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;
int kt[10000003];
long long cnt[10000003];
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  vector<int> nto;
  for (int i = 2; i <= (int)1e7; ++i) {
    if (kt[i]) continue;
    nto.emplace_back(i);
    for (int j = i; j <= (int)1e7; j += i) kt[j] = i;
  }
  int n;
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    int x;
    cin >> x;
    ++cnt[x];
  }
  for (int i = (int)1e7 - 1; i; --i) {
    cnt[i] += cnt[i + 1];
  }
  for (int i = (int)1e7; i > 1; --i) {
    if (kt[i] != i) cnt[kt[i]] += cnt[i];
    cnt[i / kt[i]] += cnt[i];
  }
  long long l = 1, r = 1e15;
  while (l <= r) {
    long long mid = l + r >> 1;
    bool flag = true;
    for (auto& x : nto) {
      long long ans = 0;
      for (long long i = x; i <= mid; i *= x) {
        ans += mid / i;
      }
      if (ans < cnt[x]) {
        flag = false;
        break;
      }
    }
    if (!flag)
      l = mid + 1;
    else
      r = mid - 1;
  }
  cout << l;
}