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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

string to_string(__int128_t a) {
    if (a == 0) return "0";
    if (a < 0) return "-"s + to_string(-a);
    string ret = "";
    while (a) {
        ret += '0' + a % 10;
        a /= 10;
    }
    reverse(ret.begin(), ret.end());
    return ret;
}

struct Rational {
    using Long = __int128_t;
    Long a, b;
    Rational() : a(0), b(1) {}
    Rational(Long a) : a(a), b(1) {}
    Rational(Long a, Long b) : a(a), b(b) { normalize(); }
    explicit operator double() const {
        return (double) a / b;
    }
    void normalize() {
        Long g = __gcd(a, b);
        a /= g, b /= g;
        if (b < 0) {
            a = -a, b = -b;
        }
    }
    Rational& operator+=(const Rational& rhs) {
        Long d = b * rhs.b;
        a = a * rhs.b + b * rhs.a;
        b = d;
        normalize();
        return *this;
    }
    Rational& operator-=(const Rational& rhs) {
        Long d = b * rhs.b;
        a = a * rhs.b - b * rhs.a;
        b = d;
        normalize();
        return *this;
    }
    Rational& operator*=(const Rational& rhs) {
        a *= rhs.a;
        b *= rhs.b;
        normalize();
        return *this;
    }
    Rational& operator/=(const Rational& rhs) {
        a *= rhs.b;
        b *= rhs.a;
        normalize();
        return *this;
    }
    Rational operator-() const {
        return Rational(-a, b);
    }
    Rational operator+(const Rational& rhs) const {
        return Rational(*this) += rhs;
    }
    Rational operator-(const Rational& rhs) const {
        return Rational(*this) -= rhs;
    }
    Rational operator*(const Rational& rhs) const {
        return Rational(*this) *= rhs;
    }
    Rational operator/(const Rational& rhs) const {
        return Rational(*this) /= rhs;
    }
    bool operator<(const Rational& rhs) const {
        return a * rhs.b < b * rhs.a;
    }
    bool operator>(const Rational& rhs) const {
        return rhs < *this;
    }
    bool operator<=(const Rational& rhs) const {
        return !(rhs < *this);
    }
    bool operator>=(const Rational& rhs) const {
        return !(*this > rhs);
    }
    bool operator==(const Rational& rhs) const {
        return !(*this < rhs) && !(rhs < *this);
    }
    bool operator!=(const Rational& rhs) const {
        return *this < rhs || rhs < *this;
    }
    friend ostream& operator<<(ostream& s, const Rational& f) {
        if (f.b == 1) {
            s << to_string(f.a);
        } else {
            s << to_string(f.a) << '/' << to_string(f.b);
        }
        return s;
    }
};

int main() {
    int n;
    cin >> n;
    vector<int> as(n);
    for (int i = 0; i < n; i++) {
        cin >> as[i];
    }
    Rational ave = 0;
    for (int i = 0; i < n; i++) {
        ave += as[i];
    }
    ave /= n;
    vector<pair<Rational, int>> dif;
    for (int i = 0; i < n; i++) {
        Rational d = ave - as[i];
        dif.emplace_back(d < 0 ? -d : d, i);
    }
    sort(dif.begin(), dif.end());
    cout << dif.front().second << endl;
}