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;
const int N = 10000001;
int num[N], n;
long long ans = LLONG_MAX;
int t1, t2;
int main() {
  ios::sync_with_stdio(false);
  cin >> n;
  int tmp;
  for (int i = 1; i <= n; i++) {
    cin >> tmp;
    if (num[tmp] && tmp < ans) {
      ans = tmp;
      t1 = num[tmp];
      t2 = i;
    }
    if (!num[tmp]) num[tmp] = i;
  }
  for (int i = 1; i < N && i < ans; i++) {
    long long s1 = 0, s2 = 0;
    for (int j = i; j < N; j += i) {
      if (!num[j])
        continue;
      else if (!s1)
        s1 = j, s2 = num[j];
      else {
        if (ans > s1 * j / i) {
          ans = s1 * j / i;
          t1 = s2;
          t2 = num[j];
        }
        break;
      }
    }
  }
  if (t1 > t2) swap(t1, t2);
  cout << t1 << ' ' << t2 << endl;
  return 0;
}
