Geometric progression with the first element a and common ratio b is a sequence of numbers a, ab, ab2, ab3, ....

You are given n integer geometric progressions. Your task is to find the smallest integer x, that is the element of all the given progressions, or else state that such integer does not exist.

Input

The first line contains integer (1 ≤ n ≤ 100) — the number of geometric progressions. 

Next n lines contain pairs of integers a, b (1 ≤ a, b ≤ 109), that are the first element and the common ratio of the corresponding geometric progression.

Output

If the intersection of all progressions is empty, then print  - 1, otherwise print the remainder of the minimal positive integer number belonging to all progressions modulo 1000000007 (109 + 7).

Examples

Input

2
2 2
4 1


Output

4


Input

2
2 2
3 3


Output

-1

Note

In the second sample test one of the progressions contains only powers of two, the other one contains only powers of three.
#include <bits/stdc++.h>
using namespace std;
const long long int modulo = 1000000007;
int esprimo[100000];
vector<int> primo;
vector<pair<int, int> > factorizacion(int x) {
  vector<pair<int, int> > f;
  for (int i = 0; i < int(primo.size()) and primo[i] <= x; i++) {
    int p = primo[i];
    int e = 0;
    while (x % p == 0) {
      x /= p;
      e++;
    }
    if (e) f.push_back(pair<int, int>(p, e));
  }
  if (x > 1) f.push_back(pair<int, int>(x, 1));
  return f;
}
int exponente(int p, vector<pair<int, int> > &f) {
  for (int i = 0; i < int(f.size()); i++)
    if (f[i].first == p) return f[i].second;
  return 0;
}
long long int eleva(long long int b, long long int e) {
  if (e == 0) return 1;
  if (e % 2 == 0) return eleva(b * b % modulo, e / 2);
  return b * eleva(b * b % modulo, e / 2) % modulo;
}
long long int mcd(long long int a, long long int b) {
  if (a < b) swap(a, b);
  if (b == 0) return a;
  return mcd(a % b, b);
}
long long int mcm(long long int a, long long int b) {
  return a / mcd(a, b) * b;
}
long long int absolut(long long int x) {
  if (x < 0) return -x;
  return x;
}
void chino(long long int a, long long int b, long long int &fa,
           long long int &fb, long long int c) {
  if (absolut(a) < absolut(b)) {
    chino(b, a, fb, fa, c);
    return;
  }
  if (b == 0) {
    if (c % a != 0) {
      cout << -1 << endl;
      exit(0);
    }
    fa = c / a;
    fb = 0;
    return;
  }
  chino(a % b, b, fa, fb, c);
  fb -= fa * (a / b);
}
void chino(long long int ini1, long long int salto1, long long int ini2,
           long long int salto2, long long int &con1, long long int &fac1,
           long long int &con2, long long int &fac2) {
  chino(salto1, -salto2, con1, con2, ini2 - ini1);
  fac1 = mcm(salto1, salto2) / salto1;
  fac2 = mcm(salto1, salto2) / salto2;
  long long int desp1 = 0;
  if (con1 < 0) {
    desp1 += -con1 / fac1;
    con1 %= fac1;
    if (con1 < 0) {
      con1 += fac1;
      desp1++;
    }
  }
  desp1 -= con1 / fac1;
  con1 %= fac1;
  con2 += desp1 * fac2;
  long long int desp2 = 0;
  if (con2 < 0) {
    desp2 += -con2 / fac2;
    con2 %= fac2;
    if (con2 < 0) {
      con2 += fac2;
      desp2++;
    }
  }
  con1 += desp2 * fac1;
}
void chino(long long int &ini, long long int &salto, long long int ininew,
           long long int saltonew) {
  long long int con, fac, connew, facnew;
  chino(ini, salto, ininew, saltonew, con, fac, connew, facnew);
  ini = ini + con * salto;
  salto = fac * salto;
}
void comprueba(vector<pair<int, int> > &fa1, vector<pair<int, int> > &fb1,
               vector<pair<int, int> > &fa2, vector<pair<int, int> > &fb2,
               int p, long long int &fac1, long long int fac2) {
  if (not(exponente(p, fb1) == 0 or fac1 != -1)) {
    fac1 = (exponente(p, fa2) + fac2 * exponente(p, fb2) - exponente(p, fa1)) /
           exponente(p, fb1);
    if (fac1 < 0) {
      cout << -1 << endl;
      exit(0);
    }
  }
  if (exponente(p, fa1) + fac1 * exponente(p, fb1) !=
      exponente(p, fa2) + fac2 * exponente(p, fb2)) {
    cout << -1 << endl;
    exit(0);
  }
}
void comprueba(vector<pair<int, int> > &fa1, vector<pair<int, int> > &fb1,
               vector<pair<int, int> > &fa2, vector<pair<int, int> > &fb2,
               vector<pair<int, int> > &f, long long int &fac1,
               long long int fac2) {
  for (int i = 0; i < int(f.size()); i++)
    comprueba(fa1, fb1, fa2, fb2, f[i].first, fac1, fac2);
}
void comprueba(vector<pair<int, int> > &fa1, vector<pair<int, int> > &fb1,
               vector<pair<int, int> > &fa2, vector<pair<int, int> > &fb2,
               long long int fac2) {
  long long int fac1 = -1;
  comprueba(fa1, fb1, fa2, fb2, fa1, fac1, fac2);
  comprueba(fa1, fb1, fa2, fb2, fb1, fac1, fac2);
  comprueba(fa1, fb1, fa2, fb2, fa2, fac1, fac2);
  comprueba(fa1, fb1, fa2, fb2, fb2, fac1, fac2);
}
void escribe(long long int a, vector<pair<int, int> > &fb, long long int fac) {
  long long int sol = a;
  for (int i = 0; i < int(fb.size()); i++) {
    long long int p = fb[i].first;
    long long int e = fb[i].second;
    e = fac * e;
    sol = sol * eleva(p, e) % modulo;
  }
  cout << sol << endl;
  exit(0);
}
void arregla(vector<pair<int, int> > &fa, vector<pair<int, int> > &fb) {
  int ib = 0;
  vector<pair<int, int> > nextfa;
  for (int ia = 0; ia < int(fa.size()); ia++, ib++) {
    for (; fb[ib].first != fa[ia].first; ib++)
      nextfa.push_back(pair<int, int>(fb[ib].first, 0));
    nextfa.push_back(fa[ia]);
  }
  for (; ib < int(fb.size()); ib++)
    nextfa.push_back(pair<int, int>(fb[ib].first, 0));
  fa = nextfa;
}
int n;
long long int a[100], b[100];
vector<pair<int, int> > fa[100], fb[100];
void intenta(int ind, long long int fac) {
  for (int i = 0; i < n; i++)
    if (i != ind) comprueba(fa[i], fb[i], fa[ind], fb[ind], fac);
  escribe(a[ind], fb[ind], fac);
}
void elimina(set<int> &s, vector<pair<int, int> > &f) {
  vector<pair<int, int> > nextf;
  for (int i = 0; i < int(f.size()); i++)
    if (s.count(f[i].first) == 0) nextf.push_back(f[i]);
  f = nextf;
}
int main() {
  for (int i = 2; i < 100000; i++) esprimo[i] = 1;
  for (int i = 2; i < 100000; i++) {
    if (esprimo[i]) {
      primo.push_back(i);
      for (int j = i + i; j < 100000; j += i) esprimo[j] = 0;
    }
  }
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a[i] >> b[i];
    fa[i] = factorizacion(a[i]);
    fb[i] = factorizacion(b[i]);
  }
  for (int i = 1; i < n; i++) {
    for (int j = 0; j < int(fb[0].size()); j++) {
      int p = fb[0][j].first;
      int e = fb[0][j].second;
      if (exponente(p, fb[i]) == 0) {
        long long int x = exponente(p, fa[i]) - exponente(p, fa[0]);
        if (x < 0 or x % e != 0) {
          cout << -1 << endl;
          exit(0);
        }
        intenta(0, x / e);
      }
    }
    for (int j = 0; j < int(fb[i].size()); j++) {
      int p = fb[i][j].first;
      int e = fb[i][j].second;
      if (exponente(p, fb[0]) == 0) {
        long long int x = exponente(p, fa[0]) - exponente(p, fa[i]);
        if (x < 0 or x % e != 0) {
          cout << -1 << endl;
          exit(0);
        }
        intenta(i, x / e);
      }
    }
  }
  set<int> s;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < int(fa[i].size()); j++)
      if (exponente(fa[i][j].first, fb[i]) == 0) s.insert(fa[i][j].first);
  for (set<int>::iterator it = s.begin(); it != s.end(); it++) {
    int p = *it;
    int e = exponente(p, fa[0]);
    for (int i = 1; i < n; i++) {
      if (exponente(p, fa[i]) != e) {
        cout << -1 << endl;
        exit(0);
      }
    }
  }
  for (int i = 0; i < n; i++) elimina(s, fa[i]);
  for (int i = 0; i < n; i++) arregla(fa[i], fb[i]);
  if (int(fb[0].size()) == 0) {
    intenta(0, 0);
  }
  long long int con = 0, salto = 1;
  for (int i = 1; i < n; i++) {
    long long int l1, ll1, l2, ll2;
    chino(fa[0][0].second, fb[0][0].second, fa[i][0].second, fb[i][0].second,
          l1, ll1, l2, ll2);
    for (int j = 0; j < int(fb[0].size()); j++) {
      long long int t1, tt1, t2, tt2;
      chino(fa[0][j].second, fb[0][j].second, fa[i][j].second, fb[i][j].second,
            t1, tt1, t2, tt2);
      if (ll1 == tt1 and ll2 == tt2) {
        if ((t1 - l1) % ll1 != 0 or (t2 - l2) % ll2 != 0 or
            (t1 - l1) / ll1 != (t2 - l2) / ll2) {
          cout << -1 << endl;
          exit(0);
        }
        long long int nextl1 = max(l1, t1);
        chino(con, salto, nextl1, ll1);
      } else {
        long long int x = t1 * tt2 - t2 * tt1;
        long long int y = l1 * tt2 - l2 * tt1;
        long long int z = ll1 * tt2 - ll2 * tt1;
        long long int xy = x - y;
        if (xy % z != 0) {
          cout << -1 << endl;
          exit(0);
        }
        intenta(0, l1 + xy / z * ll1);
      }
    }
  }
  intenta(0, con);
}
