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
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
    static int MAX = (int)1e7+1;
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner input = new Scanner(System.in);
		int n = input.nextInt();
		int arr[] = new int[n];
		int index[] = new int[MAX];
		int count[] = new int[MAX];
		long res =Long.MAX_VALUE;
		int rind1=-1;
		int rind2 = -1;
		int ind1=-1;
		int ind2 = -1;
		long tres = Long.MAX_VALUE;
		for(int i =0;i<n;i++){
		    arr[i] = input.nextInt();
		    if(count[arr[i]]>0  && arr[i]<res){
		        rind1 = index[arr[i]];
		        rind2 = i;
		        res = arr[i];
		    }
		    index[arr[i]] = i;
		    count[arr[i]]++;
		}

		for(int i =1;i<MAX;i++){
		    ind1 = -1;ind2 = -1;
		    for(int j = i;j<MAX;j+=i){
		        if(count[j]>0 && ind1 != -1){
		            ind2 = index[j];
		            break;
		        }else if(count[j]>0){
		            ind1 = index[j];
		        }
		    }
		    if(ind1 != -1 && ind2 != -1){
		        long a = arr[ind1];
		        long b = arr[ind2];
		        tres = (a*b)/i;
		    }
		    if(tres<res){
		        res = tres;
		        rind1 = Math.min(ind1,ind2);
		        rind2 = Math.max(ind1,ind2);
		        
		    }
		}
		System.out.println((rind1+1)+" "+(rind2+1));
		
		
	}
}
