Problem: We have caught N sardines. The _deliciousness_ and _fragrantness_ of the i-th sardine is A_i and B_i, respectively.  We will choose one or more of these sardines and put them into a cooler. However, two sardines on bad terms cannot be chosen at the same time.  The i-th and j-th sardines (i \neq j) are on bad terms if and only if A_i \cdot A_j + B_i \cdot B_j = 0.  In how many ways can we choose the set of sardines to put into the cooler? Since the count can be enormous, print it modulo 1000000007.

Submission attempts (in order):
import math
MOD = 1000000007
N = int(input())
d_p = dict()
d_m = dict()
zz = 0 # a=b=0
for n in range(N):
    a,b = map(int,input().split())
    if a==0 and b==0:
        zz += 1
        continue
    if a==0:
        n_sign = 0
    elif b==0:
        n_sign = 1
    
    else:    
        n_sign = ((a<0) + (b<0))%2
        a = abs(a)
        b = abs(b)
        gcd = math.gcd(a,b)
        a//=gcd
        b//=gcd
        

        #print(n_sign,a,b)
    # print(n_sign,a,b)


    if n_sign==1:
        s =str(b/a)
        d_m[s] = d_m.get(s,0) + 1
    elif n_sign==0:
        s =str(a/b)
        d_p[s] = d_p.get(s,0) + 1      
    
print (d_p,d_m)

ans = 1
for k,v in d_m.items():
    if k in d_p:
        ans *= (2**v + 2**d_p[k] - 1)
        
        d_p.pop(k)
    else:
        ans *= 2**v
    ans %= MOD

for k,v in d_p.items():
    ans *= 2**v
    ans %= MOD
ans -= 1
ans += zz
ans %= MOD
print (ans)


import math
MOD = 1e+9+7
N = int(input())

d_p = dict()
d_m = dict()
ans = 1
zz = 0

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

    if a==0 and b==0:
        zz += 1
        continue
    if a==0:
        n_sign = 0
        b = 0
    elif b==0:
        n_sign = 1
        a = 0

    else:    
        n_sign = ((a<0) + (b<0))%2
        a = abs(a)
        b = abs(b)
        gcd = math.gcd(a,b)
        a//=gcd
        b//=gcd

    if n_sign==1:
        s =str(b)+'/'+str(a)
        d_m[s] = d_m.get(s,0) + 1
    elif n_sign==0:
        s =str(a)+'/'+str(b)
        d_p[s] = d_p.get(s,0) + 1      

for k,v in d_m.items():
    if k in d_p:
        ans *= (2**v + 2**d_p[k] - 1)
        d_p.pop(k)
    else:
        ans *= 2**v
    ans %= MOD

for k,v in d_p.items():
    ans *= 2**v
    ans %= MOD
    
ans -= 1
ans += zz
ans %= MOD
print (ans)


import math
MOD = 1000000007
N = int(input())
d_p = dict()
d_m = dict()
zz = 0
for n in range(N):
    a,b = map(int,input().split())

    if a==0 and b==0:
        zz += 1
        continue
    if a==0:
        n_sign = 1
        a=0
        b=0
    elif b==0:
        n_sign = 0
        a=0
        b=0  


    else:    
        n_sign = ((a<0) + (b<0))%2
        a = abs(a)
        b = abs(b)
        gcd = math.gcd(a,b)
        a//=gcd
        b//=gcd
        #print(n_sign,a,b)

    

    if n_sign==1:
        s =str(b)+'/'+str(a)
        d_m[s] = d_m.get(s,0) + 1
    elif n_sign==0:
        s =str(a)+'/'+str(b)
        d_p[s] = d_p.get(s,0) + 1      
    
print (d_m,d_p)

ans = 1
for k,v in d_m.items():
    if k in d_p:
        ans *= (2**v + 2**d_p[k] - 1)
        
        d_p.pop(k)
    else:
        ans *= 2**v
    ans %= MOD

for k,v in d_p.items():
    ans *= 2**v
    ans %= MOD
ans -= 1
ans += zz
ans %= MOD
print (ans)


import math
MOD = 1000000007
N = int(input())
d_p = dict()
d_m = dict()
zz = 0
for n in range(N):
    a,b = map(int,input().split())

    if a==0 and b==0:
        zz += 1
        continue
    if a==0:
        n_sign = 0
    elif b==0:
        n_sign = 1
    
    else:    
        n_sign = ((a<0) + (b<0))%2
        a = abs(a)
        b = abs(b)
        gcd = math.gcd(a,b)
        a//=gcd
        b//=gcd
        

        #print(n_sign,a,b)
    # print(n_sign,a,b)


    if n_sign==1:
        s =str(b/a)
        d_m[s] = d_m.get(s,0) + 1
    elif n_sign==0:
        s =str(a/b)
        d_p[s] = d_p.get(s,0) + 1      
    
print (d_p,d_m)

ans = 1
for k,v in d_m.items():
    if k in d_p:
        ans *= (2**v + 2**d_p[k] - 1)
        
        d_p.pop(k)
    else:
        ans *= 2**v
    ans %= MOD

for k,v in d_p.items():
    ans *= 2**v
    ans %= MOD
ans -= 1
ans += zz
ans %= MOD
print (ans)


import math
MOD = 1000000007
N = int(input())

d_p = dict()
d_m = dict()
ans = 1
zz = 0

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

    if a==0 and b==0:
        zz += 1
        continue
    if a==0:
        n_sign = 0
        b = 0
    elif b==0:
        n_sign = 1
        a = 0

    else:    
        n_sign = ((a<0) + (b<0))%2
        a = abs(a)
        b = abs(b)
        gcd = math.gcd(a,b)
        a//=gcd
        b//=gcd

    if n_sign==1:
        s =str(b)+'/'+str(a)
        d_m[s] = d_m.get(s,0) + 1
    elif n_sign==0:
        s =str(a)+'/'+str(b)
        d_p[s] = d_p.get(s,0) + 1      

for k,v in d_m.items():
    if k in d_p:
        ans *= (2**v + 2**d_p[k] - 1)
        d_p.pop(k)
    else:
        ans *= 2**v
    ans %= MOD

for k,v in d_p.items():
    ans *= 2**v
    ans %= MOD

ans -= 1
ans += zz
ans %= MOD
print (ans)


Verdicts: Wrong Answer

Runtime Error

Wrong Answer

Wrong Answer

Accepted