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:
import math
MOD =1000000007


def pow_k(x, n):
    if n == 0:
        return 1

    K = 1
    while n > 1:
        if n % 2 != 0:
            K *= x
        x *= x
        n //= 2
        # print(K,x)
        x%=MOD
    return K * x


n = int(input())

a_b_d = {}

a_zero_cnt = 0
b_zero_cnt = 0
ab_zero_cnt = 0

for i in range(n):
    a, b = map(int, input().split()) 
    if a==0 and b!=0:
        a_zero_cnt += 1
    elif  a!=0 and b==0:
        b_zero_cnt += 1
    elif a == 0 and b == 0:
        ab_zero_cnt += 1
    else:
        gcd_ab = math.gcd(a,b)
        a = a//gcd_ab
        b = b//gcd_ab
        if a > 0 and b < 0:
            a *= -1
            b *= -1
        elif a < 0 and b < 0:
            a *= -1
            b *=-1
        a_b_d.setdefault((a,b),0)
        a_b_d[(a,b)] += 1


done_list = set()
pair_cnt = []
uniq_cnt = 0
for k,v in a_b_d.items():
    comp_pair1 = (-k[1], k[0])
    comp_pair2 = (k[1], -k[0])
    if k in done_list:
        continue
    if comp_pair1 in a_b_d:
        done_list.add(comp_pair1)
        pair_cnt.append((v,a_b_d[comp_pair1]))
    elif comp_pair2 in a_b_d:
        done_list.add(comp_pair2)
        pair_cnt.append((v,a_b_d[comp_pair2]))
    else:
        uniq_cnt += v

# print(a_b_d)

ans = pow_k(2,uniq_cnt) % MOD
for pair in pair_cnt:
    ans *= (pow_k(2,pair[0]) + pow_k(2,pair[1]) -1 )
    ans%=MOD

zero_m = max(pow_k(2,a_zero_cnt) + pow_k(2,b_zero_cnt) -1, 1)
ans *= zero_m
ans -= 1
print(ans%MOD)

Submission status: Wrong Answer

Solution code:
import sys
input = sys.stdin.readline
import collections
from collections import defaultdict

n=int(input())
a= [list(map(int, input().split())) for i in range(n)]
b=defaultdict(int)
c=defaultdict(int)
b0=0
c0=0
mod=1000000007
ans=1
for i,j in a:
    if i!=0 and j!=0:
        b[i/j]+=1
        c[j/i]+=1
    elif i==0 and j!=0:
        b0+=1
    elif i!=0 and j==0:
        c0+=1
    else:
        ans+=1
w=[]
if c0!=0 or b0!=0:
    ans*=pow(2,c0+b0,mod)-((pow(2,c0,mod)-1)*(pow(2,b0,mod)-1))



for k,v in b.items():
    if c[-k]!=0:
        ans*=(pow(2,c[-k]+v,mod)-(pow(2,c[-k],mod)-1)*(pow(2,v,mod)-1))
        w.append((pow(2,c[-k]+v,mod)-(pow(2,c[-k],mod)-1)*(pow(2,v,mod)-1)))
        ans%=mod
    else:
        ans*=pow(2,v)
        ans%=mod

w=collections.Counter(w)
w=list(w.most_common())
for i,j in w:
    ans*=pow(i*j//2,mod-2,mod)
print(ans%mod-1)

Submission status: Wrong Answer

Solution code:
import math
MOD =1000000007


def pow_k(x, n):
    if n == 0:
        return 1

    K = 1
    while n > 1:
        if n % 2 != 0:
            K *= x
        x *= x
        n //= 2
        # print(K,x)
        x%=MOD
    return K * x


n = int(input())

a_b_d = {}

a_zero_cnt = 0
b_zero_cnt = 0
ab_zero_cnt = 0

for i in range(n):
    a, b = map(int, input().split()) 
    if a==0 and b!=0:
        a_zero_cnt += 1
    elif  a!=0 and b==0:
        b_zero_cnt += 1
    elif a == 0 and b == 0:
        ab_zero_cnt += 1
    else:
        gcd_ab = math.gcd(a,b)
        a = a//gcd_ab
        b = b//gcd_ab
        if a > 0 and b < 0:
            a *= -1
            b *= -1
        elif a < 0 and b < 0:
            a *= -1
            b *=-1
        a_b_d.setdefault((a,b),0)
        a_b_d[(a,b)] += 1


done_list = set()
pair_cnt = []
uniq_cnt = 0
for k,v in a_b_d.items():
    comp_pair1 = (-k[1], k[0])
    comp_pair2 = (k[1], -k[0])
    if k in done_list:
        continue
    if comp_pair1 in a_b_d:
        done_list.add(comp_pair1)
        pair_cnt.append((v,a_b_d[comp_pair1]))
    elif comp_pair2 in a_b_d:
        done_list.add(comp_pair2)
        pair_cnt.append((v,a_b_d[comp_pair2]))
    else:
        uniq_cnt += v

print(a_b_d)

ans = pow_k(2,uniq_cnt) % MOD
for pair in pair_cnt:
    ans *= (pow_k(2,pair[0]) + pow_k(2,pair[1]) -1 )
    ans%=MOD

zero_m = max(pow_k(2,a_zero_cnt) + pow_k(2,b_zero_cnt) -1, 1)
ans *= zero_m
ans -= 1
print(ans%MOD)

Submission status: Wrong Answer

Solution code:
import sys
from collections import defaultdict as dd
from math import gcd
input = sys.stdin.readline
N = int(input())
mod = 10 ** 9 + 7
d = dd(int)
a = [tuple(map(int, input().split())) for _ in range(N)]
for x, y in a:
  g = gcd(abs(x), abs(y))
  if (x, y) == (0, 0):
    N -= 1
    continue
  d[(x // g, y // g)] += 1
res = 1
u = 0
itr = list(d.keys())
#print(itr)
for x, y in itr:
  t = d[(y, -x)] + d[(-y, x)]
  if t == 0: u += d[(x, y)]
for x, y in itr:
  t = 0
  if (y, -x) == (-y, x):
    t = d[(y, -x)]
  else:
    t = d[(y, -x)] + d[(-y, x)]

  if t:
    v = 0
    v += pow(2, d[(x, y)], mod) - 1
    v %= mod
    v += pow(2, t, mod) - 1
    v %= mod
    v += 1
    v %= mod
    res *= v
    res %= mod
    #print(res, v)
  d[(x, y)] = 0
#print(itr, u, res)
print(res * pow(2, u, mod) - 1 % mod)

Submission status: Wrong Answer

Solution code:
import bisect
n = int(input())
a = [list(map(int, input().split())) for _ in range(n)]
mod = 1000000007
x = []
y = []
ex = [0,0]
ex2 = 0
for i in range(n):
    if (a[i][0]==0 and a[i][1]==0):
        ex2 += 1
    elif (a[i][0]*a[i][1]>0):
        if (a[i][0]!=0):
            x.append(a[i][1]/a[i][0])
        else:
            ex[0] += 1
    else:
        if (a[i][1]!=0):
            y.append(-a[i][0]/a[i][1])
        else:
            ex[1] += 1
x.sort()
y.sort()
#print(x,y)
xl = 0
yl = 0
xu = []
yu = []
xn = 0
yn = 0
while (xl<len(x) and yl<len(y)):
    if (x[xl] > y[yl]):
        yl += 1
    elif (x[xl] < y[yl]):
        xl += 1
    else:
        #print(xl,yl,x,y)
        p = bisect.bisect_right(x,x[xl])
        q = bisect.bisect_right(y,y[yl])
        xn += (p-xl)
        yn += (q-yl)
        xu.append(p-xl)
        yu.append(q-yl)
        xl = p
        yl = q
xu.append(ex[0])
yu.append(ex[1])
#print(xn,yn,xu,yu)
ans = pow(2,n-xn-yn-ex2,mod)
#if (n-xn-yn>0):
    #t = 1
    #for i in range(1,n-xn-yn+1):
        #t *= i
        #t %= mod
    #ans += t
for i in range(len(xu)):
    ans *= (pow(2,xu[i],mod)+pow(2,yu[i],mod)-1)
    ans %= mod
if (ex2==0):
    print((ans-1)%mod)
else:
    print((ans)%mod)

Submission status: Wrong Answer

Solution code:
import sys
import math
import heapq
sys.setrecursionlimit(10**7)
INTMAX = 9223372036854775807
INTMIN = -9223372036854775808
DVSR = 1000000007
def POW(x, y): return pow(x, y, DVSR)
def INV(x, m=DVSR): return pow(x, m - 2, m)
def DIV(x, y, m=DVSR): return (x * INV(y, m)) % m
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def II(): return int(sys.stdin.readline())
def FLIST(n):
    res = [1]
    for i in range(1, n+1): res.append(res[i-1]*i%DVSR)
    return res

def gcd(x, y):
    if x < y:
        x = x ^ y
        y = x ^ y
        x = x ^ y
    div = x % y
    while div != 0:
        x = y
        y = div
        div = x % y
    return y


N=II()
MP1={}
A0 = 0
B0 = 0
AB0 = 0
RES=1
for i in range(N):
    A, B = LI()
    if A*B != 0:
        G = gcd(abs(A),abs(B))
        A //= G
        B //= G
        v = (abs(A), abs(B), A*B > 0)
        if not v in MP1:
            MP1[v] = 1
        else:
            MP1[v] += 1

    if A == 0 and B != 0: A0 += 1
    if A != 0 and B == 0: B0 += 1

# print(MP1)

VIS = set()
for (vv, n) in MP1.items():
    (A, B, isPos) = vv
    v = (B, A, not isPos)
    if not v in VIS and not vv in VIS:
        VIS.add(v)
        VIS.add(vv)
        if v in MP1:
            m = MP1[v]
            RES = (RES*POW(2, n))%DVSR + (RES*POW(2, m))%DVSR - RES
            RES %= DVSR
        else:
            RES *= POW(2, n)
            RES %= DVSR

if A0 and B0:
    RES = (RES*POW(2, A0))%DVSR + (RES*POW(2, B0))%DVSR
elif A0:
    RES = RES*POW(2, A0)%DVSR
elif B0:
    RES = RES*POW(2, B0)%DVSR

print((RES-1)%DVSR)

Submission status: Wrong Answer

Solution code:
def main():
    import sys
    input = sys.stdin.buffer.readline
    n = int(input())
    mod = 10**9 + 7
    C = []
    for i in range(n):
        a,b = map(int, input().split())
        if b == 0:
            C.append(0)
            continue
        C.append(a/b)
    import numpy as np
    C = np.array(C)
    C_p = C[C>=0]
    C_n = C[C<0]
    from collections import Counter as cc
    C_p,C_n = cc(C_p),cc(C_n)
    count= 0
    re = 1
    for c in C_p:
        if c == 0:
            re *= C_p[c]
            count += C_p[c]
            continue

        if -1/c in C_n:
            count += C_n[-1/c] + C_p[c]
            re *= (2**C_n[-1/c] + 2**C_p[c] -1)%mod
    ans = pow(2,n-count,mod)*re%mod -1
    print(ans)


if __name__ == '__main__':
    main()

Submission status: Wrong Answer

Solution code:
import sys
import math
import heapq
sys.setrecursionlimit(10**7)
INTMAX = 9223372036854775807
INTMIN = -9223372036854775808
DVSR = 1000000007
def POW(x, y): return pow(x, y, DVSR)
def INV(x, m=DVSR): return pow(x, m - 2, m)
def DIV(x, y, m=DVSR): return (x * INV(y, m)) % m
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def II(): return int(sys.stdin.readline())
def FLIST(n):
    res = [1]
    for i in range(1, n+1): res.append(res[i-1]*i%DVSR)
    return res

def gcd(x, y):
    if x < y:
        x = x ^ y
        y = x ^ y
        x = x ^ y
    div = x % y
    while div != 0:
        x = y
        y = div
        div = x % y
    return y


N=II()
MP1={}
A0 = 0
B0 = 0
AB0 = 0
RES=1
for i in range(N):
    A, B = LI()
    if A*B != 0:
        G = gcd(abs(A),abs(B))
        A //= G
        B //= G
        v = (abs(A), abs(B), A*B > 0)
        if not v in MP1:
            MP1[v] = 1
        else:
            MP1[v] += 1

    if A == 0 and B != 0: A0 += 1
    if A != 0 and B == 0: B0 += 1

# print(MP1)

VIS = set()
for (vv, n) in MP1.items():
    (A, B, isPos) = vv
    v = (B, A, not isPos)
    if not v in VIS and not vv in VIS:
        VIS.add(v)
        VIS.add(vv)
        if v in MP1:
            m = MP1[v]
            RES = (RES*POW(2, n))%DVSR + (RES*POW(2, m))%DVSR - RES
            RES %= DVSR
        else:
            RES *= POW(2, n)
            RES %= DVSR

if A0 and B0:
    RES = (RES*POW(2, A0))%DVSR + (RES*POW(2, B0))%DVSR
elif A0:
    RES = RES*POW(2, A0)%DVSR
elif B0:
    RES = RES*POW(2, B0)%DVSR

print(RES-1)

Submission status: Wrong Answer

Solution code:
from math import gcd

n = int(input())
MOD = 10**9+7
p_map = {}
n_map = {}
p_z_map = {}
n_z_map = {}
z_map = 0
for _ in range(n):
    ab = list(map(int, input().split()))
    ab_gcd = gcd(ab[0], ab[1])
    if ab_gcd == 0:
        ab_gcd = 1
    a = ab[0]//ab_gcd
    b = ab[1]//ab_gcd

    key = "{}_{}".format(a, b)
    if a*b > 0:
        if key not in p_map:
            p_map[key] = 1
        else:
            p_map[key] += 1
    elif a == 0 and b == 0:
        z_map += 1
    elif a != 0 and b == 0:
        if key not in p_z_map:
            p_z_map[key] = 0
        else:
            p_z_map[key] += 1
    elif a == 0 and b != 0:
        if key not in n_z_map:
            n_z_map[key] = 0
        else:
            n_z_map[key] += 1
    else:
        if key not in n_map:
            n_map[key] = 1
        else:
            n_map[key] += 1

ans = 1
for k, v in p_map.items():

    a = int(k.split("_")[0])
    b = int(k.split("_")[1])
    n_num = 0
    key_a = "{}_{}".format(-b, a)
    key_b = "{}_{}".format(b, -a)
    if key_a in n_map:
        n_num += n_map.pop(key_a)
    if key_b in n_map:
        n_num += n_map.pop(key_b)
    res = 0
    res += pow(2, v, MOD)-1
    if n_num > 0:
        res += pow(2, n_num, MOD)-1
    res += 1
    ans *= res
    ans %= MOD

n_num = sum(n_map.values())
ans *= pow(2, n_num, MOD)
ans %= MOD

p_z_num = sum(p_z_map.values())
n_z_num = sum(n_z_map.values())
res = 0
if p_z_num > 0:
    res += pow(2, p_z_num, MOD)-1
if n_num > 0:
    res += pow(2, n_z_num, MOD)-1
res %= MOD
res += 1
ans *= res
ans %= MOD


if z_map > 0:
    ans += z_map
ans %= MOD
ans -= 1
print(ans)

Submission status: Wrong Answer

Solution code:
from collections import Counter
import sys
input = sys.stdin.buffer.readline

N = int(input())

def gcd(n, m):
    if m == 0:
        return n
    return gcd(m, n % m)

def make(a, b):
    if a * b == 0:
        return (0, 0, 0)

    s = 1 if a * b >= 0 else -1
    a, b = abs(a), abs(b)

    g = gcd(a, b)
    a //= g
    b //= g

    return (a, b, s)

ABS = Counter([make(*map(int, input().split())) for _ in range(N)])
K = list(ABS.keys())

ans = 1
MOD = 10**9 + 7

for a, b, s in K:
    if s == 0:
        ans = (ans * (ABS[(0, 0, 0)] + 1)) % MOD
        continue
    p = ABS[(a, b, s)]
    n = ABS[(b, a, -s)]

    ABS[(a, b, s)] = 0
    ABS[(b, a, -s)] = 0

    cnt = pow(2, p, MOD) + pow(2, n, MOD) - 1
    ans = (ans * cnt) % MOD

print((ans - 1) % MOD)

Submission status: Wrong Answer

Solution code:
import math 

MOD = 10**9 + 7
N = int(input())
ABC = []
zero_cases = 0
for i in range(N):
    a, b = map(int, input().split())
    if a == 0 and b == 0:
        zero_cases = 1
    elif a * b >=0 and a != 0:
        ABC.append([ math.atan2(abs(b),abs(a)), abs(a), abs(b),1])
    else:
        ABC.append([math.atan2(abs(a),abs(b)), abs(b), abs(a), -1])
ABC.sort()
if ABC:
    current_arg = ABC[-1][0]
else:
    current_arg = -1
group = []
daiich = 0
daini = 0
while ABC:
    current = ABC.pop()
    if current[0] == current_arg:
        if current[3]==1:
            daiich += 1
        else:
            daini += 1
    else:
        group += [[daiich, daini]]
        daiich = 0
        daini = 0
        if current[3]==1:
            daiich += 1
        else:
            daini += 1
        if ABC:
            current_arg = current[0]
else:
    group += [[daiich, daini]]
    daiich = 0
    daini = 0

ans = 1 + zero_cases
for u, v in group:
    ans *= (2**u + 2**v -1)
    ans %= MOD
print(ans-1)

Submission status: Wrong Answer

Solution code:
N=int(input())
C=10**9+7
dic={}
dic[0]=[0]*2
zero=0
def gcd(x, y):
    if y == 0:
        return x
    else:
        return gcd(y, x % y)
def pow_k(x, n):
    if n == 0:
        return 1
    K = 1
    while n > 1:
        if n % 2 != 0:
            K= (K%C)*(x%C)%C
        x = ((x%C)**2)%C
        n //= 2
    return (K%C) * (x%C) %C
for i in range(N):
  a,b=map(int,input().split())
  if a==0:
    if b==0:
      zero+=1
    else:
      dic[0][0]+=1
    continue
  else:
    if b==0:
      dic[0][1]+=1
      continue 
  d=gcd(a,b)
  a=a//d
  b=b//d

  if a*b>0:
    a=abs(a)
    b=abs(b)
    if (a,b) in dic.keys():
  	   dic[(a,b)][0]+=1
    else:
      dic[(a,b)]=[1,0]
  else:
    a=abs(a)
    b=abs(b)
    if (b,a) in dic.keys():
    	dic[(b,a)][1]+=1
    else:
      dic[(b,a)]=[0,1]
if zero==N:
  k=0
else:
  k=1
  for i in dic.values():
    a,b=i[0],i[1]
    j=(pow_k(2,a)+pow_k(2,b)-1)%C
    k= k*j%C
print((zero+k-1)%C)

Submission status: Wrong Answer

Solution code:
import sys
from collections import defaultdict as dd
from math import gcd
input = sys.stdin.readline
N = int(input())
mod = 10 ** 9 + 7
d = dd(int)
a = [tuple(map(int, input().split())) for _ in range(N)]
for x, y in a:
  g = gcd(abs(x), abs(y))
  if g == 0: g = 1
  d[(x // g, y // g)] += 1
res = 1
u = 0
itr = list(d.keys())
#print(itr)
for x, y in itr:
  t = d[(y, -x)] + d[(-y, x)]
  if t == 0: u += d[(x, y)]
for x, y in itr:
  t = 0
  if (x, y) == (0, 0):
    continue
  elif (y, -x) == (-y, x):
    t = d[(y, -x)]
  else:
    t = d[(y, -x)] + d[(-y, x)]

  if t:
    v = 0
    v += pow(2, d[(x, y)], mod) - 1
    v %= mod
    v += pow(2, t, mod) - 1
    v %= mod
    v += 1
    v %= mod
    res *= v
    res %= mod
    #print(res, v)
  d[(x, y)] = 0
#print(itr, u, res)
print(res * pow(2, u, mod) - 1 % mod)

Submission status: Wrong Answer

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

mod=10**9+7
n=int(input())
dic={}
cnt=0
for _ in range(n):
  a,b=map(int,input().split())
  if a!=0 and b!=0:
    g=gcd(abs(a),abs(b))
    if a*b>0:
      if (abs(a)//g,abs(b)//g) not in dic:
        dic[(abs(a)//g,abs(b)//g)]=1
      else:
        dic[(abs(a)//g,abs(b)//g)]+=1
    else:
      if (-abs(a)//g,abs(b)//g) not in dic:
        dic[(-abs(a)//g,abs(b)//g)]=1
      else:
        dic[(-abs(a)//g,abs(b)//g)]=1
  else:
    if a==0 and b==0:
      cnt+=1
    elif a==0:
      if (1,0) not in dic:
        dic[(1,0)]=1
      else:
        dic[(1,0)]+=1
    elif b==0:
      if (0,1) not in dic:
        dic[(0,1)]=1
      else:
        dic[(0,1)]+=1
ans=1
s=set()
for a,b in dic.keys():
  if (a,b) in s:
    continue
  s.add((a,b))
  if a*b!=0:
    if a>0:
      if (-b,a) in dic:
        s.add((-b,a))
        cnt1=dic[(a,b)]
        cnt2=dic[(-b,a)]
        ans*=(pow(2,cnt1,mod)+pow(2,cnt2,mod)-1)%mod
        ans%=mod
      else:
        ans*=pow(2,dic[(a,b)])
        ans%=mod
    elif a<0:
      if (b,-a) in dic:
        s.add((b,-a))
        cnt1=dic[(a,b)]
        cnt2=dic[(b,-a)]
        ans*=(pow(2,cnt1,mod)+pow(2,cnt2,mod)-1)%mod
        ans%=mod
      else:
        ans*=pow(2,dic[(a,b)])
        ans%=mod
  else:
    if (b,a) in dic:
      s.add((b,a))
      cnt1=dic[(a,b)]
      cnt2=dic[(b,a)]
      ans*=(pow(2,cnt1,mod)+pow(2,cnt2,mod)-1)%mod
      ans%=mod
    else:
      ans*=pow(2,dic[(a,b)])
      ans%=mod
print((ans+cnt-1)%mod)

Submission status: Wrong Answer

Solution code:
import bisect
n = int(input())
a = [list(map(int, input().split())) for _ in range(n)]
mod = 1000000007
x = []
y = []
ex = [0,0]
ex2 = 0
for i in range(n):
    if (a[i][0]==0 and a[i][1]==0):
        ex2 += 1
    elif (a[i][0]*a[i][1]>0):
        if (a[i][0]!=0):
            x.append(a[i][1]/a[i][0])
        else:
            ex[0] += 1
    else:
        if (a[i][1]!=0):
            y.append(-a[i][0]/a[i][1])
        else:
            ex[1] += 1
x.sort()
y.sort()
#print(x,y)
xl = 0
yl = 0
xu = []
yu = []
xn = 0
yn = 0
while (xl<len(x) and yl<len(y)):
    if (x[xl] > y[yl]):
        yl += 1
    elif (x[xl] < y[yl]):
        xl += 1
    else:
        #print(xl,yl,x,y)
        p = bisect.bisect_right(x,x[xl])
        q = bisect.bisect_right(y,y[yl])
        xn += (p-xl)
        yn += (q-yl)
        xu.append(p-xl)
        yu.append(q-yl)
        xl = p
        yl = q
xu.append(ex[0])
yu.append(ex[1])
#print(xn,yn,xu,yu)
ans = pow(2,n-xn-yn-ex2,mod)
#if (n-xn-yn>0):
    #t = 1
    #for i in range(1,n-xn-yn+1):
        #t *= i
        #t %= mod
    #ans += t
for i in range(len(xu)):
    ans *= (pow(2,xu[i],mod)+pow(2,yu[i],mod)-1)
    ans %= mod

print((ans-1)%mod)

Submission status: Wrong Answer

Solution code:

from collections import Counter
mod = 1000000007

n = int(input())
a_div_b = []
a_0 = 0
b_0 = 0
a_b_0 = 0
for _ in range(n):
    a, b = map(int, input().split())
    if a == 0 or b == 0:
        if a == 0 and b == 0:
            a_b_0 += 1
            break
        if a == 0:
            a_0 += 1
        if b == 0:
            b_0 += 1
        break
    if a * b < 0:
        a_div_b.append(a/b)
    else:
        a_div_b.append(b/a)

cnt = Counter(a_div_b)
cnt2 = sorted(cnt.items())
lst = []
total = 0
for num, _ in cnt2:
    if num > 0:
        break
    a1 = cnt[num]
    a2 = cnt[-num]
    if a1 * a2 != 0:
        total += a1 + a2
        lst.append([a1, a2])
if a_0 > 0 and b_0 > 0:
    total += a_0 + b_0
    lst.append([a_0, b_0])
n -= a_b_0
ans = pow(2, n - total, mod)
for a, b in lst:
    ans = (ans * (pow(2, a, mod) + pow(2, b, mod) - 1)) % mod
ans = (ans - 1 + a_b_0) % mod
    
print(ans)

Submission status: Wrong Answer

Solution code:
n = int(input())
t = []#num a/b
l = []#num p,m
z = [0,0,0,0]
d = 10
e = 0
for i in range(d):
    t.append([])
    l.append([])
for i in range(n):
    a,b = map(int,input().split())
    if(a*b == 0):
        if(a + b != 0):
            if(a == 0):
                z[0] += 1
            else:
                z[1] += 1
        else:
            e = 1
    elif(abs(a)== abs(b)):
        if(a*b > 0):
            z[2] += 1
        else:
            z[3] += 1
    elif(abs(a/b) > 1):
        u = abs(a/b)
        m = int(u%d)
        if(u in t[m]):
            if(a*b >= 0):
                l[m][t[m].index(u)][0] += 1
            else:
                l[m][t[m].index(u)][1] += 1
        else:
            t[m].append(u)
            if(a*b > 0):
                l[m].append([1,0,0,0])
            else:
                l[m].append([0,1,0,0])
    else:
        u = abs(b/a)
        m = int(u%d)
        if(u in t[m]):
            if(a*b >= 0):
                l[m][t[m].index(u)][2] += 1
            else:
                l[m][t[m].index(u)][3] += 1
        else:
            t[m].append(u)
            if(a*b > 0):
                l[m].append([0,0,1,0])
            else:
                l[m].append([0,0,0,1])
ans = 2**z[0]+2**z[1]-1
ans *= 2**z[2]+2**z[3]-1
for i in range(d):
    for j in range(len(t[i])):
        com1 = 2**l[i][j][0]+2**l[i][j][3]-1
        com2 = 2**l[i][j][1]+2**l[i][j][2]-1
        ans *= com1
        ans *= com2
        ans %= 1000000007
print(ans%1000000007 -1 + e)

Submission status: Wrong Answer

Solution code:
from fractions import Fraction


def compress(string):
    string.append(-2)
    n = len(string)
    begin, end, cnt = 0, 1, 1
    ans = []
    while end < n:
        if string[begin] == string[end]:
            end, cnt = end + 1, cnt + 1
        else:
            ans.append((string[begin], cnt))
            begin, end, cnt = end, end + 1, 1
    return ans

  
from collections import defaultdict


n = int(input())
info = [list(map(int, input().split())) for i in range(n)]
MOD = 10 ** 9 + 7
res1 = []
res2 = []
ind = []
cnt_00 = 0
cnt_a0 = 0
cnt_b0 = 0
INF = 10 ** 18
for i in range(n):
    a, b = info[i]
    if a == 0 and b == 0:
        cnt_00 += 1
        continue
    if a == 0:
        cnt_a0 += 1
        continue
    if b == 0:
        cnt_b0 += 1
        continue
    res1.append(Fraction(a, b))
    res2.append(Fraction(- b, a))
    ind.append(i)
memo_r = defaultdict(int)
memo_l = defaultdict(int)

for i in range(len(res1)):
    l, r = res1[i], res2[i]
    memo_r[r] += 1
    memo_l[l] += 1

ans = 1
used = set()
for r in memo_r:
    if r in used:
        continue
    cnt_r = memo_r[r]
    cnt_l = 0
    if r in memo_l:
        cnt_l += memo_l[r]
    if r == 1.0:
        tmp = cnt_l + cnt_r + 1
    else:
        tmp = (pow(2, cnt_l, MOD) - 1) + (pow(2, cnt_r, MOD) - 1) + 1
    ans *= tmp
    used.add(-1 / r)

ans = ans + ans * cnt_a0 + ans * cnt_b0  + cnt_b0 * cnt_a0 * ans + cnt_00
print((ans - 1) % MOD)

Submission status: Wrong Answer

Solution code:
N = int(input())
MOD = 1000000007
s, zero = {}, 0

for _ in range(N):
    A, B = map(int, input().split())
    if A == 0 and B == 0:
        zero += 1
    elif B == 0:
        if s.get(float('inf')) == None:
            s[float('inf')] = 1
        else:
            s[float('inf')] += 1
    else:
        if s.get(A/B) == None:
            s[A/B] = 1
        else:
            s[A/B] += 1

f, ans = 0, 1
while len(s) > 0:
    k1, v1 = s.popitem()
    if k1 == 0:
        key = float('inf')
    else:
        key = -1/k1
    if key in s.keys():
        v2 = s.pop(key)
        Cv1, Cv2 = pow(2, v1, MOD), pow(2, v2, MOD)     # pow(2, n, MOD) は二項定理による組み合わせの総和
        C = ((Cv1 + Cv2) % MOD + (MOD - 1)) % MOD
        ans = (ans * C) % MOD
    else:
        f += v1

ans = ((ans * pow(2, f, MOD)) % MOD  + (MOD - 1)) % MOD
ans = (ans + zero) % MOD
print(ans)

Submission status: Wrong Answer

Solution code:
import sys
import math
from collections import defaultdict
from bisect import bisect_left, bisect_right

sys.setrecursionlimit(10**7)
def input():
    return sys.stdin.readline()[:-1]

mod = 10**9 + 7

def I(): return int(input())
def LI(): return list(map(int, input().split()))
def LIR(row,col):
    if row <= 0:
        return [[] for _ in range(col)]
    elif col == 1:
        return [I() for _ in range(row)]
    else:
        read_all = [LI() for _ in range(row)]
        return map(list, zip(*read_all))

#################

#通分
def f(a,b):
    f = math.gcd(a,b)
    return a//f, b//f

N = I()
A,B = LIR(N,2)

beki = [1]*(N+1)
for i in range(1,N+1):
    beki[i] = beki[i-1]*2
    beki[i] %= mod


dplus = defaultdict(int)
dplus2 = defaultdict(int)
dminus = defaultdict(int)
dminus2 = defaultdict(int)
zero = 0
for i in range(N):
    if A[i] == 0 or B[i] == 0:
        zero += 1
    else:
        if A[i]*B[i] > 0:
            a,b = f(abs(A[i]),abs(B[i]))
            dplus[(a,b)] += 1
            dplus2[(a,b)] += 1
        else:
            a,b = f(abs(A[i]),abs(B[i]))
            dminus[(b,a)] += 1
            dminus2[(b,a)] += 1

ans = 1
count = 0

for k in dplus.keys():
    if dminus[k]:
        temp = beki[dplus[k]] + beki[dminus[k]] - 1
        ans *= temp
        ans %= mod
    else:
        count += dplus[k]

for k in dminus2.keys():
    if dplus2[k]:
        continue
    else:
        count += dminus2[k]

ans *= beki[count]
temp = ans-1
temp2 = ans*zero
ans = temp+temp2
ans %= mod
print(ans)

Submission status: Wrong Answer

Solution code:
#!/usr/bin/env python3
import sys

MOD = 1000000007  # type: int

def func(b, w):
    return ((pow(2, b, MOD) + pow(2, w, MOD)) % MOD + MOD - 1) % MOD 

def solve(N: int, A: "List[int]", B: "List[int]"):
    from fractions import Fraction
    from collections import Counter
    C = [Fraction(a, b) for a, b in zip(A, B) if 0 not in (a, b)]
    D = [-Fraction(b, a) for a, b in zip(A, B) if 0 not in (a, b)]
    E = Counter(C)
    F = Counter(D)
    G = []
    used = set()
    for e, f in zip(E, F):
        if e in used or f in used:
            continue
        G.append((e, E[e], F[e]))
        used.add(e)
        used.add(f)
    ans = 1
    #print(G)
    for e, b, w in G:
        # print(b, w, func(b, w))
        ans = (ans * func(b, w)) % MOD
    #H = sum(1 if 0 in (a, b) else 0 for a, b in zip(A, B))
    #print(ans)
    #ans = (ans * func(H, 0)) % MOD
    return (ans-1+MOD)%MOD
        

# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools
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))
    print(solve(N, A, B))

def test():
    import doctest
    doctest.testmod()

if __name__ == '__main__':
    #test()
    main()

Submission status: Wrong Answer

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

mod=10**9+7
n=int(input())
fact=[1]
revfact=[1]
for i in range(1,2*10**5+1):
  fact.append((fact[-1]*i)%mod)
  revfact.append(pow(fact[-1],mod-2,mod))
dic={}
cnt=0
for _ in range(n):
  a,b=map(int,input().split())
  if a!=0 and b!=0:
    g=gcd(abs(a),abs(b))
    if a*b>0:
      if (abs(a)//g,abs(b)//g) not in dic:
        dic[(abs(a)//g,abs(b)//g)]=1
      else:
        dic[(abs(a)//g,abs(b)//g)]+=1
    else:
      if (-abs(a)//g,abs(b)//g) not in dic:
        dic[(-abs(a)//g,abs(b)//g)]=1
      else:
        dic[(-abs(a)//g,abs(b)//g)]=1
  else:
    if a==0 and b==0:
      cnt+=1
    elif a==0:
      if (1,0) not in dic:
        dic[(1,0)]=1
      else:
        dic[(1,0)]+=1
    elif b==0:
      if (0,1) not in dic:
        dic[(0,1)]=1
      else:
        dic[(0,1)]+=1
ans=1
s=set()
for a,b in dic.keys():
  if (a,b) in s:
    continue
  s.add((a,b))
  if a*b!=0:
    if a>0:
      if (-b,a) in dic:
        s.add((-b,a))
        cnt1=dic[(a,b)]
        cnt2=dic[(-b,a)]
        tmp=1
        for i in range(1,cnt1+1):
          tmp+=(fact[cnt1]*revfact[i]*revfact[cnt1-i])%mod
        for i in range(1,cnt2+1):
          tmp+=(fact[cnt2]*revfact[i]*revfact[cnt2-i])%mod
        ans*=tmp
        ans%=mod
      else:
        ans*=pow(2,dic[(a,b)])
        ans%=mod
    elif a<0:
      if (b,-a) in dic:
        s.add((b,-a))
        cnt1=dic[(a,b)]
        cnt2=dic[(b,-a)]
        tmp=1
        for i in range(1,cnt1+1):
          tmp+=(fact[cnt1]*revfact[i]*revfact[cnt1-i])%mod
        for i in range(1,cnt2+1):
          tmp+=(fact[cnt2]*revfact[i]*revfact[cnt2-i])%mod
        ans*=tmp
        ans%=mod
      else:
        ans*=pow(2,dic[(a,b)])
        ans%=mod
  else:
    if (b,a) in dic:
      s.add((b,a))
      cnt1=dic[(a,b)]
      cnt2=dic[(b,a)]
      tmp=1
      for i in range(1,cnt1+1):
        tmp+=(fact[cnt1]*revfact[i]*revfact[cnt1-i])%mod
      for i in range(1,cnt2+1):
        tmp+=(fact[cnt2]*revfact[i]*revfact[cnt2-i])%mod
      ans*=tmp
      ans%=mod
    else:
      ans*=pow(2,dic[(a,b)])
      ans%=mod
print(ans+cnt-1)

Submission status: Wrong Answer

Solution code:
n=int(input())
dic={}
sus_a=0
sus_b=0
sus_ab=0
for i in range(n):
  a,b=map(int,input().split())
  if a==0 and b==0:
    sus_ab += 1
    continue
  elif a==0:
    sus_a+=1
    continue
  elif b==0:
    sus_b+=1
    continue
  x=a*1.0/b
  if x in dic.keys():
    dic[x] += 1
  else:
    dic[x] = 1
ans=1
for k,v in dic.items():
  if v==0:
    continue
  if -1.0/k not in dic:
    ans *= 2
  else:
    ans *= (2**v+2**(dic[-1.0/k])-1)
    dic[-1.0/k]=0

if sus_a * sus_b >0:
  ans *= (2**sus_a + 2**sus_b-1)
elif sus_a >0:
  ans *= 2**sus_a
elif sus_b>0:
  ans *= 2**sus_b
print((ans+sus_ab-1) % 1000000007)

Submission status: Wrong Answer

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

MOD = 10 ** 9 + 7

dic = defaultdict(int)

All_zero = 0

S = set()
N = int(input())
ans = 0 #仲が悪い数を数える
for i in range(N):
    a, b = map(int, input().split())
    if a == 0 and b == 0: #なんでもOK
        All_zero += 1
    elif a == 0:
        S.add((0, 1))
        dic[(0, 1)] += 1
    elif b == 0:
        S.add((1, 0))
        dic[(1, 0)] += 1
    else:
        GCD = gcd(a, b)
        a //= GCD
        b //= GCD
        if a < 0: #aを必ず正にする
            a *= -1
            b *= -1
        S.add((a, b))
        dic[(a, b)] += 1
        

lst = []
for a, b in S:
    tmp1 = dic[(a, b)]
    A = a
    B = b
    if B < 0:
        B *= -1
        A *= -1
    tmp2 = dic[(B, -A)]
    dic[(B, -A)] = 0
    if tmp1 > 0:
        lst.append((tmp1, tmp2))

# print (lst)

ans = 1
for a, b in lst:
    tmp = (pow(2, a, MOD) - 1) + (pow(2, b, MOD) - 1) + 1 #左側を入れる、右側を入れる、両方入れない
    ans *= tmp
    ans %= MOD

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