Problem:
Score : 300 points

Problem Statement

There are N people living on a number line.

The i-th person lives at coordinate X_i.

You are going to hold a meeting that all N people have to attend.

The meeting can be held at any integer coordinate. If you choose to hold the meeting at coordinate P, the i-th person will spend (X_i - P)^2 points of stamina to attend the meeting.

Find the minimum total points of stamina the N people have to spend.

Constraints

All values in input are integers.

1 \leq N \leq 100

1 \leq X_i \leq 100

Input

Input is given from Standard Input in the following format:

N
X_1 X_2 ... X_N

Output

Print the minimum total stamina the N people have to spend.

Sample Input 1

2
1 4

Sample Output 1

5

Assume the meeting is held at coordinate 2. In this case, the first person will spend (1 - 2)^2 points of stamina, and the second person will spend (4 - 2)^2 = 4 points of stamina, for a total of 5 points of stamina. This is the minimum total stamina that the 2 people have to spend.

Note that you can hold the meeting only at an integer coordinate.

Sample Input 2

7
14 14 2 13 56 2 37

Sample Output 2

2354

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
using ll = long long; //10^19 < 9223372036854775807
#define REP(i,n) for(ll i=0;i<ll(n);i++)

float mean(vector<int> v) {
    int size = v.size();
    float sum = 0;
    for (int i = 0; i < size; i++){
        sum += v[i];
    }
    return sum / size;
}

int main(void)
{
    int N;
    cin >> N;

    vector<int> X(N);
    REP (i, N) {
        cin >> X[i];
    }

    REP (i, N) {
        cin >> X[i];
    }
    sort(X.begin(),X.end());

    int middle1 = ceil(mean(X));
    int middle2 = floor(mean(X));
    int total1 = 0;
    int total2 = 0;
    REP (i, N) {
        total1 += (X[i] - middle1) * (X[i] - middle1);
        total2 += (X[i] - middle2) * (X[i] - middle2);
    }

    cout << min(total1,total2) << endl;

    return 0;
}