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 Main {
    static final long INF = 1_000_000_000_000_000L;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[n];
        int max = 0;

        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
            max = Math.max(max, a[i]);

        }
        int[] count = new int[max + 1];
        for (int i = 0; i < n; i++) {
            count[a[i]]++;
        }
        long min = INF;
        int ansI = -1, ansJ = -1;
        for (int d = 1; d <= max; d++) {
            int c = 0;
            int f = -1, s = -1;
            for (int i = d; i <= max && c < 2; i += d) {
                int x = count[i];
                while (x-- > 0 && c < 2) {
                    if (c == 0)
                        f = i;
                    else
                        s = i;
                    ++c;
                }
            }
            if (c < 2)
                continue;
            long x = f * (long) s / d;
            if (min > x) {
                min = x;
                ansI = f;
                ansJ = s;
            }
        }

        int c = 0;
        int[] res = new int[2];
        for (int i = 0; i < n && c < 2; i++) {
            if (ansI == a[i] || ansJ == a[i])
                res[c++] = i + 1;
        }
        Arrays.sort(res);
        System.out.print(res[0] + " " + res[1]);
        sc.close();
    }
}