#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<unordered_set>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
#include<array>
#include<chrono>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
//constexpr ll mod = 998244353;
constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int>P;

#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;

template<typename T>
void chmin(T& a, T b) {
	a = min(a, b);
}
template<typename T>
void chmax(T& a, T b) {
	a = max(a, b);
}
template<typename T>
void cinarray(vector<T>& v) {
	rep(i, v.size())cin >> v[i];
}
template<typename T>
void coutarray(vector<T>& v) {
	rep(i, v.size()) {
		if (i > 0)cout << " "; cout << v[i];
	}
	cout << "\n";
}
ll mod_pow(ll x, ll n, ll m = mod) {
	if (n < 0) {
		ll res = mod_pow(x, -n, m);
		return mod_pow(res, m - 2, m);
	}
	if (abs(x) >= m)x %= m;
	if (x < 0)x += m;
	//if (x == 0)return 0;
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % m;
		x = x * x % m; n >>= 1;
	}
	return res;
}
struct modint {
	int n;
	modint() :n(0) { ; }
	modint(ll m) {
		if (m < 0 || mod <= m) {
			m %= mod; if (m < 0)m += mod;
		}
		n = m;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
bool operator<(modint a, modint b) { return a.n < b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
	if (n == 0)return modint(1);
	modint res = (a * a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }
modint operator/=(modint& a, modint b) { a = a / b; return a; }
const int max_n = 1 << 20;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}
modint combP(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[a - b];
}

ll gcd(ll a, ll b) {
	a = abs(a); b = abs(b);
	if (a < b)swap(a, b);
	while (b) {
		ll r = a % b; a = b; b = r;
	}
	return a;
}
typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-8;
const ld pi = acosl(-1.0);
template<typename T>
void addv(vector<T>& v, int loc, T val) {
	if (loc >= v.size())v.resize(loc + 1, 0);
	v[loc] += val;
}
/*const int mn = 100005;
bool isp[mn];
vector<int> ps;
void init() {
	fill(isp + 2, isp + mn, true);
	for (int i = 2; i < mn; i++) {
		if (!isp[i])continue;
		ps.push_back(i);
		for (int j = 2 * i; j < mn; j += i) {
			isp[j] = false;
		}
	}
}*/

//[,val)
template<typename T>
auto prev_itr(set<T>& st, T val) {
	auto res = st.lower_bound(val);
	if (res == st.begin())return st.end();
	res--; return res;
}

//[val,)
template<typename T>
auto next_itr(set<T>& st, T val) {
	auto res = st.lower_bound(val);
	return res;
}
using mP = pair<modint, modint>;
mP operator+(mP a, mP b) {
	return { a.first + b.first,a.second + b.second };
}
mP operator+=(mP& a, mP b) {
	a = a + b; return a;
}
mP operator-(mP a, mP b) {
	return { a.first - b.first,a.second - b.second };
}
mP operator-=(mP& a, mP b) {
	a = a - b; return a;
}

mt19937 mt(time(0));

const string drul = "DRUL";
string senw = "SENW";
//DRUL,or SENW
int dx[4] = { 1,0,-1,0 };
int dy[4] = { 0,1,0,-1 };
//-----------------------------------------


using T = ld;
T dot(LP a, LP b) {
	return (T)a.first * (T)b.first + (T)a.second * (T)b.second;
}
T cross(LP a, LP b) {
	return (T)a.first * (T)b.second - (T)a.second * (T)b.first;
}
T norm2(LP a) {
	return (T)a.first * (T)a.first + (T)a.second * (T)a.second;
}
int ccw(LP a, LP b, LP c) {
	b.first -= a.first; b.second -= a.second;
	c.first -= a.first; c.second -= a.second;
	if (cross(b, c) > 0)return 1;
	if (cross(b, c) < 0)return -1;
	if (dot(b, c) < 0)return 2;
	if (norm2(b) < norm2(c))return -2;
	return 0;
}
typedef vector<LP> polygon;
polygon ConvexHull(polygon p) {
	int n = p.size();
	int k = 0;
	sort(all(p));
	p.erase(unique(all(p)), p.end());
	n = p.size();
	polygon ch(2 * n);
	for (int i = 0; i < n; ch[k++] = p[i++]) {
		while (k >= 2 && ccw(ch[k - 2], ch[k - 1], p[i]) <= 0)--k;
	}
	for (int i = n - 2, t = k + 1; i >= 0; ch[k++] = p[i--]) {
		while (k >= t && ccw(ch[k - 2], ch[k - 1], p[i]) <= 0)--k;
	}
	ch.resize(k - 1);
	return ch;
}
void solve() {
	int n; cin >> n;
	vector<ll> x(n), y(n);
	vector<pair<ld, int>> vp;
	rep(i, n) {
		cin >> x[i] >> y[i];
		if (x[i] == 0 && y[i] == 0)continue;
		ld t = atan2(y[i], x[i]);
		vp.push_back({ t,i });
	}
	sort(all(vp));
	int len = vp.size();
	vector<ld> dif(len);
	rep(i, len) {
		if (i + 1 < len)dif[i] = vp[i + 1].first - vp[i].first;
		else {
			dif[i] = 2 * pi + vp[0].first - vp[i].first;
		}
	}
	//coutarray(dif);
	rep(i, len) {
		vp.push_back({ vp[i].first + 2 * pi, vp[i].second });
	}
	vector<ll> rx(vp.size() + 1);
	vector<ll> ry(vp.size() + 1);
	vector<ld> rdif(vp.size()+1);
	rep(i, vp.size()) {
		int id = vp[i].second;
		rx[i + 1] = rx[i] + x[id];
		ry[i + 1] = ry[i] + y[id];
		rdif[i + 1] = rdif[i] + dif[i % len];
	}

	polygon p;
	rep(i, len) {
		int r = lower_bound(all(vp), pair<ld,int>{ vp[i].first + 2 * pi,-1 }) - vp.begin();
		//[i,r)
		p.push_back({ rx[r] - rx[i],ry[r] - ry[i] });
		//cout << "hello " << i << "\n";
		for (int j = r - 1; j > i; j--) {
			int pre = (i - 1 + len) % len;

			ld val = dif[pre] + rdif[j] - rdif[i];
			//cout << "?? " << val << "\n";
			//if(true){
			if (val > pi+eps) {
				p.push_back({ rx[j] - rx[i],ry[j] - ry[i] });
			}
			else break;
		}
	}
	p.push_back({ 0,0 });
	p = ConvexHull(p);
	modint ans = 0;
	rep(i, p.size()) {
		//cout << p[i].first << " " << p[i].second << "\n";
		int ni = (i + 1) % p.size();
		modint dx = p[ni].first - p[i].first;
		modint sy = p[ni].second + p[i].second;
		ans += (modint)-dx * sy;
	}
	ans /= 2;
	//cout << "?? " << ans << "\n";
	ans += 1;
	modint dec = 0;
	rep(i, p.size()) {
		int ni = (i + 1) % p.size();
		ll dx = abs(p[ni].first - p[i].first);
		ll dy = abs(p[ni].second - p[i].second);
		ll g = gcd(dx, dy);
		dec += g;
	}
	dec /= 2;
	ans += dec;
	cout << ans << "\n";
}

signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(10);
	init_f();
	//init();
	//expr();
	//while(true)
	//int t; cin >> t;rep(i,t)
	solve();
	return 0;
}