#include #include using namespace std; using namespace atcoder; using mint = modint1000000007; const int mod = 1000000007; //using mint = modint998244353; //const int mod = 998244353; //const int INF = 1e9; //const long long LINF = 1e18; #define rep(i, n) for (int i = 0; i < (n); ++i) #define rep2(i,l,r)for(int i=(l);i<(r);++i) #define rrep(i, n) for (int i = (n-1); i >= 0; --i) #define rrep2(i,l,r)for(int i=(r-1);i>=(l);--i) #define all(x) (x).begin(),(x).end() #define allR(x) (x).rbegin(),(x).rend() #define endl "\n" #define P pair template inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; } template inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; } bool comp(const P& lh, const P& rh) { return lh.second * rh.first < rh.second * lh.first; } long long gcd(long long a, long long b) { if (b == 0) return a; else return gcd(b, a%b); } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); vector

v; int n; cin >> n; int c = 0; rep(i, n) { long long a, b; cin >> a >> b; if ((0 == a) && (0 == b))continue; if (a < 0) { a = -a; b = -b; } v.emplace_back(a, b); } n = v.size(); sort(all(v), comp); v.resize(n * 2); rep(i, n) v[i + n] = { -v[i].first, -v[i].second }; vector>point(v.size()); point[0] = { 0,0 }; rep(i, (int)v.size() - 1) { point[i + 1] = { point[i].first + v[i].first, point[i].second + v[i].second }; } mint s2 = 0; rep(i, point.size()) { int j = (i + 1) % point.size(); s2 += point[j].second * point[i].first - point[j].first * point[i].second; } // s2 = 辺上 + 内部 * 2 - 2 mint on = 0, in = 0; rep(i, v.size()) on += abs(gcd(v[i].first, v[i].second)); in = (s2 + 2 - on) / 2; mint ans = in + on; cout << ans.val() << endl; return 0; }