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)

#[derive(Debug, PartialEq)]
struct Frame {
    index: usize,
    value: i32,
}
#[cfg(test)]
mod tests;

fn main() {
    let n = read_usize();
    let v = read_line_vec(Some(n));
    let mut frames = parse_frame(v);
    let ave = frames.iter().fold(0, |a, b| a + b.value) as f64 / n as f64;
    let ans = find_frame(ave, frames);
    println!("{}", ans);
}

fn find_frame(ave: f64, frames: Vec<Frame>) -> i32 {
    let mut min_index = -1;
    let mut min_diff = 101.0;
    for i in frames {
        if (i.value as f64 - ave).abs() < min_diff {
            min_index = i.index as i32;
            min_diff = (i.value as f64 - ave).abs();
        }
    }
    min_index
}

fn parse_frame(v: Vec<String>) -> Vec<Frame> {
    let mut ans = Vec::with_capacity(v.len());
    for (i, e) in v.into_iter().enumerate() {
        ans.push(Frame {
            index: i,
            value: e.parse().unwrap(),
        });
    }
    ans
}

fn read_usize() -> usize {
    let handle = std::io::stdin();
    let mut buf = String::new();
    handle.read_line(&mut buf).unwrap();
    buf.trim().parse().unwrap()
}

fn read_line_vec(cap: Option<usize>) -> Vec<String> {
    let handle = std::io::stdin();
    let mut buf = String::new();
    handle.read_line(&mut buf).unwrap();
    match cap {
        Some(n) => {
            let mut v: Vec<String> = Vec::with_capacity(n);
            v = buf
                .trim()
                .split_whitespace()
                .map(|a| a.parse().unwrap())
                .collect();
            v
        }
        None => buf
            .trim()
            .split_whitespace()
            .map(|a| a.parse().unwrap())
            .collect(),
    }
}