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 in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<iostream>
#include<string>
#include<algorithm>
#include<vector>
#include<queue>
#include<map>
#include<math.h>
#include<iomanip>
#include<set>
#include<numeric>
#include<cstring>
#include<cstdio>
#include<functional>
#include<bitset>
#include<limits.h>
#include<cassert>
#include<iterator>
#include<complex>
#include<stack>
#include<unordered_map>
#include<unordered_set>
#include<time.h>
#include<random>
#include<array>
using namespace std;
using ll = long long;
#define rep(i, a, b) for(int i = a; i < b; i++)
#define rrep(i, a, b) for(int i = b - 1; i >= a; i--)
#define ALL(a) a.begin(), a.end()
using pii = pair<int,int>;
using piii = pair<pii,int>;
using pll = pair<long long, long long>;
using plll = pair<pll, long long>;
// #pragma GCC optimize("Ofast")
#define pcnt __builtin_popcount
#define buli(x) __builtin_popcountll(x)
#define pb push_back
#define mp make_pair
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );
#define isSquare(x) (sqrt(x)*sqrt(x) == x)
template<class T>inline bool chmax(T &a, const T &b) {if(a<b){a = b; return 1;} return 0; };
template<class T>inline bool chmin(T &a, const T &b) {if(a>b){a = b; return 1;} return 0; };
inline void in(void){return;}
template <typename First, typename... Rest> void in(First& first, Rest&... rest){cin >> first;in(rest...);return;}
inline void out(void){cout << "\n";return;}
template <typename First, typename... Rest> void out(First first, Rest... rest){cout << first << " ";out(rest...);return;}
const double EPS = 1e-9;
const int mod = 1e9 + 7;
const int INF = 1e9;
const long long INFLL = 1e18;
void iosetup() {
    cin.tie(nullptr);ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
}
template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 >& p) {
    os << p.first << " " << p.second;
    return os;
}
template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
    is >> p.first >> p.second;
    return is;
}
template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
    for(int i = 0; i < (int) v.size(); i++) {
        os << v[i] << (i + 1 != v.size() ? " " : "");
    }
    return os;
}
template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
    for(T &in : v) is >> in;
    return is;
}
template<class S, class T> pair<S,T> operator+(const pair<S,T> &s, const pair<S, T>& t){return pair<S,T>(s.first+t.first, s.second+t.second);}
template<class S, class T> pair<S,T> operator-(const pair<S,T> &s, const pair<S, T>& t){return pair<S,T>(s.first-t.first, s.second-t.second);}
template<class S, class T> pair<S,T> operator*(const pair<S,T> &s, const S& t){return pair<S,T>(s.first*t, s.second*t);}
template <typename T> void Exit(T first){cout << first << endl;exit(0); };
template< int mod > struct ModInt {
    unsigned x; ModInt() : x(0) {}
    ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
    ModInt &operator+=(const ModInt &p) {if((x += p.x) >= mod) x -= mod;return *this;}
    ModInt &operator-=(const ModInt &p) {if((x += mod - p.x) >= mod) x -= mod;return *this;}
    ModInt &operator*=(const ModInt &p) {x = (int) (1LL * x * p.x % mod);return *this;}
    ModInt &operator/=(const ModInt &p) {*this *= p.inverse();return *this;}
    ModInt operator-() const { return ModInt(-x); }
    ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
    ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
    ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
    ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
    bool operator==(const ModInt &p) const { return x == p.x; }
    bool operator!=(const ModInt &p) const { return x != p.x; }
    ModInt inverse() const {int a = x, b = mod, u = 1, v = 0, t;
    while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); }return ModInt(u);}
    ModInt pow(int64_t n) const {ModInt ret(1), mul(x); while(n > 0) {if(n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}
    friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x;}
    friend istream &operator>>(istream &is, ModInt &a) { int64_t t; is >> t; a = ModInt< mod >(t); return (is); }
    static int get_mod() { return mod; }
}; using modint = ModInt< mod >;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};
const pii dxy[4] = {pii(1,0), pii(0, 1), pii(-1, 0), pii(0, -1)};
const int calender[13] = {0, 31,28,31,30,31,30,31,31,30,31,30,31};
const int ucalender[13] = {0, 31,29,31,30,31,30,31,31,30,31,30,31};
bool range(int a, int b, int x){if(a <= x and x < b)return true;else return false;}
bool range(int a, int b, int c, int d, pii p){if(a <= p.first and p.first < b and c <= p.second and p.second < d) return true;else return false;}

long long modpow(long long a, long long n, long long mod) {
    long long res = 1;
    while (n > 0) {
        if (n & 1) res = res * a % mod;
        a = a * a % mod;
        n >>= 1;
    }
    return res;
}

int main(){
    iosetup();
    int N; cin >> N;
    vector<pll> P(N), Q, R; cin >> P;
    rep(i, 0, N){
        if(P[i].first == 0 and P[i].second == 0) continue;
        if(P[i].first < 0 and P[i].second < 0){
            P[i].first *= -1;
            P[i].second *= -1;
        }else if(P[i].first >= 0 and P[i].second < 0){
            P[i].first *= -1;
            P[i].second *= -1;
        }
        if(P[i].first!=0 and P[i].second != 0){
            ll g = gcd(P[i].first, P[i].second);
            P[i].first /= g;
            P[i].second /= g;
        }else{
            if(P[i].first == 0 and P[i].second != 0) P[i].second = 1;
            else if(P[i].first != 0 and P[i].second == 0) P[i].first = 1;
        }
        if(P[i].first >= 0 and P[i].second >= 0) Q.emplace_back(P[i]);
        else R.emplace_back(P[i]);
    }

    sort(ALL(Q), [](pll a, pll b){
        return atan2(a.first, a.second) < atan2(b.first, b.second);
    });
    for(auto& e: R){
        auto tmp = e.second;
        e.second = -e.first;
        e.first = tmp;
    }
    sort(ALL(R), [](pll a, pll b){
        return atan2(a.first, a.second) < atan2(b.first, b.second);
    });
    modint ans = 1;
    map<pll, int> MP, MP2;
    for(auto e: Q)MP[e]++;
    for(auto e: R)MP2[e]++;
    for(auto e: MP){
        ans *= modpow(2, MP2[e.first], mod) + modpow(2, e.second, mod) - 1;
        MP2.erase(e.first);
    }
    for(auto e: MP2){
        ans *= modpow(2, e.second, mod);
    }
    ans -=1;
    cout << ans << endl;





    return 0;
}