Problem: You are given a tuple generator f^{(k)} = (f_1^{(k)}, f_2^{(k)}, ..., f_n^{(k)}), where f_i^{(k)} = (a_i ⋅ f_i^{(k - 1)} + b_i) mod p_i and f^{(0)} = (x_1, x_2, ..., x_n). Here x mod y denotes the remainder of x when divided by y. All p_i are primes.

One can see that with fixed sequences x_i, y_i, a_i the tuples f^{(k)} starting from some index will repeat tuples with smaller indices. Calculate the maximum number of different tuples (from all f^{(k)} for k ≥ 0) that can be produced by this generator, if x_i, a_i, b_i are integers in the range [0, p_i - 1] and can be chosen arbitrary. The answer can be large, so print the remainder it gives when divided by 10^9 + 7

Input

The first line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of elements in the tuple.

The second line contains n space separated prime numbers — the modules p_1, p_2, …, p_n (2 ≤ p_i ≤ 2 ⋅ 10^6).

Output

Print one integer — the maximum number of different tuples modulo 10^9 + 7.

Examples

Input

4
2 3 5 7


Output

210


Input

3
5 3 3


Output

30

Note

In the first example we can choose next parameters: a = [1, 1, 1, 1], b = [1, 1, 1, 1], x = [0, 0, 0, 0], then f_i^{(k)} = k mod p_i.

In the second example we can choose next parameters: a = [1, 1, 2], b = [1, 1, 0], x = [0, 0, 1].

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
string u =
    "This is only for test puprpose, it is not my code. I just want to check "
    "if I have corrected the code.";
const int MOD = 1000000007;
map<int, pair<int, int> > lcm;
map<int, int> mp[2000010];
int a[200010], p[2000010];
bool use[2000010];
void ins(int x) {
  if (x == 1) return;
  for (auto it = mp[x].begin(); it != mp[x].end(); it++) {
    int pd = it->first, po = it->second;
    use[pd] = true;
    if (po > lcm[pd].first)
      lcm[pd] = {po, 1};
    else if (po == lcm[pd].first)
      lcm[pd].second++;
  }
}
int main() {
  ios::sync_with_stdio(false);
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  sort(a, a + n);
  int maxx = a[n - 1];
  for (int i = 1; i <= maxx; i++) p[i] = i;
  for (int i = 2; i <= maxx; i++)
    if (p[i] == i)
      for (int j = i + i; j <= maxx; j += i) p[j] = i;
  for (int i = 2; i <= maxx; i++) {
    int tmp = i;
    while (tmp > 1) {
      mp[i][p[tmp]]++;
      tmp /= p[tmp];
    }
  }
  for (int i = n - 1; i >= 0; i--) {
    if (use[a[i]]) a[i]--;
    ins(a[i]);
    use[a[i]] = true;
  }
  bool tf = false;
  for (int i = n - 1; !tf && i >= 0; i--) {
    int x = a[i];
    if (x == 1) {
      tf = true;
      break;
    }
    bool tf2 = true;
    for (auto it = mp[x].begin(); tf2 && it != mp[x].end(); it++) {
      int pd = it->first, po = it->second;
      if (!(lcm[pd].first > po || lcm[pd].first == po && lcm[pd].second > 1))
        tf2 = false;
    }
    if (tf2) tf = true;
  }
  long long ans = 1;
  for (auto it = lcm.begin(); it != lcm.end(); it++)
    for (int i = 0; i < it->second.first; i++) ans = (ans * it->first) % MOD;
  if (tf) ans = (ans + 1) % MOD;
  cout << ans << "\n";
}