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G. Minimum Possible LCM

time limit per test

4 secondsmemory limit per test

1024 megabytesinput

standard inputoutput

standard outputYou are given an array $$$a$$$ consisting of $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$.

Your problem is to find such pair of indices $$$i, j$$$ ($$$1 \le i < j \le n$$$) 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 $$$n$$$ ($$$2 \le n \le 10^6$$$) — 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.

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

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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