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 <vector>
#include <numeric>
#include <algorithm>
#include <cmath>
#include <climits>
#include <map>
#include <set>

constexpr int SINT_MAX = std::numeric_limits<int>::max();
constexpr int SINT_MIN = std::numeric_limits<int>::min();

using namespace std;
using vi = vector<int>;
using vvi = vector<vi>;
using ll = long long;
using vll = vector<ll>;
using vvll = vector<vll>;

template<class T>
T choose(bool b, T t, T f)
{
    if (b) return t;
    else return f;    
}

const char *YesNo(bool b)
{
    return choose(b, "Yes", "No");
}

const char *YESNO(bool b)
{
    return choose(b, "YES", "NO");
}

template<template<class...> class ContT, class ValueT, size_t Dim>
struct vec_type
{
    using type = ContT<typename vec_type<ContT, ValueT, Dim-1>::type>;
};

template<template<class...> class ContT, class ValueT>
struct vec_type<ContT, ValueT, 0>
{
    using type = ValueT;
};

template<class ValueT, size_t Dim = 1>
using vec_t = typename vec_type<std::vector, ValueT, Dim>::type;


template<class ValueT, size_t Dim, class = typename std::enable_if<Dim == 0>::type>
auto make_vec(ValueT value = ValueT()) -> ValueT
{
    return value;
}

template<class ValueT, size_t Dim, class... Rest>
auto make_vec(size_t size0, Rest... rest)
{
    auto vec = make_vec<ValueT, Dim-1>(rest...);
    return std::vector(size0, vec);
}

int diffabs(int l, int r)
{
    if (l < r) return r-l;
    else return l-r;    
}

 
constexpr uint_fast64_t MOD = 1e9 + 7;
 
template<class StoreT, class AddT, class MulT, StoreT MOD>
class ModInt
{
    using self_type = ModInt<StoreT, AddT, MulT, MOD>;
    StoreT i;
 
public:
    ModInt()
        : i(0)
    {}
    ModInt(StoreT i)
    {
        while(i < 0) i += MOD;
        this->i = i;
    }
 
    ModInt(const self_type& i) = default;
    constexpr self_type &operator=(const self_type& i) = default;
 
    constexpr uint_fast32_t getI() const noexcept
    {
        return i;
    }
 
    ModInt& operator +=(self_type rhs)
    {
        AddT i64 = static_cast<AddT>(i);
        StoreT a32 = static_cast<StoreT>((i64 + rhs.i) % MOD);
        i = a32;
        return *this;
    }
 
    constexpr ModInt operator +(self_type rhs) const noexcept
    {
        self_type newInt(*this);
        newInt += rhs;
        return newInt;
    }
 
    ModInt& operator -=(self_type rhs)
    {
        AddT i64 = static_cast<AddT>(i);
        StoreT a32 = static_cast<StoreT>((i64 + MOD - rhs.i) % MOD);
        i = a32;
        return *this;
    }
 
    constexpr ModInt operator -(self_type rhs) const noexcept
    {
        self_type newInt(*this);
        newInt -= rhs;
        return newInt;
    }
 
    ModInt& operator *=(self_type rhs)
    {
        MulT i64 = static_cast<MulT>(i);
        StoreT a32 = static_cast<StoreT>((i64 * rhs.i) % MOD);
        i = a32;
        return *this;
    }
 
    constexpr ModInt operator *(self_type rhs) const noexcept
    {
        self_type newInt(*this);
        newInt *= rhs;
        return newInt;
    }
 
    constexpr ModInt operator /(self_type rhs) const noexcept
    {
        self_type newInt(*this);
        self_type rhsInv = rhs.inv();
        newInt *= rhsInv;
        return newInt;
    }
 
    constexpr bool operator ==(self_type rhs) const noexcept
    {
        return i == rhs.i;
    }
 
    constexpr bool operator <(self_type rhs) const noexcept
    {
        return i < rhs.i;
    }
 
    constexpr bool operator >(self_type rhs) const noexcept
    {
        return rhs < *this;
    }
 
    constexpr ModInt pow(int n) const noexcept
    {
        ModInt a = *this;
        ModInt res = 1;
 
        while (n > 0)
        {
            if (n & 1)
            {
                res *= a;
            }
            a *= a;
            n >>= 1;
        }
        return res;
    }
 
    constexpr self_type inv() const noexcept
    {
        return pow(MOD - 2);
    }
};
 
template<class StoreT, class AddT, class MulT, StoreT MOD>
std::ostream& operator <<(std::ostream& ost, ModInt<StoreT, AddT, MulT, MOD> i)
{
    ost << i.getI();
    return ost;
}
 
using UModInt = ModInt<uint_fast32_t, uint_fast32_t, uint_fast64_t, MOD>;
using SModInt = ModInt<int_fast32_t, int_fast32_t, int_fast64_t, MOD>;
 

template<class ModIntT>
class BinomialFactory
{
    std::vector<ModIntT> stock;
    std::vector<ModIntT> inv;
 
public:
    explicit BinomialFactory(int N)
    {
        stock.resize(N + 1);
        inv.resize(N + 1);
        stock[0] = 1;
        inv[0] = 1;
        for (int i = 1; i <= N; i++)
        {
            stock[i] = stock[i - 1] * i;
            inv[i] = stock[i].inv();
        }
    }
 
    ModIntT bi(int n, int r) const
    {
        if (r == 0 || r == n) return 1;
 
        return stock[n] * inv[n - r] * inv[r];
    }
};


///////////////////////////////////////////////////

int main()
{
    int N;
    cin >> N;

    map<pair<int,int>,int> g;
    for (int i = 0; i < N; i++)
    {
        int a, b;
        cin >> a >> b;

        int l = gcd(a, b);
        a /= l;
        b /= l;
        
        if (a < 0)
        {
            a = -a;
            b = -b;
        }
        
        g[{a, b}]++;
    }

    vector<pair<int,int>> C;
    for (auto p : g)
    {
        if (auto it = g.find({p.first.second, -p.first.first}); it != g.end())
        {
            C.emplace_back(p.second, it->second);
        }
        else if (auto it = g.find({-p.first.second, p.first.first}); it != g.end())
        {
            // skip
        }
        else
        {
            C.emplace_back(p.second, 0);
        }
        
    }
    
    UModInt ans = 1;
    for (auto p : C)
    {
        UModInt t = 2;
        ans *= (t.pow(p.first) + t.pow(p.second) - 1);
    }
    ans -= 1;

    cout << ans << endl;
}