Average Value

You are given an array $a$ of $n$ integers. Find any index $i$ ($1 \le i \le n$) such that the element $a\_i$ equals to the geometric mean of all the other elements. In other words, find any index $i$ that satisfies the following formula: $a\_i = \root{n-1}\of{\prod\_{\substack{k=1 \\\ k \neq i}}^n a\_k}\text{.}$

The first line contains one integer $n$ ($2 \leq n \leq 10^5$): the length of the array.

The second line contains $n$ integers $a\_1, a\_2, \ldots, a\_n$ ($a\_k \geq 1$; the total number of digits in all numbers does not exceed $300\\,000$).

It is guaranteed that the answer exists for the given array.

Output one integer: the index of the element that equals to geometric mean of the others items. It there are several answers, output any one of them.