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: Accepted)

#include <stdio.h>
#include <stdint.h>
#include <inttypes.h>
#include <stdlib.h>
#include <string.h>

typedef unsigned long long int uint64;
typedef long long int          int64;
 
#define MAX(a,b) ((a)>(b)?(a):(b))
#define MIN(a,b) ((a)<(b)?(a):(b))
#define ABS(a) ((a)>(0)?(a):-(a))

void get_N (int64 *n)
{
  int cnt;
  
  cnt = scanf("%lld", n);

  return;
}

void get_NK (int64 *n, int64 *k)
{
  int cnt;
  
  cnt = scanf("%lld %lld", n, k);

  return;
}

void get_N1234 (int64 *n1, int64 *n2, int64 *n3, int64 *n4)
{
  int cnt;

  if (n2 == NULL) {
    cnt = scanf("%lld", n1);
    return;
  }
  if (n3 == NULL) {
    cnt = scanf("%lld %lld", n1, n2);
    return;
  }
  if (n4 == NULL) {
    cnt = scanf("%lld %lld %lld", n1, n2, n3);
    return;
  }
  cnt = scanf("%lld %lld %lld %lld", n1, n2, n3, n4);
  return;
}

void omit_LF (void)
{
  char c;
  int  cnt;
  
  cnt = scanf("%c", &c);
  return;
}

char *get_S (int64 n)
{
  char *buf;
  int  i;
  int  cnt;

  buf = malloc((size_t)(n * sizeof(char)));
  if (buf == NULL) {
    return NULL;
  }

  cnt = scanf("%s", buf);

  return buf;
}

char *get_SN (int64 max, int64 *size)
{
  char *buf;
  int  i;
  int  n;

  buf = malloc((size_t)(max * sizeof(char)));
  if (buf == NULL) {
    return NULL;
  }

  scanf("%s", buf);

  n = strlen(buf);

  *size = n;
  
  return buf;
}

int64 *get_NSeq (int64 n)
{
  int64 *buf;
  int64 i;

  buf = malloc((size_t)(n * sizeof(int64)));
  for (i=0; i<n; i++) {
    get_N(&buf[i]);
  }

  return buf;
}

typedef struct _tmp_t {
  int64    a;
  int64    b;
} tmp_t;


int compare_a(const void *a, const void *b)
{
  tmp_t *x;
  tmp_t *y;

  x = (tmp_t *)a;
  y = (tmp_t *)b;

  if (x->a > y->a) return 1;
  if (x->a < y->a) return -1;

  return 0;
}

int compare_b(const void *a, const void *b)
{
  tmp_t *x;
  tmp_t *y;

  x = (tmp_t *)a;
  y = (tmp_t *)b;

  if (x->b > y->b) return 1;
  if (x->b < y->b) return -1;

  return 0;
}

void qsort_a (tmp_t *array, int size)
{
  qsort(array, size, sizeof(tmp_t), compare_a);
}

void qsort_b (tmp_t *array, int size)
{
  qsort(array, size, sizeof(tmp_t), compare_b);
}

int64 get_jou(int64 v, int64 i) {
  int64 j;
  int64 r;

  if (i == 0) return 1;
  
  r = 1;
  for (j=1; j<=i; j++) {
    r = r*v;
  }
  return r;
}

int64 check_val (int64 N, int64 K, int64 max) {
  int64 j,v;

  v = 1;
  for (j=1; j<=max; j++) {
    v = v*K;
    if ((N / v) > 0) {
      continue;
    } else {
      return 0;
    }
  }
  return 1;
}

int main()
{
  int64 N;
  int64 *x;
  int64 i;
  int64 min = 101;
  int64 max = 0;
  int64 minHp = 0xFFFFFFFF;
  int64 p,hp;

  get_N(&N);

  x = get_NSeq(N);

  for (i=0; i<N; i++) {
    if (x[i] > max) max = x[i];
    if (x[i] < min) min = x[i];
  }

  for (p=min; p<=max; p++) {
    hp = 0;
    for (i=0; i<N; i++) {
      hp += (x[i] - p) * (x[i] - p);
    }
    if (minHp > hp) {
      minHp = hp;
    }
  }

  printf("%lld", minHp);

  return 0;
}