You are given an array a consisting of n integers a_1, a_2, ..., a_n.

Your problem is to find such pair of indices i, j (1 ≤ i < j ≤ n) that lcm(a_i, a_j) is minimum possible.

lcm(x, y) is the least common multiple of x and y (minimum positive number such that both x and y are divisors of this number).

Input

The first line of the input contains one integer n (2 ≤ n ≤ 10^6) — the number of elements in a.

The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^7), where a_i is the i-th element of a.

Output

Print two integers i and j (1 ≤ i < j ≤ n) such that the value of lcm(a_i, a_j) is minimum among all valid pairs i, j. If there are multiple answers, you can print any.

Examples

Input


5
2 4 8 3 6


Output


1 2


Input


5
5 2 11 3 7


Output


2 4


Input


6
2 5 10 1 10 2


Output


1 4
#include <bits/stdc++.h>
using namespace std;
int freq[10000005];
vector<int> pos[10000005];
int main() {
  cin.tie(0)->sync_with_stdio(0);
  cin.tie(NULL);
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    int x;
    cin >> x;
    pos[x].push_back(i);
    freq[x]++;
  }
  long long cmmmc = LONG_LONG_MAX;
  int sol1 = -1, sol2 = -1;
  for (int i = 10000000; i >= 1; i--) {
    int nr1 = -1, nr2 = -1;
    for (int j = i; j <= 10000000; j += i) {
      if (freq[j] == 0) {
        continue;
      }
      if (nr1 == -1) {
        if (freq[j] >= 2) {
          nr1 = j;
          nr2 = j;
          break;
        } else
          nr1 = j;
      } else {
        if (nr2 == -1) {
          nr2 = j;
          break;
        }
      }
    }
    if (nr1 == -1 || nr2 == -1) continue;
    long long sus = 1LL * nr1 * nr2;
    if (sus / i < cmmmc) {
      cmmmc = sus / i;
      sol1 = nr1;
      sol2 = nr2;
    }
  }
  if (sol1 == sol2) {
    cout << min(pos[sol1][0], pos[sol1][1]) << " "
         << max(pos[sol1][0], pos[sol1][1]);
  } else {
    cout << min(pos[sol1][0], pos[sol2][0]) << " "
         << max(pos[sol1][0], pos[sol2][0]);
  }
}
