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
import java.util.Arrays;
import java.util.Scanner;

public class Round552Div3G {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int[] x = new int[n];
        int m = 0;
        for (int i = 0; i < n; ++i) {
            x[i] = scanner.nextInt();
            m = Integer.max(x[i], m);
        }
        int[] pos = new int[m + 1];
        Arrays.fill(pos, -1);
        long minLCM = Long.MAX_VALUE;
        int[] index = new int[2];
        for (int i = 0; i < n; ++i) {
            if (pos[x[i]] >= 0 && x[i] < minLCM) {
                minLCM = x[i];
                index[0] = pos[x[i]];
                index[1] = i;
            }
            pos[x[i]] = i;
        }
        for (int i = 1; i <= m; ++i) {
            int k = 0;
            int[] t = new int[2];
            for (int j = i; j <= m && k < 2; j += i) {
                if (pos[j] >= 0) {
                    t[k++] = j;
                }
            }
            if (k == 2 && (long) t[0] / i * t[1] < minLCM) {
                minLCM = (long) t[0] / i * t[1];
                index[0] = pos[t[0]];
                index[1] = pos[t[1]];
            }
        }

        if (index[0] > index[1]) {
            int t = index[0];
            index[0] = index[1];
            index[1] = t;
        }

        System.out.println((index[0] + 1) + " " + (index[1] + 1));
    }
}
