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 pos[10000000 + 5];
int main() {
  int n, input, ansx, ansy;
  cin >> n;
  long long mi = 1ll << 60, ma = -1;
  for (int i = 1; i <= n; i++) {
    cin >> input;
    if (pos[input] && input < mi) {
      ansx = pos[input];
      ansy = i;
      mi = input;
    }
    pos[input] = i;
    if (input > ma) ma = input;
  }
  int ans[5] = {};
  for (int i = 1; i <= ma; i++) {
    long long t = i;
    int tmp = 0;
    for (int j = i, times = 1; j <= ma; j += i, times++) {
      if (pos[j]) {
        ans[tmp++] = pos[j];
        t *= times;
        if (tmp == 2) break;
      }
    }
    if (tmp < 2) continue;
    if (t < mi) {
      mi = t;
      ansx = (ans[0] < ans[1]) ? ans[0] : ans[1];
      ansy = (ans[0] < ans[1]) ? ans[1] : ans[0];
    }
  }
  cout << ansx << " " << ansy << "\n";
  return 0;
}
