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Boring Number

Time limit: 1000 ms
Memory limit: 128 MB

You are given an array $A$ of $N$ integers. Find the index $i$ of an element such that the absolute difference between $A_i$ and the arithmetic mean of all the $N$ integers is minimum. If the solution is not unique, find the smallest index $i$ .

Standard input

The first line contains a single integer $N$ .

The second line contains the $N$ elements of the array $A$ .

Standard output

Print the answer on the first line.

Constraints and notes

$1 \leq N \leq 10^3$
$1 \leq A_i \leq 10^5$

Input	Output	Explanation
4 1 2 3 4	2	The arithmetic mean of the numbers is $2.5$ . The absolute difference between the mean and $A_2$ or $A_3$ is $0.5$ , but you should output the smallest index.
3 1 2 2	2	The artihmetic mean is $1.(6)$ , $A_2$ and $A_3$ have the minimum absolute difference of $0.(3)$
3 2 1 1	2	The artihmetic mean is $1.(3)$ , $A_2$ and $A_3$ have the minimum absolute difference of $0.(3)$

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