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++ (Clang 10.0.0) (judge verdict: Wrong Answer)

#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>
#include <climits>
#include <cstring>
#include <cassert>


using namespace std;
#define SZ(x) (int)(x.size())
#define REP(i, n) for(int i=0;i<n;++i)
#define FOR(i, a, b) for(int i=a;i<b;++i)
#define RREP(i, n) for(int i=n-1;i>=0;--i)
#define RFOR(i, a, b) for(int i=b-1;i>=a;--i)

#define all(x) begin(x),end(x)
#define dump(x) cerr<<#x<<" = "<<(x)<<endl
#define debug(x) cerr<<#x<<" = "<<(x)<<" (L"<<__LINE__<<")"<< endl;

using ll = long long;
using vi = vector<int>;
using vvi = vector<vi>;
using vll = vector<ll>;
using vvll = vector<vll>;
using P = pair<int, int>;
const double eps = 1e-8;
const ll MOD = 1000000007;
const int INF = INT_MAX / 2;
const ll LINF = LLONG_MAX / 2;

template<class T>
bool chmax(T &a, const T &b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template<class T>
bool chmin(T &a, const T &b) {
    if (b < a) {
        a = b;
        return true;
    }
    return false;
}


template<typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> p) {
    os << p.first << ":" << p.second;
    return os;
}

template<class T>
ostream &operator<<(ostream &os, const vector<T> &v) {
    os << "[";
    REP(i, SZ(v)) {
        if (i) os << ", ";
        os << v[i];
    }
    return os << "]";
}

// edit
ll gcd(ll a, ll b) {
    if (a < b) swap(a, b);
    if (a % b == 0) return b;
    return gcd(b, a % b);

}

pair<ll, ll> yaku(pair<ll, ll> p){
    if(p.first == 0){
        return make_pair(0ll, 1ll);
    }else if(p.second == 0){
        return make_pair(1ll, 0ll);
    }
    
    ll g = gcd(p.first, p.second);
    return make_pair(p.first / g, p.second / g);
}
    
class Mint {
    using u64 = std::uint_fast64_t;
    u64 Modulus = MOD;
    
public:
    u64 a;
    
    constexpr Mint(const u64 x = 0) noexcept : a(x % Modulus) {}
    
    constexpr u64 &value() noexcept { return a; }
    
    constexpr const u64 &value() const noexcept { return a; }
    
    constexpr Mint operator+(const Mint rhs) const noexcept {
        return Mint(*this) += rhs;
    }
    
    constexpr Mint operator-(const Mint rhs) const noexcept {
        return Mint(*this) -= rhs;
    }
    
    constexpr Mint operator*(const Mint rhs) const noexcept {
        return Mint(*this) *= rhs;
    }
    
    constexpr Mint operator/(const Mint rhs) const noexcept {
        return Mint(*this) /= rhs;
    }
    
    constexpr Mint &operator+=(const Mint rhs) noexcept {
        a += rhs.a;
        if (a >= Modulus) {
            a -= Modulus;
        }
        return *this;
    }
    
    constexpr Mint &operator-=(const Mint rhs) noexcept {
        if (a < rhs.a) {
            a += Modulus;
        }
        a -= rhs.a;
        return *this;
    }
    
    constexpr Mint &operator*=(const Mint rhs) noexcept {
        a = a * rhs.a % Modulus;
        return *this;
    }
    
    constexpr Mint &operator/=(Mint rhs) noexcept {
        u64 exp = Modulus - 2;
        while (exp) {
            if (exp % 2) {
                *this *= rhs;
            }
            rhs *= rhs;
            exp /= 2;
        }
        return *this;
    }
    
    constexpr Mint &pow(int rhs) noexcept {
        u64 exp = static_cast<u64>(rhs);
        Mint base(a);
        a = 1;
        while (exp) {
            if (exp % 2) {
                *this *= base;
            }
            base *= base;
            exp /= 2;
        }
        return *this;
    }
    
};

void solve() {
    int N;
    cin >> N;
    
    vector<ll> A(N), B(N);
    
    REP(i, N){
        cin >> A[i] >> B[i];
    }
    
    map<pair<ll,ll>, ll> Pos, Neg;
    ll zero = 0;
    
    REP(i, N){
        if(A[i] == 0 || B[i] == 0){
            zero++;
            continue;
        }
        
        if(A[i] / abs(A[i]) * B[i] / abs(B[i]) > 0){
            auto p = yaku(make_pair(abs(A[i]), abs(B[i])));
            Pos[p]++;
        }else{
            auto p = yaku(make_pair(abs(B[i]), abs(A[i])));
            Neg[p]++;
        }
    }
    
    Mint ans = zero + 1;
    
    set<pair<ll,ll>> st;
    for(auto e : Pos){
        st.insert(e.first);
    }
    for(auto e : Neg){
        st.insert(e.first);
    }
    
    for(auto e : st){
        Mint left = Mint(2).pow(Pos[e]);
        Mint right = Mint(2).pow(Neg[e]);
        Mint tmp = left + right - 1;
        ans *= tmp;
    }
    ans = ans - 1;
    
    cout << ans.value() << endl;
    

    
}



int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
//    std::ifstream in("input.txt");
//    std::cin.rdbuf(in.rdbuf());

    solve();


    return 0;
}