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 mN = 1e7 + 10;
bitset<mN + 1> ip;
int mp[mN];
void sieve() {
  ip.set();
  ip[0] = ip[1] = 0;
  for (int i = 2; i * i < mN; i++) {
    if (ip[i])
      for (int j = i * i; j < mN; j += i) {
        ip[j] = 0;
        if (!mp[j]) mp[j] = i;
      }
  }
  for (int i = 2; i < mN; ++i) {
    if (ip[i]) mp[i] = i;
    mp[i] = max(mp[i], mp[i / mp[i]]);
  }
}
long long cnt[mN];
vector<pair<long long, long long> > vec;
bool ok(long long n) {
  for (int i = 0; i < vec.size(); ++i) {
    long long tmp = n, c = 0;
    while (tmp) {
      c += tmp / vec[i].first;
      tmp /= vec[i].first;
    }
    if (c < vec[i].second) return 0;
  }
  return 1;
}
int k, v;
int main() {
  sieve();
  scanf("%d", &k);
  for (int i = 0; i < k; ++i) {
    scanf("%d", &v);
    ++cnt[v];
  }
  if (cnt[1] == k) return puts("1");
  for (int i = mN - 2; i >= 2; --i) cnt[i] += cnt[i + 1];
  for (int i = mN - 1; i >= 2; --i) {
    if (ip[i]) continue;
    cnt[mp[i]] += cnt[i];
    cnt[i / mp[i]] += cnt[i];
  }
  for (int i = 2; i < mN; ++i)
    if (ip[i] && cnt[i]) vec.push_back(pair<long long, long long>(i, cnt[i]));
  long long s = 0, e = 1e13 + 100, m, bst;
  while (s <= e) {
    m = s + ((e - s) >> 1);
    if (ok(m))
      e = m - 1, bst = m;
    else
      s = m + 1;
  }
  cout << bst;
}