
    if a * b == 0:
        if a == b == 0:
            zero[0] += 1
        elif a == 0:
            zero[1] += 1
        else:
            zero[2] += 1
        continue
    g = gcd(a, b)
    a //= g
    b //= g
    if a < 0:
        a *= -1
        b *= -1
    if b >= 0:
        s = str(a) + "-" + str(b)
        plus[s] += 1
    else:
        s = str(-b) + "-" + str(a)
        minus[s] += 1

pm = [[zero[1], zero[2]]]
cnt = sum(zero)
for key, value in plus.items():
    if minus[key] != 0:
        pm.append([value, minus[key]])
        cnt += value + minus[key]
        
ans = pow(2, n - cnt, MOD)

for p, m in pm:
    ans *= (pow(2, p, MOD) + pow(2, m, MOD) - 1)
    ans %= MOD
ans += zero[0] - 1
ans %= MOD
print(ans)

Solution (Python):
from collections import defaultdict, deque
import math

kMod = 1000000007

N = int(input())
key2count = defaultdict(lambda: [0, 0])

for _ in range(N):
    a, b = map(int, input().split())
    g = math.gcd(a, b)
    if a < 0 or a == 0 and b < 0:
        a, b = -a, -b
    if g > 0:
        a, b = a//g, b//g
    idx = 0
    if b <= 0:
        idx = 1
        a, b = -b, a
    key2count[(a, b)][idx] += 1

ans = 1
for key, val in key2count.items():
    if key == (0, 0):
        continue
    plus, minus = val
    ans *= (pow(2, plus, kMod) + pow(2, minus, kMod)-1)
    ans %= kMod

ans += sum(key2count[(0, 0)])

print((ans + kMod-1) % kMod)

Solution (Python):
from collections import defaultdict
from math import gcd as g
n = int(input())
mod = 10**9+7
sardines = set()
Ddic = defaultdict(int)
ans = 1
zcount = 0
for i in range(n):
  a,b = map(int,input().split())
  if a == 0 and b == 0:
    zcount += 1
    continue

  if a == 0:
    Ddic[(0,1)] += 1
    sardines.add((0,1))
    continue

  if b == 0:
    sardines.add((1,0))
    Ddic[(1,0)] += 1
    continue

  A,B = abs(a),abs(b)
  G = g(A,B)
  a //= G
  b //= G

  if b < 0:
    a = -a
    b = -b

  Ddic[(a,b)] += 1
  sardines.add((a,b))

for i in sardines:
  if i == (0,0) or (i[0] <= 0 and Ddic[(i[1],-i[0])] != 0):continue
  if i[0] <= 0:
    ans *= (2**Ddic[i] + 2**(Ddic[(i[1],-i[0])]))-1
  else:
    ans *= (2**Ddic[i] + 2**(Ddic[(-i[1],i[0])]))-1

  ans %= mod
print((ans+zcount-1)%mod)

Solution (Python):
import math
n = int(input())
from collections import defaultdict
d = defaultdict(list)
s = set()
zc = 0
for i in range(n):
    a,b = map(int, input().split())
    g = math.gcd(a,b)
    if g!=0:
        a //= g; b //= g
        if a<0:
            a,b = -a, -b
        elif a==0 and b<0:
            b *= -1
        d[a,b].append(i)
    if a==b==0:
        zc += 1
v = 1
s = set()
M = 10**9+7
for (a,b),val in d.items():
    aa,bb = b,-a
    if aa<0:
        aa,bb = -aa, -bb
    elif aa==0 and bb<0:
        bb *= -1
    if (a,b) in s or (aa,bb) in s:
        continue
    if (aa,bb) in d.keys():
        v *= (pow(2, len(val), M) + pow(2, len(d[aa,bb]), M) - 1)
    else:
        v *= pow(2, len(val), M)
    v %= M
    s.add((a,b))
    s.add((aa,bb))
v -= 1
v += zc
print(v%M)

Solution (Python):
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())
zero = 0
iwasies = []
for i in range(N):
	A, B = map(int, input().split())
	if A == 0 and B == 0:
		zero += 1
	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 + zero - 1) % MOD)

Solution (Python):
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)%MOD)

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

MOD = 1000000007  
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

        
        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
        
    
        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))
        
        
    
    ans %= MOD

    ans += both_zero - 1
    ans %= MOD

    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))  
    A = [int()] * (N)  
    B = [int()] * (N)  
    for i in range(N):
        A[i] = int(next(tokens))
        B[i] = int(next(tokens))
    solve(N, A, B)



if __name__ == "__main__":
    main()

Solution (Python):
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)%MOD)

Solution (Python):
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
from math import gcd
mod = 10**9+7
def pow_mod(base, exp):  
    
    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:
            if b < 0:
                a, b = -a, -b
            g = gcd(a, b)
            a //= g
            b //= g
            ab_fr = (a, b)
            n += 1
            if ab_fr in Cnt:
                Cnt[ab_fr] += 1
            else:
                Cnt[ab_fr] = 1
            inv = (-b, a) if a > 0 else (b, -a)
            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():
        a, b = ab_fr
        inv = (-b, a) if a > 0 else (b, -a)
        cnt2 = Cnt[inv]
        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()

Solution (Python):
import sys
import math
from collections import defaultdict
from collections import deque

sys.setrecursionlimit(1000000)
MOD = 10 ** 9 + 7
input = lambda: sys.stdin.readline().strip()
NI = lambda: int(input())
NMI = lambda: map(int, input().split())
NLI = lambda: list(NMI())
SI = lambda: input()



class MyFraction:

    def __init__(self, a, b):
        assert b != 0, "分母が0です"

        if b < 0:
            a, b = -a, -b
        if a == 0:
            b = 1

        g = math.gcd(a, b)
        self.numerator = a // g
        self.denominator = b // g

    def __str__(self):
        return "{0}/{1}".format(self.numerator, self.denominator)


def main():
    N = NI()
    AB = defaultdict(int)
    Y, Z = 0, 0
    for i in range(N):
        a, b = NMI()
        if a == b == 0:
            Z += 1
            continue
        if b == 0:
            Y += 1
            continue

        if str(MyFraction(a, b)) in AB:
            AB[str(MyFraction(a, b))] += 1
        else:
            AB[str(MyFraction(a, b))] = 1

    C = defaultdict(lambda: ())
    ans = 1
    flag = True
    for ab, k in list(AB.items()):
        a, b = ab.split("/")
        a = int(a)
        b = int(b)
        if a > 0:
            if str(MyFraction(-b, a)) in AB:
                t = AB[str(MyFraction(-b, a))]
            else:
                t = 0
        elif a < 0:
            if str(MyFraction(b, -a)) in AB:
                continue
            t = 0
        else:
            flag = False
            t = Y
        C[(a, b)] = (k, t)

    for k, t in list(C.values()):
        tmp = pow(2, k, MOD) + pow(2, t, MOD) - 1
        ans = ans * tmp % MOD

    if flag:
        tmp = pow(2, Y, MOD)
        ans = ans * tmp % MOD
    print((ans + Z - 1)%MOD)


if __name__ == "__main__":
    main()

Solution (Python):
from collections import defaultdict
from itertools import groupby, accumulate, product, permutations, combinations
from math import gcd

def reduction(x,y):
    g = gcd(x,y)
    return abs(x)//g,abs(y)//g

def solve():
    mod = 10**9+7
    dplus = defaultdict(lambda: 0)
    dminus = defaultdict(lambda: 0)
    N = int(input())
    x0,y0,xy0 = 0,0,0
    for i in range(N):
        x,y = map(int, input().split())
        if x==0 and y==0:
            xy0 += 1
        elif x==0 and y!=0:
            x0 += 1
        elif y==0:
            y0 += 1
        elif x*y>0:
            dplus[reduction(x,y)] += 1
        else:
            dminus[reduction(-y,x)] += 1
    ans = pow(2,x0,mod)+pow(2,y0,mod)-1
    other = N-x0-y0-xy0
    for k,v in dplus.items():
        ans *= pow(2,dminus[k],mod)+pow(2,v,mod)-1
        other -= dminus[k]+v
    ans *= pow(2,other,mod)
    ans += xy0-1
    ans %= mod
    return ans
print(solve())

Solution (Python):
from operator import itemgetter
from math import gcd
from collections import Counter

N = int(input())
mod = int(1e9+7)

zero = 0
P = {}
for i in range(N):
  a,b = list(map(int, input().split()))
  if a == 0 and b == 0:
    zero += 1
    continue
  g = gcd(a,b)
  a,b = a//g, b//g
  if b < 0:
    a,b = -a,-b
  if b == 0 and a < 0:
    a,b = -a,b  
  
  rot90 = a<=0
  if rot90:
    a,b = b,-a
  
  if not (abs(a),b) in P:
    P[(a,b)] = [0,0]
  if not rot90 :
    P[(a,b)][0] += 1
  else:
    P[(a,b)][1] += 1
    
ans = 1
for k,v in P.items():
  
  s,t = v
  wk = 1 + pow(2,s,mod) - 1 + pow(2,t,mod) - 1
  ans *= wk
  ans %= mod
  
ans += zero

print((ans - 1) % mod)

Solution (Python):
from operator import itemgetter
from math import gcd
from collections import Counter

N = int(input())
mod = int(1e9+7)

zero = 0
P = {}
for i in range(N):
  a,b = list(map(int, input().split()))
  if a == 0 and b == 0:
    zero += 1
    continue
  g = gcd(a,b)
  a,b = a//g, b//g
  if b < 0:
    a,b = -a,-b
  if b == 0 and a < 0:
    a,b = -a,b  
  
  rot90 = a<=0
  if rot90:
    a,b = b,-a
  
  if not (abs(a),b) in P:
    P[(a,b)] = [0,0]
  if not rot90 :
    P[(a,b)][0] += 1
  else:
    P[(a,b)][1] += 1
    
ans = 1
for k,v in P.items():
  
  s,t = v
  wk = 1 + pow(2,s,mod) - 1 + pow(2,t,mod) - 1
  ans *= wk
  ans %= mod
  
ans += zero

print((ans - 1) % mod)

Solution (Python):
import sys
import itertools

import time
import math
import heapq
from collections import defaultdict
from collections import Counter
sys.setrecursionlimit(10 ** 7)
 
INF = 10 ** 18
MOD = 10 ** 9 + 7
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines



def gcd(a, b):
    if b == 0:
        return a
    return gcd(b, a % b)

N = int(input())
zero = 0
d = defaultdict(lambda: [0, 0])
for i in range(N):
    x, y = map(int, input().split())
    if x == 0 and y == 0:
        zero += 1
        continue
    g = gcd(x, y)
    x //= g
    y //= g
    if y < 0:
        x = -x
        y = -y
    if y == 0 and x < 0:
        x = -x
    rotate = x <= 0
    if rotate:
        x, y = y, -x
        d[(x, y)][0] += 1
    else:
        d[(x, y)][1] += 1

ans = 1
for v in d.values():
    now = 1
    now += (2 ** v[0] - 1) % MOD
    now += (2 ** v[1] - 1) % MOD
    ans *= now
    ans %= MOD
print((ans - 1 + zero) % MOD)

Solution (Python):
import sys
import itertools

import time
import math
import heapq
from collections import defaultdict
from collections import Counter
sys.setrecursionlimit(10 ** 7)
 
INF = 10 ** 18
MOD = 10 ** 9 + 7
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines



def gcd(a, b):
    if b == 0:
        return a
    return gcd(b, a % b)

N = int(input())
zero = 0
d = defaultdict(lambda: [0, 0])
for i in range(N):
    x, y = map(int, input().split())
    if x == 0 and y == 0:
        zero += 1
        continue
    g = gcd(x, y)
    x //= g
    y //= g
    if y < 0:
        x = -x
        y = -y
    if y == 0 and x < 0:
        x = -x
    rotate = x <= 0
    if rotate:
        x, y = y, -x
        d[(x, y)][0] += 1
    else:
        d[(x, y)][1] += 1

ans = 1
for v in d.values():
    now = 1
    now += (2 ** v[0] - 1) % MOD
    now += (2 ** v[1] - 1) % MOD
    ans *= now
    ans %= MOD
print((ans - 1 + zero) % MOD)

Solution (Python):
from math import gcd

N = int(input())
X = [list(map(int, input().split())) for _ in range(N)]

d = {}
for a, b in X:
    if a == b == 0:
        pass
    elif a == 0:
        b = 1
    elif b == 0:
        a = 1
    else:
        v = gcd(a, b)
        a //= v
        b //= v

    if a != 0 and a * b >= 0:
        pair = (abs(a), abs(b))
        if pair not in d:
            d[pair] = [0, 0]
        d[pair][0] += 1
    else:
        pair = (abs(b), abs(a))
        if pair not in d:
            d[pair] = [0, 0]
        d[pair][1] += 1

MOD = 10 ** 9 + 7
zero = 0
ans = 1
for p in d:
    if p == (0, 0):
        zero = d[p][1]
    else:
        a, b = d[p]
        ans *= pow(2, a, MOD) + pow(2, b, MOD) - 1
        ans %= MOD

print((ans + zero - 1) % MOD)

Solution (Python):

from math import gcd

N = int(input())
X = [list(map(int, input().split())) for _ in range(N)]

d = {}
for a, b in X:
    if a == b == 0:
        pass
    elif a == 0:
        if b > 0:
            b = 1
        else:
            b = -1
    elif b == 0:
        if a > 0:
            a = 1
        else:
            a = -1
    else:
        v = gcd(a, b)
        a //= v
        b //= v

    if a != 0 and a * b >= 0:
        pair = (abs(a), abs(b))
        if pair not in d:
            d[pair] = [0, 0]
        d[pair][0] += 1
    else:
        pair = (abs(b), abs(a))
        if pair not in d:
            d[pair] = [0, 0]
        d[pair][1] += 1

MOD = 10 ** 9 + 7
zero = 0
ans = 1
for p in d:
    if p == (0, 0):
        zero = d[p][1]
    else:
        a, b = d[p]
        ans *= pow(2, a, MOD) + pow(2, b, MOD) - 1
        ans %= MOD

print((ans + zero - 1) % MOD)

Solution (Python):
from math import gcd
from collections import defaultdict as d
n=int(input())
m=10**9+7
s=d(lambda:[0,0])
p=-1
for i in range(n):
    a,b=map(int,input().split())
    if a==b==0:p+=1
    else:
        g=gcd(a,b)
        a=a//g
        b=b//g
        if a<0 or a==0<b:a,b=-a,-b
        if b<0:s[(-b,a)][1]+=1
        else:s[(a,b)][0]+=1
q=1
for i in s:
    k,l=s[i]
    q=q*(pow(2,k,m)+pow(2,l,m)-1)%m
print((q+p)%m)

Solution (Python):
from math import gcd
N=int(input())
a,b,g=0,0,0
X=[]
zeroandzero=0
D=dict()
for i in range(N):
  a,b=map(int,input().split())
  if a==b==0:
    zeroandzero+=1
    N-=1
    continue
  g=gcd(a,b)
  a//=g
  b//=g
  if b<0:
    a,b=-a,-b
  D[(a,b)]=D.get((a,b),0)+1
E=dict()
K=list(D.keys())
mod=10**9+7
inv2=(mod+1)//2
P=pow(2,N,mod)
for i in range(len(K)):
  if E.get(K[i],0):
    continue
  g=list(K[i])
  if g[0]<0:
    g=(K[i][1],-K[i][0])
  else:
    g=(-K[i][1],K[i][0])
  E[g]=1
  g=(D[K[i]],D.get(g,0))
  if g[1]:
    P=P*pow(inv2,g[0]+g[1],mod)*(pow(2,g[0],mod)+pow(2,g[1],mod)-1)%mod
print((P-1+zeroandzero)%mod)

Solution (Python):
N=int(input())
AB=[list(map(int,input().split())) for i in range(N)]
from collections import defaultdict
d=defaultdict(int)
d2=defaultdict(int)
a0=0
b0=0
c0=0
from math import gcd
for a,b in AB:
    if a==b==0:
        c0+=1
    elif a==0:
        a0+=1
    elif b==0:
        b0+=1
    else:
        if a<0:
            a,b=-a,-b
        g=gcd(a,b)
        a,b=a//g,b//g
        if b>0:
            d[(a,b)]+=1
        else:
            d2[(-b,a)]+=1
m=10**9+7
a=1
for k,v in d.items():
    if k in d2:
        a=a*(pow(2,v,m)+pow(2,d2[k],m)-1)%m
    else:
        a=a*pow(2,v,m)%m
for k,v in d2.items():
    if k not in d:
        a=a*pow(2,v,m)%m
print((a*(pow(2,a0,m)+pow(2,b0,m)-1)-1+c0)%m)

Solution (Python):

from math import gcd
from collections import defaultdict

N = int(input())
X = [list(map(int, input().split())) for _ in range(N)]

d = {}
for a, b in X:
    if a == b == 0:
        pass
    elif a == 0:
        if b > 0:
            b = 1
        else:
            b = -1
    elif b == 0:
        if a > 0:
            a = 1
        else:
            a = -1
    else:
        v = gcd(a, b)
        a //= v
        b //= v

    if a != 0 and a * b >= 0:
        pair = (abs(a), abs(b))
        if pair not in d:
            d[pair] = [0, 0]
        d[pair][0] += 1
    else:
        pair = (abs(b), abs(a))
        if pair not in d:
            d[pair] = [0, 0]
        d[pair][1] += 1

MOD = 10 ** 9 + 7
zero = 0
ans = 1
for p in d:
    if p == (0, 0):
        zero = d[p][1]
    else:
        a, b = d[p]
        ans *= pow(2, a, MOD) + pow(2, b, MOD) - 1
        ans %= MOD

print((ans + zero - 1) % MOD)

Solution (Python):

from collections import defaultdict, Counter
from itertools import product, groupby, count, permutations, combinations
from math import pi, sqrt
from collections import deque
from bisect import bisect, bisect_left, bisect_right
from string import ascii_lowercase
from functools import lru_cache
from fractions import Fraction
import sys
sys.setrecursionlimit(10000)
INF = float("inf")
YES, Yes, yes, NO, No, no = "YES", "Yes", "yes", "NO", "No", "no"
dy4, dx4 = [0, 1, 0, -1], [1, 0, -1, 0]
dy8, dx8 = [0, -1, 0, 1, 1, -1, -1, 1], [1, 0, -1, 0, 1, 1, -1, -1]


def inside(y, x, H, W):
    return 0 <= y < H and 0 <= x < W


def ceil(a, b):
    return (a + b - 1) // b


def sum_of_arithmetic_progression(s, d, n):
    return n * (2 * s + (n - 1) * d) // 2


def gcd(a, b):
    if b == 0:
        return a
    return gcd(b, a % b)


def lcm(a, b):
    g = gcd(a, b)
    return a / g * b


MOD = 1000000007


def func(v1, v2):
    ans = 1
    ans += pow(2, v1, MOD) - 1
    ans += pow(2, v2, MOD) - 1

    return ans % MOD


def solve():
    N = int(input())

    num_zero = 0

    d = defaultdict(lambda: [0, 0])
    for _ in range(N):
        A, B = map(int, input().split())
        if A == 0 and B == 0:
            num_zero += 1
            continue
        elif A == 0:
            d[(0, 0)][0] += 1
        elif B == 0:
            d[(0, 0)][1] += 1
        else:
            g = gcd(abs(A), abs(B))
            A //= g
            B //= g
            if B > 0:
                if A > 0:
                    d[(A, B)][1] += 1
                else:
                    d[(B, -A)][0] += 1
            else:
                if A < 0:
                    d[(-A, -B)][1] += 1
                else:
                    d[(-B, A)][0] += 1

    ans = 1
    for k, v in d.items():
        ans *= func(v[0], v[1])
        ans %= MOD

    print((ans + num_zero + MOD - 1) % MOD)


def main():
    solve()


if __name__ == '__main__':
    main()

Solution (Python):


from collections import defaultdict
from math import gcd
N = int(input())
MOD = 10**9 + 7
d = defaultdict(lambda: [0, 0])
zeros = 0
for _ in range(N):
    x, y = map(int, input().split())
    if x == 0 and y == 0:
        zeros += 1
    elif x == 0:
        d[(0, 0)][0] += 1
    elif y == 0:
        d[(0, 0)][1] += 1
    else:
        if y < 0:
            x = -x
            y = -y
        g = gcd(abs(x), abs(y))
        x //= g
        y //= g
        if x < 0:
            d[(y, -x)][0] += 1
        else:
            d[(x, y)][1] += 1
ans = 1
for k, v in d.items():
    ans *= pow(2, v[0], MOD)+pow(2, v[1], MOD)-1
    ans %= MOD
ans = (ans + zeros - 1) % MOD  
print(ans)

Solution (Python):

import sys, io, os, re
import bisect
from pprint import pprint
from math import sin, cos, pi, radians, sqrt, floor, ceil
from copy import copy, deepcopy
from collections import deque, defaultdict
from fractions import gcd
from functools import reduce

def array1(n): return [0] * n
def array2(n, m): return [[0] * m for x in range(n)]
def array3(n, m, l): return [[[0] * l for y in xrange(m)] for x in xrange(n)]

n1 = lambda: int(sys.stdin.readline().strip())
nn = lambda: list(map(int, sys.stdin.readline().strip().split()))
f1 = lambda: float(sys.stdin.readline().strip())
fn = lambda: list(map(float, sys.stdin.readline().strip().split()))
s1 = lambda: sys.stdin.readline().strip()
sn = lambda: list(sys.stdin.readline().strip().split())
nl = lambda n: [n1() for _ in range(n)]
fl = lambda n: [f1() for _ in range(n)]
sl = lambda n: [s1() for _ in range(n)]
nm = lambda n: [nn() for _ in range(n)]
fm = lambda n: [fn() for _ in range(n)]
sm = lambda n: [sn() for _ in range(n)]

mod = 1000000007

N = n1()
(A, B) = ([], [])
for i in range(N):
    a, b = nn()
    g = gcd(a, b)
    if g != 0: a //= g; b //=g
    A.append(a)
    B.append(b)

d = defaultdict(int)
for i in range(N):
    d[(A[i], B[i])] += 1

ans = 1
n = 0
if (0, 0) in d:
    n = d.pop((0, 0))

while len(d) > 0:
    
    (x, y), n1 = d.popitem()
    if y < 0: x *= -1; y *= -1

    n2 = 0
    if (y, -x) in d: n2 += d.pop((y, -x))
    if (-y, x) in d: n2 += d.pop((-y, x))

    ans = (ans * ((pow(2,n1,mod) -1 + pow(2,n2,mod) - 1) % mod + 1)) % mod

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

Solution (Python):
import sys

readline = sys.stdin.readline
MOD = 10 ** 9 + 7
INF = float('INF')
sys.setrecursionlimit(10 ** 5)


def main():
    import fractions
    import math
    from collections import Counter
    n = int(readline())
    counter = Counter()
    a0, b0 = 0, 0
    lonely = 0

    for i in range(n):
        a, b = map(int, readline().split())
        if a == 0 and b == 0:
            lonely += 1
        elif a == 0:
            a0 += 1
        elif b == 0:
            b0 += 1
        else:
            fr = fractions.Fraction(a, b)
            counter[(fr.numerator, fr.denominator)] += 1

    ans = 1  
    keys = list(counter.keys())
    for key in keys:
        nm1, dn1 = key[0], key[1]
        cnt1 = counter[(nm1, dn1)]
        nm2, dn2 = -(nm1 // abs(nm1)) * dn1, abs(nm1)
        cnt2 = counter[(nm2, dn2)]
        ans = ans * ((pow(2, cnt1, MOD) - 1) + (pow(2, cnt2, MOD) - 1) + 1)
        ans %= MOD
        counter[(nm1, dn1)] = 0
        counter[(nm2, dn2)] = 0

    ans *= ((pow(2, a0, MOD) - 1) + (pow(2, b0, MOD) - 1) + 1)
    ans %= MOD
    ans += lonely
    ans -= 1
    ans %= MOD

    print(ans)


if __name__ == '__main__':
    main()