//#pragma warning(disable:4996) //#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include //#include #include #include #include #include //#include //< in.txt > out.txt using namespace std; //std::ios::sync_with_stdio(false); //std::cin.tie(0); const long long MOD = 1e9 + 7; const long long INF = 1e18; typedef long long LL; typedef long double LD; typedef unsigned long long ULL; //typedef boost::multiprecision::cpp_int bigint; typedef pair PLL; typedef pair PI; typedef pair pdl; typedef pair pdd; typedef vector VLL; typedef vector VVLL; typedef vector VI; typedef vector> VVI; typedef unsigned long long ULL; template using pqueue = priority_queue, function>; template inline void chmin(T& a, T b) { a = min(a, b); } template inline void chmax(T& a, T b) { a = max(a, b); } //y/xのfloorを求める LL floor_(LL y, LL x) { if (x < 0) { x *= -1; y *= -1; } if (y >= 0) { return y / x; } else { if ((-y) % x == 0) { return y / x; } else { return -((-y) / x) - 1; } } } inline LL mod(LL a, LL m) { LL res = a % m; return res >= 0 ? res : res + m; } void input(); void solve(); void daminput(); void naive(); void outputinput(); int main() { std::cin.tie(0); std::ios::sync_with_stdio(false); cout << fixed << setprecision(12); input(); //daminput(); solve(); //naive(); //outputinput(); return 0; } ////////////////////////////////////////////////// ////////////////////////////////////////////////// //最大公約数 //O(log max(a,b)) template T GCD(T a, T b) { if (b == 0)return a; return GCD(b, (T)(a % b)); } //最大公約数(複数) //O(nlog max(a_i))? template T GCD(vector v) { for (int n = 1; n < v.size(); n++) { v[n] = GCD(v[n], v[n - 1]); } return v[v.size() - 1]; } //最小公倍数 template T LCM(T a, T b) { return a * b / GCD(a, b); } //最小公倍数(複数) template T LCM(vector v) { for (int n = 1; n < v.size(); n++) { v[n] = LCM(v[n], v[n - 1]); } return v[v.size() - 1]; } //ax+by=gcd(a,b)の解 LL extgcd(LL a, LL b, LL& x, LL& y) { LL d = a; if (b != 0) { d = extgcd(b, a % b, y, x); y -= (a / b) * x; } else { x = 1; y = 0; } return d; } //ax=gcd(a,m) mod mなるxを返す LL ModInv(LL a, LL m) { LL x, y; extgcd(a, m, x, y); return x; } //x = b1 mod m1 //x = b2 mod m2 //なる連立合同式を解く mod lcm(m1,m2)において解が存在するならば(x,lcm(m1,m2))を、存在しないならば(0,-1)を返す PLL SimCongruence(LL b1, LL m1, LL b2, LL m2) { LL p, q; LL d = extgcd(m1, m2, p, q); if ((b1 - b2) % d != 0) { return PLL(0, -1); } else { //? LL m = m1 / d * m2; LL tmp = (b2 - b1) / d * p % (m2 / d); LL r = mod(b1 + m1 * tmp, m); return PLL(r, m); } } //garnerのアルゴリズム x=b[k] mod m[k] (0 < k < K) の解xをmod Mで求める(ただしm[-]は互いに素) //O(K^2log(max(m[k]))) LL Garner(VLL& b, VLL& m, LL M) { int K = m.size(); //番兵 m.push_back(M); //const[k] := t0+t1m0+...+tkm0m1...m{k-1} mod mk VLL con(K + 1, 0); //coeff[k] := m0...m{k-1} mod mk VLL coeff(K + 1, 1); for (int k = 0; k < K; k++) { //solve t*coeff[k]=b[k]-const[k] mod mk LL t = mod((b[k] - con[k]) * ModInv(coeff[k], m[k]), m[k]); for (int i = k + 1; i <= K; i++) { con[i] = mod(con[i] + t * coeff[i], m[i]); coeff[i] = mod(coeff[i] * m[k], m[i]); } } return con.back(); } //garnerのアルゴリズムでx=b[k] mod m[k] (0 < k < K) の解xをmod Mで求める際、m[-]が互いに素でないならば実行する //そもそも解が存在しないならば-1を返す //O(K^2log(max(m[k]))) LL PreGarner(VLL& b, VLL& m, LL M) { LL res = 1; int K = b.size(); for (int i = 0; i < K; i++) { for (int j = 0; j < i; j++) { LL g = GCD(m[i], m[j]); if ((b[i] - b[j]) % g != 0) { return -1; } m[i] /= g; m[j] /= g; LL gi = GCD(m[i], g); LL gj = g / gi; do { g = GCD(gi, gj); gi *= g, gj /= g; } while (g != 1); m[i] *= gi; m[j] *= gj; b[i] %= m[i]; b[j] %= m[j]; } } for (int i = 0; i < K; i++) { res = mod(res * m[i], M); } return res; } int N; VLL X, Y; void input() { cin >> N; X.resize(N); Y.resize(N); for (int n = 0; n < N; n++) { cin >> X[n] >> Y[n]; } } void daminput() { } void solve() { LL res = PreGarner(X, Y, MOD); if (res == -1) { cout << -1 << "\n"; return; } bool flag = true; for (int n = 0; n < X.size(); n++) { if (X[n] != 0) { flag = false; break; } } LL res2 = Garner(X, Y, MOD); if (!flag) { cout << res2 << "\n"; } else { cout << res << "\n"; } } void naive() { } void outputinput() { }