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: Runtime Error

Solution code:
import math
import collections
from collections import defaultdict

N = int(input())
iwa = []
mod = 10**9+7

for i in range(N):
    a, b = map(int,input().split())
    if a == 0 and b == 0:
        continue
    elif b == 0:
        iwa.appned((1,0))
    elif a == 0:
        iwa.append((0,1))
    elif b > 0:
        c = math.gcd(a,b)
        iwa.append((a/c, b/c))#bは正
    else:
        c = math.gcd(a,b)
        iwa.append((-a/c, -b/c))#bは正
        
S = set(iwa)
I = collections.Counter(iwa)
#print(I)
jdg = defaultdict(int)

ans = 1
for i in S:
    if jdg[i] == 1:
        continue
    elif i == (1,0) or i == (0,1):
        k = I[(1,0)]
        l = I[(0,1)]
        if min(k,l) == 0:
            ans *= pow(2,max(l,k),mod)
        else:
            ans *= (pow(2,l,mod)-1) + (pow(2,k,mod)-1)+1
        jdg[(1,0)] = 1
        jdg[(0,1)] = 1
    else:
        k = I[i]
        a, b = i
        if a < 0:
            l = I[(b,-a)]
            jdg[(b, -a)] = 1
        else:
            l = I[(-b,a)]
            jdg[(-b,a)] = 1
        if min(l,k) == 0:
            ans *= pow(2,max(l,k),mod)
        else:
            ans *= (pow(2,l,mod)-1) + (pow(2,k,mod)-1)+1
        jdg[i] = 1
print(ans-1)

Submission status: Runtime Error

Solution code:
import math
import collections
from collections import defaultdict

N = int(input())
iwa = []
mod = 10**9+7

for i in range(N):
    a, b = map(int,input().split())
    if a == 0 and b == 0:
        continue
    elif b == 0:
        iwa,appned((1,0))
    elif a == 0:
        iwa.append((0,1))
    elif b > 0:
        c = math.gcd(a,b)
        iwa.append((a/c, b/c))#bは正
    else:
        c = math.gcd(a,b)
        iwa.append((-a/c, -b/c))#bは正
        
S = set(iwa)
I = collections.Counter(iwa)
#print(I)
jdg = defaultdict(int)

ans = 1
for i in S:
    if jdg[i] == 1:
        continue
    elif i == (1,0) or i == (0,1):
        k = I[(1,0)]
        l = I[(0,1)]
        if min(k,l) == 0:
            ans *= pow(2,max(l,k),mod)
        else:
            ans *= (pow(2,l,mod)-1) + (pow(2,k,mod)-1)+1
        jdg[(1,0)] = 1
        jdg[(0,1)] = 1
    else:
        k = I[i]
        a, b = i
        if a < 0:
            l = I[(b,-a)]
            jdg[(b, -a)] = 1
        else:
            l = I[(-b,a)]
            jdg[(-b,a)] = 1
        if min(l,k) == 0:
            ans *= pow(2,max(l,k),mod)
        else:
            ans *= (pow(2,l,mod)-1) + (pow(2,k,mod)-1)+1
        jdg[i] = 1
print(ans-1)

Submission status: Runtime Error

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

iwashi01 = 0
iwashi10 = 0
iwashi00 = 0
iwashi = dict()
for i in range(N):
    a, b = map(int, input().split())
    g = math.gcd(abs(a), abs(b))
    a //= g; b //= g
    if a == 0 and b == 0:
        iwashi00 += 1
    elif a == 0:
        iwashi01 += 1
    elif b == 0:
        iwashi10 += 1            
    else:
        if a > 0 and b > 0:
            iwashi.setdefault((a, b), [0, 0])
            iwashi[(a, b)][0] += 1
        elif a < 0 and b < 0:
            a *= -1
            b *= -1
            iwashi.setdefault((a, b), [0, 0])
            iwashi[(a, b)][0] += 1
        elif a > 0 and b < 0:
            a, b = -b, a
            iwashi.setdefault((a, b), [0, 0])
            iwashi[(a, b)][1] += 1
        elif a < 0 and b > 0:
            a *= -1
            b *= -1
            a, b = -b, a
            iwashi.setdefault((a, b), [0, 0])
            iwashi[(a, b)][1] += 1

r = 2**iwashi01 % mod - 1 + 2**iwashi10 % mod - 1 + 1
for s, t in iwashi.values():
    r *= 2**s % mod -1 + 2**t % mod -1 + 1
    r %= mod
print(r + iwashi00 - 1)

Submission status: Runtime Error

Solution code:
import math
mod = 10**9+7
N = int(input())
 
iwashi01 = 0
iwashi10 = 0
iwashi00 = 0
iwashi = dict()
for i in range(N):
    a, b = map(int, input().split())
    g = math.gcd(abs(a), abs(b))
    a //= g; b //= g
    if a == 0 and b == 0:
        iwashi00 += 1
    elif a == 0:
        iwashi01 += 1
    elif b == 0:
        iwashi10 += 1            
    else:
        if a*b > 0:
            if a < 0 and b < 0:
                a *= -1
                b *= -1
            iwashi.setdefault((a, b), [0, 0])
            iwashi[(a, b)][0] += 1
        if a*b < 0:
            if a < 0 and b > 0:
                a *= -1
                b *= -1
            a, b = -b, a
            iwashi.setdefault((a, b), [0, 0])
            iwashi[(a, b)][1] += 1

r = 2**iwashi01 % mod - 1 + 2**iwashi10 % mod - 1 + 1
for s, t in iwashi.values():
    r *= 2**s % mod -1 + 2**t % mod -1 + 1
    r %= mod
print(r + iwashi00 - 1)

Submission status: Runtime Error

Solution code:
import math
mod = 10**9+7
N = int(input())
 
iwashi01 = 0
iwashi10 = 0
iwashi00 = 0
iwashi = dict()
for i in range(N):
    a, b = map(int, input().split())
    g = math.gcd(abs(a), abs(b))
    a //= g; b //= g
    if a == 0 and b == 0:
        iwashi00 += 1
    elif a == 0:
        iwashi01 += 1
    elif b == 0:
        iwashi10 += 1            
    else:
        if a*b > 0:
            if a < 0 and b < 0:
                a *= -1
                b *= -1
            iwashi.setdefault((a, b), [0, 0])
            iwashi[(a, b)][0] += 1
        if a*b < 0:
            if a < 0 and b > 0:
                a *= -1
                b *= -1
            a, b = -b, a
            iwashi.setdefault((a, b), [0, 0])
            iwashi[(a, b)][1] += 1
 
r = 2**iwashi01 % mod - 1 + 2**iwashi10 % mod - 1 + 1
for s, t in iwashi.values():
    r *= 2**s % mod -1 + 2**t % mod -1 + 1
    r %= mod
    print(r + iwashi00 - 1)

Submission status: Runtime Error

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

iwashi01 = 0
iwashi10 = 0
iwashi00 = 0
iwashi = dict()
for i in range(N):
    a, b = map(int, input().split())
    g = math.gcd(abs(a), abs(b))
    a //= g; b //= g
    if a == 0 and b == 0:
        iwashi00 += 1
    elif a == 0:
        iwashi01 += 1
    elif b == 0:
        iwashi10 += 1            
    else:
        if a*b > 0:
            if a < 0 and b < 0:
                a *= -1
                b *= -1
            iwashi.setdefault((a, b), [0, 0])
            iwashi[(a, b)][0] += 1
        if a*b < 0:
            if a < 0 and b > 0:
                a *= -1
                b *= -1
            a, b = -b, a
            iwashi.setdefault((a, b), [0, 0])
            iwashi[(a, b)][1] += 1

r = 2**iwashi01 % mod - 1 + 2**iwashi10 % mod - 1 + 1
for s, t in iwashi.values():
    r *= 2**s % mod -1 + 2**t % mod -1 + 1
        r %= mod
    print(r + iwashi00 - 1)

Submission status: Runtime Error

Solution code:


def I(): return int(input())
def MI(): return map(int, input().split())
def LI(): return list(map(int, input().split()))

def main():
    mod=10**9
    N=I()
    from math import gcd
    from collections import defaultdict
    dd = defaultdict(int)
    temp0=0

    for i in range(N):
        a,b=MI()
        if a*b==0:
            assert 0
        
        if (a,b)==(0,0):
            temp0+=1
            continue
        
        if a<0:
            a*=-1
            b*=-1
        
        #(+,+)と(+,-)だけにする
        if a*b!=0:
            g=gcd(abs(a),abs(b))
            a=a//g
            b=b//g
            if a*b>0:#(+,+)
                dd[(a,b)]+=1
                dd[b,-a]+=0
                
            else:#(+,-)
                dd[(a,b)]+=1
                dd[(-b,a)]+=0
            
        elif (a,b)!=(0,0):
            #assert 0
            if a==0:
                b=1
            else:
                a=1
                
            dd[(a,b)]+=1
            dd[(b,a)]+=0
        

    ans=1
    
    for k,v in dd.items():
        a,b=k
        if b<=0:
            continue
        #+,+だけ見る
        
        if a*b!=0:
            v=dd[k]
            v2=dd[(b,-a)]
        else:
            v=dd[k]
            v2=dd[(b,a)]
        temp=pow(2,v,mod)+pow(2,v2,mod)-1
        
        ans=(ans*temp)%mod

    ans=(ans-1+temp0)%mod
    print(ans)
        
        
            
            
    #せんぶ０の組みをひく
        
    

main()

Submission status: Runtime Error

Solution code:
from decimal import Decimal
import sys
sys.setrecursionlimit(10**9)

mod = 1000000007
def main():
    N = int(input())

    dic = {}
    seen = set()
    def save_count(x):
        if not x in seen:
            dic[x] = 1
            seen.add(x)
        else:
            dic[x] += 1


    for _ in range(N):
        A,B = map(int,input().split())
        tan = Decimal(B) / Decimal(A)
        save_count(tan)

        if tan != Decimal("0"):
            tan_inv = Decimal("-1") / tan
            save_count(tan_inv)

    ans = 0
    p_sum = 0
    for key,val in dic.items():
        p = 0
        if val > 1:
            p = pow(3,val,mod)*pow(2,N-val,mod) - (pow(2,N,mod)+(val)*pow(2,N-1,mod))
        if key != 0:
            p //= 2
        # print(p)

        ans += p%mod


    # print(dic,ans)
    mod_sum = pow(2,N,mod) - 1
    # print(mod_sum,ans)
    ans = (mod_sum - ans) % mod
    print(ans)

if __name__ == "__main__":
  main()

Submission status: Runtime Error

Solution code:
from fractions import Fraction
from collections import defaultdict

N = int(input())
AB = [tuple(map(int, input().split())) for _ in range(N)]
MOD = 10**9 + 7

d = defaultdict(int)
cnt_0 = 0
for a,b in AB:
    if a == b == 0:
        cnt_0 += 1
    else:
        d[Fraction(a,b)] += 1


ans = 1
ks = list(d.keys())
for k in ks:
    if d[k] == 0:
        continue

    # 傾きkから一つ以上選んで -1/k の方からは選ばない + 傾き -1/k から一つ以上選んで k の方からは選ばない + どちらからも選ばない
    ans *= (((pow(2, d[k], MOD) - 1) + (pow(2, d[Fraction(-1, k)], MOD) - 1) + 1)% MOD)
    ans %= MOD
    d[k] = 0
    d[Fraction(-1, k)] = 0


print((ans + cnt_0 - 1) % MOD)

Submission status: Runtime Error

Solution code:
import sys
import math
readline = sys.stdin.readline

def main():
  p = 1000000007
  N = int(readline().strip())
  A = {}
  B = {}
  ans = 0
  for i in range(N):
    s = ''
    ai, bi = map(int, readline().split())
    if ai == 0 and bi == 0:
      ans += 1
      continue
    gi = math.gcd(ai, bi)
    ai = int(ai / gi)
    bi = int(bi / gi)
    if ai != 0 and bi != 0:
      if ai < 0 and bi < 0:
        ai = -ai
        bi = -bi
      elif ai < 0:
        ai = -ai
        s = '-'
      elif bi < 0:
        bi = -bi
        s = '-'
    elif ai == 0 and bi != 0:
      ai = 0
      bi = 1
    elif bi == 0 and ai != 0:
      ai = 1
      bi = 0
      s = '-'
    xi = s + str(ai) + '/' + str(bi)
    if s == '':
      s = '-'
    else:
      s = ''
    yi = s + str(bi) + '/' + str(ai)
    if xi in A:
      A[xi] += 1
    else:
      A[xi] = 1
      B[xi] = yi
    C = {}
    for i in B:
      if i in C:
        continue
      elif B[i] not in B:
        C[i] = [A[i], 0]
      elif B[i] in C:
        continue
      else:
        C[i] = [A[i], A[B[i]]]
  r = 1
  for i in C:
    r = r * (pow(2, C[i][0], p) + pow(2, C[i][1], p) -1) % p
  r -= 1
  ans += r
  print(ans)

if __name__ == '__main__':
  main()

Submission status: Runtime Error

Solution code:
import sys
from collections import defaultdict
from math import gcd

read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

MOD = 10**9 + 7
P = 2 ** 127 - 1

N = int(readline())
m = map(int, read().split())
A, B = zip(*zip(m, m))

pow2 = [1] * (N + 10)
for n in range(1, N + 10):
    pow2[n] = pow2[n - 1] * 2 % MOD

def to_standard_form(a, b):
    if a == 0:
        return -1, 0
    x = pow(a, P-2, P) * b % P
    return x

def pair_key(key):
    if key == -1:
        return 0
    if key == 0:
        return -1
    return P - pow(key, P-2, P)

counter = defaultdict(int)
origin = 0
for a, b in zip(A, B):
    if a == b == 0:
        origin += 1
        continue
    key = to_standard_form(a, b)
    counter[key] += 1
    counter[pair_key(key)] += 0

answer = origin
k = 1

for key, cnt in counter.items():
    key1 = pair_key(key)
    if key < key1:
        x, y = cnt, counter[key1]
        k *= pow(2, x, MOD) + pow(2, y, MOD) - 1
        k %= MOD

answer += k - 1
answer %= MOD
print(answer)

Submission status: Runtime Error

Solution code:
import sys
input = sys.stdin.readline
from fractions import Fraction
def solve():
    N = int(input())
    AB = [tuple(map(int,input().split())) for i in range(N)]
    MOD = 10**9+7

    from collections import Counter
    ctr = Counter()
    az = bz = zz = 0
    for a,b in AB:
        if a==b==0:
            zz += 1
        elif a==0:
            az += 1
        elif b==0:
            bz += 1
        else:
            f = Fraction(a,b)
        ctr[f] += 1
    ans = pow(2,az,MOD) + pow(2,bz,MOD) - 1

    used = set()
    for f1,v in ctr.items():
        if f1 in used: continue
        f2 = -1/f1
        if f2 in ctr:
            used.add(f2)
        r = pow(2,v,MOD) + pow(2,ctr[f2],MOD) - 1
        ans *= r
        ans %= MOD
    ans += zz - 1
    ans %= MOD
    print(ans)
solve()

Submission status: Runtime Error

Solution code:
import sys
input = sys.stdin.readline
from fractions import Fraction
def solve():
    N = int(input())
    AB = [tuple(map(int,input().split())) for i in range(N)]
    MOD = 10**9+7

    from collections import Counter
    ctr = Counter()
    az = bz = zz = 0
    for a,b in AB:
        if a==b==0:
            zz += 1
        elif a==0:
            az += 1
        elif b==0:
            bz += 1
        f = Fraction(a,b)
        ctr[f] += 1
    ans = pow(2,az,MOD) + pow(2,bz,MOD) - 1

    used = set()
    for f1,v in ctr.items():
        if f1 in used: continue
        f2 = -1/f1
        if f2 in ctr:
            used.add(f2)
        r = pow(2,v,MOD) + pow(2,ctr[f2],MOD) - 1
        ans *= r
        ans %= MOD
    ans += zz - 1
    ans %= MOD
    print(ans)
solve()

Submission status: Runtime Error

Solution code:
n=int(input())
from math import gcd
from collections import defaultdict
abd=defaultdict(int)
mod=10**9+7
ab=[]
wzero=0
azero=0
bzero=0
for i in range(n):
    a,b=map(int,input().split())
    if a==0 and b==0:
        wzero+=1
        continue
    elif a==0 and b!=0:
        azero+=1
        continue
    elif a!=0 and b==0:
        bzero+=1
        continue
    x=gcd(a,b)
    a//=x
    b//=x
    ab.append((a,b))
    abd[(a,b)]+=1

kumid=defaultdict(int)
for i in range(len(ab)):
    a,b=ab[i]
    cnt=abd[(-b,a)]+abd[(b,-a)]
    kumid[cnt]+=1
maxkey=max(kumid.keys())
ans=1

for i in range(maxkey,1,-1):
    if kumid[i]!=0:
        j=kumid[i]
        kumid[j]-=i
        tmp=2**i+2**j-1
        ans*=(tmp%mod)
        ans%=mod
#print(kumid)
ans*=(kumid[1]+1)
ans%=mod
ans*=2**kumid[0]%mod
ans%=mod
ans*=(2**azero+2**bzero-1)%mod
ans%=mod
ans+=wzero
ans=(ans+mod-1)%mod
print(ans)

Submission status: Runtime Error

Solution code:
n=int(input())
from math import gcd
from collections import defaultdict
abd=defaultdict(int)
mod=10**9+7
ab=[]
wzero=0
azero=0
bzero=0
for i in range(n):
    a,b=map(int,input().split())
    if a==0 and b==0:
        wzero+=1
        continue
    elif a==0 and b!=0:
        azero+=1
        continue
    elif a!=0 and b==0:
        bzero+=1
        continue
    x=gcd(a,b)
    a//=x
    b//=x
    ab.append((a,b))
    abd[(a,b)]+=1

n-=(wzero+azero+bzero)
kumid=defaultdict(int)
for i in range(n):
    a,b=ab[i]
    cnt=abd[(-b,a)]+abd[(b,-a)]
    kumid[cnt]+=1
maxkey=max(kumid.keys())
ans=1

for i in range(maxkey,1,-1):
    if kumid[i]!=0:
        j=kumid[i]
        kumid[j]-=i
        tmp=2**i+2**j-1
        ans*=(tmp%mod)
        ans%=mod
#print(kumid)
ans*=(kumid[1]+1)
ans%=mod
ans*=2**kumid[0]%mod
ans%=mod
ans*=(2**azero+2**bzero-1)%mod
ans%=mod
ans+=wzero
ans=(ans+mod-1)%mod
print(ans)

Submission status: Runtime Error

Solution code:
import sys
input = sys.stdin.readline
from collections import *
from math import gcd

N = int(input())
cnt = defaultdict(int)
abzero = 0
azero = 0
bzero = 0

for _ in range(N):
    A, B = map(int, input().split())
    
    if A==0 and B==0:
        abzero += 1
    elif A==0:
        azero += 1
    elif B==0:
        bzero += 1
        
    G = gcd(abs(A), abs(B))
    A //= G
    B //= G
    
    if (A<0 and B>0) or (A<0 and B<0):
        A *= -1
        B *= -1
    
    cnt[(A, B)] += 1

Submission status: Runtime Error

Solution code:
n=int(input())
from math import gcd
from collections import defaultdict
abd=defaultdict(int)
ab=[]
wzero=0
azero=0
bzero=0
for i in range(n):
    a,b=map(int,input().split())
    if a==0 and b==0:
        wzero+=1
        continue
    elif a==0 and b!=0:
        azero+=1
        continue
    elif a!=0 and b==0:
        bzero+=1
        continue
    x=gcd(a,b)
    a//=x
    b//=x
    ab.append((a,b))
    abd[(a,b)]+=1

n-=(wzero+azero+bzero)
kumid=defaultdict(int)
for i in range(n):
    a,b=ab[i]
    cnt=abd[(-b,a)]+abd[(b,-a)]
    kumid[cnt]+=1
maxkey=max(kumid.keys())
ans=1

for i in range(maxkey,1,-1):
    if kumid[i]!=0:
        j=kumid[i]
        kumid[j]-=i
        tmp=2**i+2**j-1
        ans*=tmp
#print(kumid)
ans*=(kumid[1]+1)

ans*=2**kumid[0]
ans*=(2**azero+2**bzero-1)
ans+=wzero
ans-=1
print(ans)

Submission status: Runtime Error

Solution code:
import sys
input = sys.stdin.readline
from collections import *
from math import gcd

N = int(input())
cnt = defaultdict(int)
abzero = 0
azero = 0
bzero = 0

for _ in range(N):
    A, B = map(int, input().split())
    
    if A==0 and B==0:
        abzero += 1
    elif A==0:
        azero += 1
    elif B==0:
        bzero += 1
        
    G = gcd(abs(A), abs(B))
    A //= G
    B //= G
    
    if (A<0 and B>0) or (A<0 and B<0):
        A *= -1
        B *= -1
    
    cnt[(A, B)] += 1

ans = 1
MOD = 10**9+7
visited = set()

for k in cnt.keys():
    if k in visited:
        continue
    
    if k[0]>0 and k[1]>0:
        k2 = (k[1], -k[0])
    else:
        k2 = (-k[1], k[0])
    
    if k2 not in cnt:
        ans *= pow(2, cnt[k], MOD)
    else:
        ans *= pow(2, cnt[k], MOD)+pow(2, cnt[k2], MOD)-1
        visited.add(k2)

ans *= pow(2, azero, MOD)+pow(2, bzero, MOD)-1
ans %= MOD
ans += abzero-1
ans %= MOD
print(ans)

Submission status: Runtime Error

Solution code:
import math

mod = 1000000007
n = int(input())
zero = 0
dic = {}
dic[(0, 1.5)] = 0
dic[(1.5, 0)] = 0
for i in range(n):
    ai, bi = map(int, input().split())
    if ai < 0:
        ai, bi = -ai, -bi
    g = math.gcd(abs(ai), abs(bi))
    ai = ai // g
    bi = bi // g
    idx = (ai, bi)
    if idx == (0, 0):
        zero += 1
    elif idx[0] == 0:
        dic[(0, 1.5)] += 1
    elif idx[1] == 0:
        dic[(1.5, 0)] += 1
    else:
        if idx in dic:
            dic[idx] += 1
        else:
            dic[idx] = 1

ans = 1
already = set([])
for key, value in dic.items():
    if key in already: continue
    a, b = key
    if a == 1.5 or b == 1.5:
        pair1 = dic[(0, 1.5)]
        pair2 = dic[(1.5, 0)]
        ans = (ans * (pow(2, pair1, mod)+pow(2, pair2, mod)-1)) % mod
        already.add((0, 1.5))
        already.add((1.5, 0))
    else:
        if b > 0: idx = (b, -a)
        else: idx = (-b, a)
        if idx in dic:
            pair1 = dic[key]
            pair2 = dic[idx]
            ans = (ans * (pow(2, pair1, mod)+pow(2, pair2, mod)-1)) % mod
            already.add(key)
            already.add(idx)
        else:
            pair1 = dic[key]
            ans = (ans * pow(2, pair1, mod)) % mod
            already.add(key)

ans = ans + zero - 1
print(ans)

Submission status: Runtime Error

Solution code:
import sys
import math
readline = sys.stdin.readline

def main():
  p = 1000000007
  N = int(readline().strip())
  A = {}
  B = {}
  ans = 0
  for i in range(N):
    s = ''
    ai, bi = map(int, readline().split())
    if ai == 0 and bi == 0:
      ans += 1
      continue
    gi = math.gcd(ai, bi)
    ai = int(ai / gi)
    bi = int(bi / gi)
    if ai != 0 and bi != 0:
      if ai < 0 and bi < 0:
        ai = -ai
        bi = -bi
      elif ai < 0:
        ai = -ai
        s = '-'
      elif bi < 0:
        bi = -bi
        s = '-'
    elif ai == 0 and bi != 0:
      ai = 0
      bi = 1
    elif bi == 0 and ai != 0:
      ai = 1
      bi = 0
      s = '-'
    xi = s + str(ai) + '/' + str(bi)
    if s == '':
      s = '-'
    else:
      s = ''
    yi = s + str(bi) + '/' + str(ai)
    if xi in A:
      A[xi] += 1
    else:
      A[xi] = 1
      B[xi] = yi
    C = {}
    for i in B:
      if i in C:
        continue
      elif B[i] not in B:
        C[i] = [A[i], 0]
      elif B[i] in C:
        continue
      else:
        C[i] = [A[i], A[B[i]]]
  r = 1
  for i in C:
    r *= ((2**C[i][0])%p + (2**C[i][1])%p -1)
    r %= p
  r -= 1
  ans += r
  print(ans)

if __name__ == '__main__':
  main()

Submission status: Runtime Error

Solution code:
import sys,math,bisect
input = sys.stdin.readline

mod = 1000000007
eps = 0.0000001

n = int(input())

ab = []
ang = []
zero = 0
for i in range(n):
    a,b = map(int,input().split())
    ab.append((a,b))
    if a == 0 and b == 0:
        zero += 1
    elif a == 0:
        ang.append((90.0,i))
    else:
        ang.append((math.degrees(math.atan(b/a)),i))
ang.sort()
n -= zero

res = 1
used = [False]*n


rest = n

for i in range(n):
    e,idx = ang[i]
    if used[idx]:
        continue
    if e > eps:
        break
    
    cnt = 1
    k = i + 1
    while k < n:
        if abs(e-ang[k][0]) <= eps:
            p = ang[k][1]
            if (not used[p] ) and ab[p][0]*ab[idx][1] == ab[p][1]*ab[idx][0]:
                cnt += 1
                used[p] = True
            k += 1
        else:
            break


    cnt2 = 0

    ok = n
    ng = i+1
    while ok-ng > 1:
        mid = (ok+ng)//2
        if ang[mid][0] >= e+90-eps:
            ok = mid
        else:
            ng = mid

    k = ok
    while k < n:
        if abs(e+90-ang[k][0]) <= eps:
            p = ang[k][1]
            if (not used[p]) and ab[p][0]*ab[idx][0] + ab[p][1]*ab[idx][1] == 0:
                cnt2 += 1
                used[p] = True
            k += 1
        else:
            break

    if cnt2 != 0:
        res = res*(pow(2,cnt,mod) + pow(2,cnt2,mod) - 1)%mod
        rest -= (cnt+cnt2)


res = res*pow(2,rest,mod)%mod - 1 + zero
print(res%mod)

Submission status: Runtime Error

Solution code:
from math import gcd
from collections import defaultdict

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

MOD = 1000000007

box = defaultdict(int)
zeros = 0
for a, b in AB:
  if a == b == 0:
    zeros += 1
  else:
    if a != 0 and b == 0:
      box[(-1, 1, 0)] += 1
    elif a == 0 and b != 0:
      box[(1, 0, 1)] += 1
    else:
      g = gcd(a, b)
      ga = a // g
      gb = b // g
      if (a // b) < 0:
        s = -1
      else:
        s = 1
    box[(s, abs(ga), abs(gb))] += 1

nakawaru = dict()
others = 0

for (s, i, j), v in box.items():
    if (-s, j, i) in box.keys():
        if (s, i, j) not in nakawaru.keys() and (-s, j, i) not in nakawaru.keys():    
            nakawaru[(s, i, j)] = (box[(s, i, j)], box[(-s, j, i)])
    else:
        others += v

seed = 1
for i, j in nakawaru.values():
    seed *= (pow(2, i, MOD) + pow(2, j, MOD) - 1)
    seed %= MOD

ans = zeros + pow(2, others, MOD) * seed - 1
ans %= MOD

print(ans)

Submission status: Runtime Error

Solution code:
import math

def m(L):
    (a,b)=L
    g=math.gcd(a,b)
    
    if b==0:
        return (1,0)
    elif b>0:
        return (a//g,b//g)
    else:
        return (-a//g,-b//g)

def w(x,y):
    if x==0:
        return 2**y
    elif y==0:
        return 2**x
    else:
        return 2**x+2**y-1
    
N=int(input())
D=[]
for i in range(N):
    (A,B)=map(int,input().split())
    D.append((A,B))

O=0
for u in range(N):
    if D[u]==(0,0):
        D.remove((0,0))
        O=1
        
M=list(map(m,D))
    
J={}

for m in M:
    if m in J:
        J[m]+=1
    else:
        J[m]=1

K={}
for u in J:
    (a,b)=u
    p=J[u]
    
    if a>=0:
        (c,d)=(-b,a)
    else:
        (c,d)=(b,-a)

    f=True
    if (a,b) in K:
        (x,y)=K[(a,b)]
        if a>=0:
            x+=p
        else:
            y+=p
        K[(a,b)]=(x,y)
        f=False

    elif f and ((c,d) in K):
        (x,y)=K[(c,d)]
        if c<=0:
            x+=p
        else:
            y+=p
        K[(c,d)]=(x,y)
        f=False
        
    elif f:
        if a>=0:
            K[(a,b)]=(p,0)
        else:
            K[(a,b)]=(0,p)

G=[w(x,y) for (x,y) in K.values()]

r=1
V=1000000007

for g in G:
    r=(r*g)%V

print(r-1+O)

Submission status: Runtime Error

Solution code:
from math import gcd
from collections import defaultdict

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

MOD = 1000000007

box = defaultdict(int)
zeros = 0
for a, b in AB:
  if a == b == 0:
    zeros += 1
  else:
    if a != 0 and b == 0:
      box[(-1, 1, 0)] += 1
    elif a == 0 and b != 0:
      box[(1, 0, 1)] += 1
    else:
      g = gcd(a, b)
      a //= g
      b //= g
      if a // b < 0:
        s = -1
      else:
        s = 1
    box[(s, abs(a), abs(b))] += 1
   
nakawaru = dict()
others = 0

for (s, i, j), v in box.items():
    if (-s, j, i) in box.keys():
        if (s, i, j) not in nakawaru.keys() and (-s, j, i) not in nakawaru.keys():    
            nakawaru[(s, i, j)] = (box[(s, i, j)], box[(-s, j, i)])
    else:
        others += v

seed = 1
for i, j in nakawaru.values():
    seed *= (pow(2, i, MOD) + pow(2, j, MOD) - 1)
    seed %= MOD

ans = zeros + pow(2, others, MOD) * seed - 1
ans %= MOD

print(ans)

Submission status: Runtime Error

Solution code:
import sys
input = sys.stdin.readline
mod = 10**9 + 7
n = int(input())
ab = [[int(x) for x in input().split()] for _ in range(n)]
from collections import defaultdict, Counter
import math

double_zero_cnt = 0 # [0, 0]の個数
a_b = [] # a/bを、約分した形で保持(a/gcd(a, b), b/gcd(a, b), 符号)
for a, b in ab:
    if a == 0 and b == 0: 
        double_zero_cnt += 1
        continue
    g = math.gcd(a, b)
    a //= g
    b //= g
    sign = 1 if a*b > 0 else -1 if a*b < 0: -1 else 0
    a_b.append((abs(a), abs(b), sign))

c = Counter(a_b) # ベクトルごとにグループ分け
key_list = list(c.keys())

d = defaultdict(list) # [a, b] あるngなペアのそれぞれの要素の個数
for key in key_list:
    a, b, sign = key
    if d[(b, a, -sign)]: # ダブルカウントしないように
        continue 
    if c[(b, a, -sign)] != 0:
        d[(a, b, sign)] = [c[(a, b, sign)], c[(b, a, -sign)]]

ans = 1 # 積算の単位元
used_cnt = double_zero_cnt # 組めないものがあるイワシの個数
for key in d.keys():
    if d[key] == []: # 前のループで調べると[]が生まれてしまう
        continue
    x, y = d[key]
    used_cnt += (x + y)
    mul = (pow(2, x, mod) + pow(2, y, mod) - 1) % mod # このグループからは、片方ずつからしか出せない。何も選ばないがダブルカウントになる。
    ans *= mul
    ans %= mod

ans *= pow(2, n - (used_cnt), mod) # まだ使われていないイワシは好きな組み合わせ可能
ans += double_zero_cnt # 両方0のものは1つにつき自分のみの1通り
ans -= 1 # 0匹は選べない
ans %= mod
print(ans)

Submission status: Runtime Error

Solution code:
import sys
input = sys.stdin.readline
mod = 10**9 + 7
n = int(input())
ab = [[int(x) for x in input().split()] for _ in range(n)]
from collections import defaultdict, Counter
import math
double_zero_cnt = 0
a_zero_cnt = 0
b_zero_cnt = 0
d = defaultdict(list) # [a, b] ngのそれぞれの個数
a_b = []
for a, b in ab:
    if a == 0 and b == 0: 
        double_zero_cnt += 1
        continue
    elif a == 0:
        a_zero_cnt += 1
        continue
    elif b == 0:
        b_zero_cnt += 1
        continue
    g = math.gcd(a, b)
    a //= g
    b //= g
    if b < 0:
        b *= (-1)
        a *= (-1) # 必ずbは正
    a_b.append((a, b))
c = Counter(a_b)
key_list = list(c.keys())
for key in key_list:
    a, b = key
    if c[(-abs(b), abs(a))] != 0:
        d[(a, b)] = [c[(a, b)], c[(-abs(b), abs(a))]]
        c[(a, b)] = 0
ans = 1
used_cnt = double_zero_cnt
for key in d.keys():
    if d[key] == []:
        continue
    x, y = d[key]
    used_cnt += (x + y)
    mul = (pow(2, x, mod) + pow(2, y, mod) - 1) % mod
    ans *= mul
    ans %= mod
if a_zero_cnt > 0 and b_zero_cnt > 0:
    ans *= (pow(2, a_zero_cnt, mod) + pow(2, b_zero_cnt, mod) - 1)
    ans %= mod
    used_cnt += a_zero_cnt + b_zero_cnt
elif a_zero_cnt > 0:
    ans *= pow(2, a_zero_cnt, mod)
    ans %= mod
    used_cnt += a_zero_cnt
elif b_zero_cnt > 0:
    ans *= pow(2, b_zero_cnt, mod)
    ans %= mod
    used_cnt += b_zero_cnt
ans *= pow(2, n - (used_cnt), mod)
ans %= mod
ans -= 1
ans += double_zero_cnt
ans %= mod
print(ans)

Submission status: Runtime Error

Solution code:
import sys
input = sys.stdin.readline
mod = 10**9 + 7
n = int(input())
ab = [[int(x) for x in input().split()] for _ in range(n)]
from collections import defaultdict, Counter
import math
double_zero_cnt = 0
a_zero_cnt = 0
b_zero_cnt = 0
d = defaultdict(list) # [a, b] ngのそれぞれの個数
a_b = []
b_a = []
for a, b in ab:
    if a == 0 and b == 0:
        double_zero_cnt += 1
        continue
    elif a == 0:
        a_zero_cnt += 1
        continue
    elif b == 0:
        b_zero_cnt += 1
        continue
    g = math.gcd(a, b)
    a //= g
    b //= g
    if b < 0:
        b *= (-1)
        a *= (-1) # 必ずbは正
    a_b.append((a, b))
c = Counter(a_b)
key_list = list(c.keys())
for key in key_list:
    a, b = key
    if a < 0:
        a *= (-1)
        b *= (-1)
    if d[(-b, a)] != []:
        continue
    if c[(-b, a)] != 0:
        d[(a, b)] = [c[(a, b)], c[(-b, a)]]
ans = 1
used_cnt = double_zero_cnt
for key in d.keys():
    if d[key] == []:
        continue
    x, y = d[key]
    used_cnt += (x + y)
    mul = (pow(2, x, mod) + pow(2, y, mod) - 1) % mod
    ans *= mul
    ans %= mod
if a_zero_cnt > 0 and b_zero_cnt > 0:
    ans *= (pow(2, a_zero_cnt, mod) + pow(2, b_zero_cnt, mod) - 1)
    ans %= mod
    used_cnt += a_zero_cnt + b_zero_cnt
elif a_zero_cnt > 0:
    ans *= pow(2, a_zero_cnt, mod)
    ans %= mod
    used_cnt += a_zero_cnt
elif b_zero_cnt > 0:
    ans *= pow(2, b_zero_cnt, mod)
    ans %= mod
    used_cnt += b_zero_cnt
ans *= pow(2, n - (used_cnt), mod)
ans %= mod
ans -= 1
ans += double_zero_cnt
ans %= mod
print(ans)