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)

#![allow(unused_imports)]

#[macro_use]
mod _input {
    use std::fmt;
    use std::io::{self, Read};
    use std::str::{self, FromStr};

    macro_rules! input {
        ($($name:ident : $t:tt),*,) => {
            input!($($name: $t),*)
        };
        ($($name:ident : $t:tt),*) => {
            let mut _scanned = ::_input::Scanned::new(::std::io::stdin(), 1024);
            $(
                let $name = _read_value!(_scanned, $t);
            )*
        };
    }

    macro_rules! _read_value {
        ($scanned:expr, ($($t:tt),*)) => {
            ($(_read_value!($scanned, $t)),*)
        };
        ($scanned:expr, [$t:tt; $n:expr]) => {
            (0..$n).map(|_| _read_value!($scanned, $t)).collect::<Vec<_>>()
        };
        ($scanned:expr, _bytes) => {
            _read_value!($scanned, String).into_bytes()
        };
        ($scanned:expr, _index) => {
            _read_value!($scanned, usize) - 1
        };
        ($scanned:expr, $t:ty) => {
            $scanned.next::<$t>()
        };
    }

    #[derive(Default)]
    pub struct Scanned {
        buf: Vec<u8>,
        pos: usize,
    }

    impl Scanned {
        pub fn new<R: Read>(mut input: R, estimated: usize) -> Self {
            let mut buf = Vec::with_capacity(estimated);
            let _ = io::copy(&mut input, &mut buf).unwrap();
            if buf.last() != Some(&b'\n') {
                buf.push(b'\n'); // input may not end with '\n'
            }
            // https://doc.rust-lang.org/src/core/char/methods.rs.html#906-908
            // assert!(str::from_utf8(&buf).unwrap().bytes().all(|c| u32::from(c) <= 0x7F));
            Scanned { buf: buf, pos: 0 }
        }

        #[inline]
        pub fn next<T: FromStr>(&mut self) -> T
        where
            T::Err: fmt::Debug,
        {
            let mut start = None;
            loop {
                match (self.buf[self.pos], start.is_some()) {
                    (b' ', true) | (b'\n', true) => break,
                    (_, true) | (b' ', false) | (b'\n', false) => self.pos += 1,
                    (_, false) => start = Some(self.pos),
                }
            }
            let target = &self.buf[start.unwrap()..self.pos];
            unsafe { str::from_utf8_unchecked(target) }.parse().unwrap()
        }
    }
}

#[allow(dead_code)]
mod output {
    use std::io::{self, BufWriter, StdoutLock, Write as _Write};

    pub fn with_stdout<F: FnMut(&mut BufWriter<StdoutLock>)>(mut f: F) {
        let stdout = io::stdout();
        let mut stdout = BufWriter::new(stdout.lock());
        f(&mut stdout);
        stdout.flush().unwrap();
    }
}

use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
use std::io::Write;
use std::ops::{
    Add, AddAssign, BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign, Div, DivAssign,
    Mul, MulAssign, Neg, Not, Rem, RemAssign, Sub, SubAssign,
};
use std::str::{self, FromStr};
use std::{char, cmp, f32, f64, fmt, i16, i32, i64, i8, thread, u16, u32, u64, u8};

fn main() {
    input! {
        n: usize,
        a: [i32; n],
    }
    let s = a.iter().cloned().sum::<i32>();
    let r = a
        .iter()
        .enumerate()
        .min_by_key(|&(_, ref v)| (s - (n as i32) * *v).abs())
        .map(|(i, _)| i)
        .unwrap();
    println!("{}", r);
}