Problem: In a far away galaxy there is war again. The treacherous Republic made k precision strikes of power ai on the Empire possessions. To cope with the republican threat, the Supreme Council decided to deal a decisive blow to the enemy forces. 

To successfully complete the conflict, the confrontation balance after the blow should be a positive integer. The balance of confrontation is a number that looks like <image>, where p = n! (n is the power of the Imperial strike), <image>. After many years of war the Empire's resources are low. So to reduce the costs, n should be a minimum positive integer that is approved by the commanders.

Help the Empire, find the minimum positive integer n, where the described fraction is a positive integer.

Input

The first line contains integer k (1 ≤ k ≤ 106). The second line contains k integers a1, a2, ..., ak (1 ≤ ai ≤ 107).

Output

Print the minimum positive integer n, needed for the Empire to win.

Please, do not use the %lld to read or write 64-but integers in С++. It is preferred to use the cin, cout streams or the %I64d specificator.

Examples

Input

2
1000 1000


Output

2000

Input

1
2


Output

2

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int NS = 1000100;
const int MS = 10000010;
int n, t;
int a[MS], b[MS];
int minp[MS], pri[MS], pos[MS], top = 0;
long long c[MS];
void prime_table() {
  for (int i = 2; i < MS; i++) {
    if (!minp[i]) {
      pri[top] = i;
      pos[i] = top++;
      for (int j = i; j < MS; j += i)
        if (!minp[j]) minp[j] = i;
    }
  }
}
int main() {
  prime_table();
  while (~scanf("%d", &n)) {
    memset(a, 0, sizeof(a));
    memset(b, 0, sizeof(b));
    memset(c, 0, sizeof(c));
    for (int i = 0; i < n; i++) scanf("%d", &t), a[t]++;
    for (int i = MS - 10; i > 1; i--) {
      c[pos[minp[i]]] += a[i] + b[i];
      b[i / minp[i]] += a[i] + b[i];
      a[i - 1] += a[i];
    }
    long long temp, s, mid, down = 1, up = 10000000000000LL;
    while (down < up) {
      t = 1;
      mid = (down + up) >> 1;
      for (int i = 0; i < top; i++) {
        s = 0, temp = mid;
        while (temp >= pri[i]) temp /= pri[i], s += temp;
        if (s < c[i]) {
          t = 0;
          break;
        }
      }
      if (t > 0)
        up = mid;
      else
        down = mid + 1;
    }
    printf("%I64d\n", up);
  }
  return 0;
}