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>
const int Mod = 1000000007;
inline int qPow(int b, long long e) {
  int a = 1;
  for (; e; e >>= 1, b = (long long)b * b % Mod)
    if (e & 1) a = (long long)a * b % Mod;
  return a;
}
int Gcd(long long a, long long b) { return b ? Gcd(b, a % b) : a; }
int exGcd(long long a, long long b, long long &x, long long &y) {
  if (!b) return x = 1, y = 0, a;
  long long d = exGcd(b, a % b, y, x);
  return y -= a / b * x, d;
}
const int MN = 105, MS = 905;
int N, A[MN], B[MN];
int pr[MS], pc;
long long a[MS], b[MS], c[MS], d[MS];
inline void X(int x) {
  for (int i = 2; i * i <= x; ++i) {
    if (x % i) continue;
    pr[++pc] = i;
    while (x % i == 0) x /= i;
  }
  if (x > 1) pr[++pc] = x;
}
inline void Z(int x, long long *C) {
  for (int i = 1; i <= pc; ++i) {
    int p = pr[i];
    C[i] = 0;
    while (x % p == 0) x /= p, ++C[i];
  }
}
inline int Merge() {
  long long Sb = 0, Sd = 0;
  for (int i = 1; i <= pc; ++i) Sb += b[i], Sd += d[i];
  if (!Sb && !Sd) {
    for (int i = 1; i <= pc; ++i)
      if (a[i] != c[i]) return 0;
    return 1;
  }
  if (!Sb || !Sd) {
    if (!Sd) std::swap(a, c), std::swap(b, d), std::swap(Sb, Sd);
    long long k = 0;
    for (int i = 1; i <= pc; ++i)
      if (d[i]) {
        k = (a[i] >= c[i] && (a[i] - c[i]) % d[i] == 0) ? (a[i] - c[i]) / d[i]
                                                        : -1;
        break;
      } else if (a[i] != c[i])
        return 0;
    if (k == -1) return 0;
    for (int i = 1; i <= pc; ++i)
      if (c[i] + k * d[i] != a[i]) return 0;
    return 1;
  }
  int ok = 0;
  for (int i = 1; i <= pc; ++i)
    if (b[i] * Sd != d[i] * Sb) {
      ok = i;
      break;
    }
  if (ok) {
    int p1 = ok, p2 = 0;
    for (int i = 1; i <= pc; ++i)
      if (b[i] * d[p1] != d[i] * b[p1]) {
        p2 = i;
        break;
      }
    long long ka = d[p2] * (c[p1] - a[p1]) - d[p1] * (c[p2] - a[p2]);
    long long kc = b[p2] * (c[p1] - a[p1]) - b[p1] * (c[p2] - a[p2]);
    long long denom = d[p2] * b[p1] - d[p1] * b[p2];
    if (denom < 0) ka = -ka, kc = -kc, denom = -denom;
    if (ka < 0 || kc < 0 || ka % denom != 0 || kc % denom != 0) return 0;
    ka /= denom, kc /= denom;
    for (int i = 1; i <= pc; ++i) {
      if (a[i] + ka * b[i] != c[i] + kc * d[i]) return 0;
      a[i] = a[i] + ka * b[i], b[i] = 0;
    }
    return 1;
  }
  long long kb = 0, kd = 0;
  for (int i = 1; i <= pc; ++i)
    if (b[i]) {
      long long g = Gcd(b[i], d[i]);
      kb = b[i] / g, kd = d[i] / g;
      break;
    }
  long long k = 0;
  for (int i = 1; i <= pc; ++i)
    if (b[i]) {
      if ((a[i] - c[i]) % (b[i] / kb)) return 0;
      k = (a[i] - c[i]) / (b[i] / kb);
      break;
    }
  for (int i = 1; i <= pc; ++i)
    if (c[i] + k * (b[i] / kb) != a[i]) return 0;
  if (k < 0) std::swap(a, c), std::swap(b, d), std::swap(kb, kd), k = -k;
  long long x, y;
  exGcd(kb, kd, x, y);
  x = ((long long)x * -k % kd + kd) % kd;
  for (int i = 1; i <= pc; ++i) a[i] += x * b[i], b[i] *= kd;
  return 1;
}
int main() {
  scanf("%d", &N);
  for (int i = 1; i <= N; ++i) {
    scanf("%d%d", &A[i], &B[i]);
    X(A[i]), X(B[i]);
  }
  std::sort(pr + 1, pr + pc + 1);
  pc = std::unique(pr + 1, pr + pc + 1) - pr - 1;
  for (int i = 1; i <= N; ++i)
    if (i == 1)
      Z(A[i], a), Z(B[i], b);
    else if (Z(A[i], c), Z(B[i], d), !Merge())
      return puts("-1"), 0;
  int Ans = 1;
  for (int i = 1; i <= pc; ++i) Ans = (long long)Ans * qPow(pr[i], a[i]) % Mod;
  printf("%d\n", Ans);
  return 0;
}
