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>
const int maxn = 200010, maxm = 2000010, mod = 1000000007;
int n;
int p[maxn];
bool np[maxm];
int pr[maxm], pn;
int mp[maxm];
int mx[maxm], nm[maxm];
bool cs[maxn];
int ans, ad;
int In() {
  register char c;
  for (; c = getchar(), c != '-' && (c < '0' || c > '9');)
    ;
  register bool f = c == '-';
  register int s = f ? 0 : c - '0';
  for (; c = getchar(), c >= '0' && c <= '9';) s = s * 10 + c - '0';
  return f ? -s : s;
}
int main() {
  for (register int i = 2; i <= 2000000; ++i) {
    if (!np[i]) pr[++pn] = i, mp[i] = i;
    for (register int j = 1; j <= pn && i * pr[j] <= 2000000; ++j) {
      np[i * pr[j]] = 1, mp[i * pr[j]] = pr[j];
      if (!(i % pr[j])) break;
    }
  }
  n = In();
  for (register int i = 1; i <= n; ++i) p[i] = In();
  std::sort(p + 1, p + n + 1);
  for (register int i = n; i >= 1; --i) {
    if (!mx[p[i]])
      mx[p[i]] = nm[p[i]] = 1;
    else {
      cs[i] = 1;
      register int x = p[i] - 1;
      for (; x > 1;) {
        register int c = 0, z = mp[x];
        for (; mp[x] == z; x /= z) ++c;
        if (c > mx[z])
          mx[z] = c, nm[z] = 1;
        else if (c == mx[z])
          ++nm[z];
      }
    }
  }
  ans = 1;
  for (register int i = 1; i <= 2000000; ++i)
    for (register int j = 1; j <= mx[i]; ++j) ans = 1ll * ans * i % mod;
  for (register int i = 1; i <= n; ++i)
    if (cs[i]) {
      register int x = p[i] - 1;
      register int tg = 1;
      for (; x > 1;) {
        register int c = 0, z = mp[x];
        for (; mp[x] == z; x /= z) ++c;
        if (c == mx[z] && nm[z] == 1) tg = 0;
      }
      if (tg) ad = 1;
    }
  printf("%d\n", (ans + ad) % mod);
  return 0;
}