Problem:
Score : 200 points

Problem Statement

Niwango-kun is an employee of Dwango Co., Ltd.

One day, he is asked to generate a thumbnail from a video a user submitted.

To generate a thumbnail, he needs to select a frame of the video according to the following procedure:

Get an integer N and N integers a_0, a_1, ..., a_{N-1} as inputs. N denotes the number of the frames of the video, and each a_i denotes the representation of the i-th frame of the video.

Select t-th frame whose representation a_t is nearest to the average of all frame representations.

If there are multiple such frames, select the frame with the smallest index.

Find the index t of the frame he should select to generate a thumbnail.

Constraints

1 \leq N \leq 100

1 \leq a_i \leq 100

All numbers given in input are integers

Input

Input is given from Standard Input in the following format:

N
a_{0} a_{1} ... a_{N-1}

Output

Print the answer.

Sample Input 1

3
1 2 3

Sample Output 1

1

Since the average of frame representations is 2, Niwango-kun needs to select the index 1, whose representation is 2, that is, the nearest value to the average.

Sample Input 2

4
2 5 2 5

Sample Output 2

0

The average of frame representations is 3.5.

In this case, every frame has the same distance from its representation to the average.

Therefore, Niwango-kun should select index 0, the smallest index among them.

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::cmp::Ordering;
use std::io::prelude::*;
use std::io::stdin;
use std::str::FromStr;

fn main() {
    let n: usize = read();
    let a: Vec<(usize, f64)> = (0..n).map(|i| (i, read())).collect();
    let arv_a: f64 = a.iter().map(|x| x.1).sum::<f64>() / a.len() as f64;
    let mut a: Vec<(usize, f64)> = a.iter().map(|&(f, x)| (f, (arv_a - x).abs())).collect();
    a.sort_by(|&(f1, x1), &(f2, x2)| match cmp_f64(&x1, &x2) {
        Ordering::Greater => Ordering::Greater,
        Ordering::Less => Ordering::Less,
        Ordering::Equal => f1.cmp(&f2),
    });
    println!("{}", a[0].0);
}

fn cmp_f64(a: &f64, b: &f64) -> Ordering {
    if a.is_nan() {
        return Ordering::Greater;
    }
    if b.is_nan() {
        return Ordering::Less;
    }
    if a < b {
        return Ordering::Less;
    } else if a > b {
        return Ordering::Greater;
    }
    return Ordering::Equal;
}

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let token: String = stdin
        .lock()
        .bytes()
        .map(|b| b.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}