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>
std::mt19937 rng(
    (int)std::chrono::steady_clock::now().time_since_epoch().count());
int findCycle(int x, int a, int b, int p) {
  int ans = 0;
  int cur = x;
  while (ans == 0 || cur != x) {
    if (ans > 2 * p) {
      return -1;
    }
    cur = (cur * a + b) % p;
    ans++;
  }
  return ans;
}
const int ms = 2002000;
const int MOD = (int)1e9 + 7;
int pri[ms];
int freq[ms];
int ans[ms], mx_freq[ms];
bool solve(int x) {
  bool valid = false;
  while (x > 1) {
    int e = 0;
    int p = pri[x];
    while (x % p == 0) {
      x /= p;
      e++;
    }
    if (ans[p] < e) {
      valid = true;
      ans[p] = e;
      mx_freq[p] = 0;
    }
    if (ans[p] == e) {
      mx_freq[p]++;
    }
  }
  return valid;
}
bool eval(int x) {
  bool valid = true;
  while (x > 1) {
    int e = 0;
    int p = pri[x];
    while (x % p == 0) {
      x /= p;
      e++;
    }
    if (ans[p] == e && mx_freq[p] == 1) {
      valid = false;
    }
  }
  return valid;
}
int main() {
  int n;
  std::cin >> n;
  for (int i = 2; i < ms; i++) {
    if (pri[i]) {
      continue;
    }
    for (int j = i; j < ms; j += i) {
      pri[j] = i;
    }
  }
  for (int i = 0; i < n; i++) {
    int p;
    scanf("%d", &p);
    freq[p]++;
  }
  bool flag = false;
  std::vector<int> wtf;
  for (int i = ms - 1; i > 0; i--) {
    if (freq[i] > 0 && !ans[i]) {
      solve(i);
      freq[i]--;
    }
    if (freq[i] > 0 && solve(i - 1)) {
      freq[i]--;
      wtf.push_back(i - 1);
    }
    if (freq[i] > 0) {
      flag = true;
    }
  }
  for (auto i : wtf) {
    flag = flag || eval(i);
  }
  long long tot = 1;
  for (int i = 1; i < ms; i++) {
    while (ans[i]--) {
      tot = tot * i % MOD;
    }
  }
  if (flag) {
    tot = (tot + 1) % MOD;
  }
  std::cout << tot << std::endl;
}