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 <bits/stdc++.h>
#include <iostream>  // cin, cout, string
#include <algorithm> // sort, min/max, upper/lower_bound, transform, count/copy_if
#include <vector>
#include <utility> // pair, swap
#include <functional>
#include <iomanip> // setprecision
#include <map>
#include <set> // multiset
#include <unordered_map>
#include <unordered_set>
#include <tuple>
#include <stack>
#include <queue> // priority_queue
#include <deque>
#include <bitset>
#include <array>
#include <list>
#include <forward_list>
#include <complex>
#include <ratio>
#include <cassert>
#include <numeric> // accumulate, itoa
#include <random>  // mt19937
#include <iterator>
#include <chrono>
#include <cstring>

using namespace std;

// #define int long long

using i64 = int64_t;
using ll = long long;
using ld = long double;

template <typename T>
using vec = vector<T>;
template <typename T>
using mat = vec<vec<T>>;
template <typename T>
using dic = unordered_map<string, T>;
template <typename T>
using pqg = priority_queue<T, vector<T>, greater<T>>; // dijkstra
// template<typename T, typename U> using P = pair<T, U>;
// template<typename... Args> using func = function<Args...>;
// template<typename T> using pq = priority_queue<T>;

using pii = pair<int, int>;
using ppi = pair<pii, int>;
using pip = pair<int, pii>;
using ppp = pair<pii, pii>;

using vi = vec<int>;
using mi = mat<int>; // Graph
using vp = vec<pii>;

constexpr int IINF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
// constexpr int INF = sizeof(int) == sizeof(long long) ? LINF : IINF;
constexpr long long MOD = 1e9 + 7;

#define _overload(_1, _2, _3, name, ...) name
#define _rep1(i, a, b) for (int i = (a), _##i = (b); i < _##i; ++i)
#define _rep2(i, n) _rep1(i, 0, n)
#define _rep3(n) _rep2(i, n)
#define rep(...) _overload(__VA_ARGS__, _rep1, _rep2, _rep3)(__VA_ARGS__)
#define _rrep1(i, a, b) for (int i = (b)-1, _##i = (a); i >= _##i; --i)
#define _rrep2(i, n) _rrep1(i, 0, n)
#define _rrep3(n) _rrep2(i, n)
#define rrep(...) _overload(__VA_ARGS__, _rrep1, _rrep2, _rrep3)(__VA_ARGS__)

#define each(i, a) for (auto &&i : a)
#define each2(i, a) for (const auto &i : a)

#define pb push_back
// emplace_back(*) == push_back(constructor(*))
#define eb emplace_back
#define pob pop_back
#define pf push_front
#define pof pop_front

#define np next_permutation
#define pp prev_permutation

// make_pair(A, B) == pair<T, U>(A, B)
#define mp make_pair
// mt(...) == tie(...)
#define mt make_tuple

#define ft first
#define sd second

#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define sz(a) (int)(a).size()
#define rev(a) reverse(all(a))
#define rs(a, l) (a).resize(l)

#define upper(s) transform(all(s), (s).begin(), topper)
#define lower(s) transform(all(s), (s).begin(), tolower)

#define sum(a) accumulate(all(a), 0)
#define elif else if
#define unless(a) if (!(a))
#define qt(a) #a

#define endl '\n'
#define dec(n) fixed << setprecision(n)
#define zfl(n) setfill(‘0’) << setw(n)

template <typename T = int, T l = 0, T r = (T)MOD>
auto rnd = bind(uniform_int_distribution<T>(l, r), mt19937(chrono::steady_clock::now().time_since_epoch().count()));

template <typename T>
inline constexpr T gcd(T a, T b)
{
    if (a == 0 || b == 0)
        return 0;
    while (b)
    {
        a = a % b;
        swap(a, b);
    }
    return a;
}
template <typename T>
inline constexpr T extgcd2(T a, T b, T &x, T &y)
{
    x = 1;
    y = 0;
    while (b)
    {
        T t = a / b;
        a -= t * b;
        swap(a, b);
        x -= t * y;
        swap(x, y);
    }
    return a;
}
template <typename T>
inline constexpr T lcm(T a, T b) { return a / gcd(a, b) * b; }

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

template <typename A, typename B>
istream &operator>>(istream &is, pair<A, B> &p)
{
    is >> p.first;
    is >> p.second;
    return is;
}
template <typename A, typename B>
ostream &operator<<(ostream &os, const pair<A, B> &p)
{
    os << p.first << " " << p.second;
    return os;
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v)
{
    for (auto &&x : v)
        is >> x;
    return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v)
{
    for (int i = 0; i < (int)v.size(); ++i)
        cout << v[i] << (i + 1 != (int)v.size() ? " " : "");
    return os;
}

#define debug(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << endl
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg>
void __f(const char *name, const Arg &arg)
{
    cerr << name << " : " << arg << endl;
}
template <typename Arg, typename... Args>
void __f(const char *names, const Arg &arg, const Args &... args)
{
    const char *comma = strchr(names + 1, ',');
    cerr.write(names, comma - names) << " : " << arg << " | ";
    __f(comma + 1, args...);
}

inline auto yes(const bool &c) { return c ? "yes" : "no"; }
inline auto Yes(const bool &c) { return c ? "Yes" : "No"; }
inline auto YES(const bool &c) { return c ? "YES" : "NO"; }
inline auto Possible(const bool &c) { return c ? "Possible" : "Impossible"; }
inline auto POSSIBLE(const bool &c) { return c ? "POSSIBLE" : "IMPOSSIBLE"; }

constexpr int lim = 100007; // 10^5+7

ll mod_inv(ll a)
{
    ll b = MOD, u = 1, v = 0, _a = a;
    while (b)
    {
        ll t = a / b;
        a -= t * b;
        swap(a, b);
        u -= t * v;
        swap(u, v);
    }
    u %= MOD;
    if (u < 0)
        u += MOD;
    return u;
}
ll mod_pow(ll a, ll n)
{
    ll res = 1;
    while (n > 0)
    {
        if (n & 1)
            res = res * a % MOD;
        a = a * a % MOD;
        n >>= 1;
    }
    return res;
}

//int count[MOD];

map<pii, int> d;

ll n;

signed main()
{
    cin.tie(0);
    cout.tie(0);
    ios_base::sync_with_stdio(false);
    cin >> n;
    ll ans = 1;
    ll ans1 = 0;
    rep(n)
    {
        ll a, b;
        cin >> a >> b;
        if (a == 0 && b == 0)
        {
            ans1 += 1;
            //d[{0, 0}] += 1;
            continue;
        }
        if (a == 0 && b != 0)
        {
            b = 1;
            d[{a, b}] += 1;
            continue;
        }
        if (b == 0 && a != 0)
        {
            a = 1;
            d[{a, b}] += 1;
            continue;
        }
        if (a < 0)
        {
            a *= -1;
            b *= -1;
        }
        ll c = gcd(a, b);
        a /= c;
        b /= c;

        d[{a, b}] += 1;
        // cout << a << " " << b << endl;
    }

    for (auto itr = d.begin(); itr != d.end(); itr++)
    {
        ll r1 = itr->first.first;
        ll n1 = itr->first.second;
        ll r2, n2;
        n2 = n1;
        r2 = -r1;
        if (n1 < 0)
        {
            n2 *= -1;
            r2 *= -1;
        }

        ll m1 = itr->second;
        ll m2 = d[{n2, r2}];
        d[{r1, n1}] = 0;
        d[{n2, r2}] = 0;

        ans *= mod_pow(2, m1) + mod_pow(2, m2) - 1;
        ans %= MOD;
        // cout << ans << " " << m1 << " " << m2 << " " << r1 << " " << n1 << endl;
    }
    ans += ans1;
    ans -= 1;
    if (ans < 0)
        ans += MOD;
    cout << ans << endl;
}