#D3645. Minimum Possible LCM
Minimum Possible LCM
Minimum Possible LCM
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
inputFormat
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.
outputFormat
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
样例
5
2 4 8 3 6
1 2