#define _USE_MATH_DEFINES #define _CRT_SECURE_NO_WARNINGS #include using namespace std; /*BigInteger #include #include #include namespace xxx = boost::multiprecision; using Bint = xxx::cpp_int; using Real = xxx::number>; */ #define int long long #define pb(x) push_back(x) #define m0(x) memset((x), 0, sizeof(x)) #define mm(x) memset((x), -1, sizeof(x)) //container #define ALL(x) (x).begin(), (x).end() #define RALL(a) (a).rbegin(), (a).rend() #define EACH(i, c) for (typeof((c).begin()) i = (c).begin(); i != (c).end(); ++i) #define EXIST(s, e) ((s).find(e) != (s).end()) #define UNIQUE(v) (v).erase(unique((v).begin(), (v).end()), (v).end()); #define PERM(c) \ sort(ALL(c)); \ for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c))) // debug #define GET_VAR_NAME(variable) #variable #define test(x) cout << GET_VAR_NAME(x) << " = " << x << endl; // bit_macro #define bit(n) (1LL << (n)) #define bitset(a, b) (a) |= (1 << (b)) #define bitunset(a, b) (a) &= ~(1 << (b)) #define bitcheck(a, b) ((((a) >> (b)) & 1) == 1) #define bitcount(a) __builtin_popcountll((a)) //typedef typedef long long lint; typedef unsigned long long ull; typedef complex Complex; typedef pair P; typedef tuple TP; typedef vector vec; typedef vector mat; //constant constexpr int INF = (int)1e18; constexpr int MOD = (int)1e9 + 7; constexpr double PI = (double)acos(-1); constexpr double EPS = (double)1e-10; constexpr int dx[] = {-1, 0, 0, 1, 0, -1, -1, 1, 1}; constexpr int dy[] = {0, -1, 1, 0, 0, 1, -1, 1, -1}; // template void chmax(T &a, T b) { a = max(a, b); } template void chmin(T &a, T b) { a = min(a, b); } // inline int toInt(string s) { int v; istringstream sin(s); sin >> v; return v; } template inline string toString(T x) { ostringstream sout; sout << x; return sout.str(); } // struct Accelerate_Cin { Accelerate_Cin() { cin.tie(0); ios::sync_with_stdio(0); cout << fixed << setprecision(20); }; }; //O(N^2) //Garnerのアルゴリズム //中国剰余定理 inline int mod(int a, int m) { int res = a % m; if (res < 0) res += m; return res; } int GCD(int a, int b) { if (b == 0) return a; else return GCD(b, a % b); } int extGCD(int a, int b, int &p, int &q) { if (b == 0) { p = 1; q = 0; return a; } int d = extGCD(b, a % b, q, p); q -= a / b * p; return d; } int modinv(int a, int m) { int x, y; extGCD(a, m, x, y); return mod(x, m); } int PreGarner(vector &b, vector &m, int MOD) { int res = 1; for (int i = 0; i < (int)b.size(); ++i) { for (int j = 0; j < i; ++j) { int g = GCD(m[i], m[j]); if ((b[i] - b[j]) % g != 0) return -1; m[i] /= g; m[j] /= g; int gi = GCD(m[i], g), 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 < (int)b.size(); ++i) (res *= m[i]) %= MOD; return res; } int Garner(vector b, vector m, int MOD) { m.push_back(MOD); vector coeffs((int)m.size(), 1); vector constants((int)m.size(), 0); //m同士で互いに素でない場合があるとき。 //preGarner(b,m,MOD); for (int k = 0; k < (int)b.size(); ++k) { int t = mod((b[k] - constants[k]) * modinv(coeffs[k], m[k]), m[k]); for (int i = k + 1; i < (int)m.size(); ++i) { (constants[i] += t * coeffs[i]) %= m[i]; (coeffs[i] *= m[k]) %= m[i]; } } return constants.back(); } signed main() { int N; cin >> N; vec X(N), Y(N); bool flag = true; for (int i = 0; i < N; i++) { cin >> X[i] >> Y[i]; if (X[i]) flag = false; } int lcm = PreGarner(X, Y, 1e18 + 100); if (lcm == -1) { cout << -1 << endl; return 0; } if (flag) { cout << lcm << endl; return 0; } cout << Garner(X, Y, 1e18 + 100) << endl; return 0; }