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 n;
int v[1000001], maxx;
long long ans = 1e17;
vector<int> f[10000001], res;
int main() {
  ios_base::sync_with_stdio(0);
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> v[i];
    if (v[i] > maxx) maxx = v[i];
    f[v[i]].push_back(i);
  }
  for (int i = 1; i <= maxx; i++) {
    vector<int> ind;
    for (int j = i; j <= maxx; j += i) {
      for (auto k : f[j]) ind.push_back(k);
      if (ind.size() >= 2) break;
    }
    if (ind.size() >= 2) {
      if (ans > 1LL * v[ind[0]] * v[ind[1]] / i)
        ans = 1LL * v[ind[0]] * v[ind[1]] / i, res = ind;
    }
  }
  sort(res.begin(), res.end());
  cout << res[0] << ' ' << res[1] << '\n';
  return 0;
}
