Minimum Possible LCM

Description:

Input:

The first line of the input contains one integer $$$n$$$ ($$$2 \le n \le 10^6$$$) — the number of elements in $$$a$$$.

The second line of the input contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^7$$$), where $$$a_i$$$ is the $$$i$$$-th element of $$$a$$$.

Output:

Print two integers $$$i$$$ and $$$j$$$ ($$$1 \le i < j \le n$$$) 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.

Sample Input:

5
2 4 8 3 6

Sample Output:

1 2

Sample Input:

5
5 2 11 3 7

Sample Output:

2 4

Sample Input:

6
2 5 10 1 10 2

Sample Output:

1 4