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 5.4.1) (judge verdict: Wrong Answer)

// (a-p)^2+(b-p)^2+(c-p)^2
// -> a^2+b^2+c^2 + 2p(a+b+c) + 3p^2
// min(n * p^2 + 2p(a+b+...+x))
// -> n * (p + (2(a+b+...+x)/n))^2 - 4 / n
// min(p + (2(a+b+...+x)/n))

#include <stdio.h>

int main(void)
{
  int n;
  scanf("%d", &n);
  
  int x[n], i;
  i = 0;
  while (i < n)
  {
    scanf("%d", &x[i]);
    i++;
  }
  
  int min, max;
  i = 0;
  while (i + 1 < n)
  {
    if (x[i] <= x[i + 1])
    {
      min = x[i];
      max = x[i + 1];
    }
    else if (x[i] > x[i + 1])
    {
      min = x[i + 1];
      max = x[i];
    }
    i++;
  }
  
  int p, k, sigma[n], ans;
  k = 0;
  p = min;
  while (p <= max && k < n)
  {
    sigma[k] = 0;
    i = 0;
    while (i < n)
    {
      sigma[k] = sigma[k] + (x[i] - p) * (x[i] - p);
      i++;
    }
    if (k >= 1)
    {
      if (sigma[k] <= sigma[k - 1])
      {
        ans = sigma[k];
      }
      else if (sigma[k] > sigma[k - 1])
      {
        ans = sigma[k - 1];
      }
    }
    else if (k == 0)
    {
      ans = sigma[k];
    }
    k++;
    p++;
  }
  printf("%d", ans);
  return 0;
}