Problem:
Score : 400 points

Problem Statement

Takahashi has N sticks that are distinguishable from each other. The length of the i-th stick is L_i.

He is going to form a triangle using three of these sticks. Let a, b, and c be the lengths of the three sticks used. Here, all of the following conditions must be satisfied:

a < b + c

b < c + a

c < a + b

How many different triangles can be formed? Two triangles are considered different when there is a stick used in only one of them.

Constraints

All values in input are integers.

3 \leq N \leq 2 \times 10^3

1 \leq L_i \leq 10^3

Input

Input is given from Standard Input in the following format:

N
L_1 L_2 ... L_N

Constraints

Print the number of different triangles that can be formed.

Sample Input 1

4
3 4 2 1

Sample Output 1

1

Only one triangle can be formed: the triangle formed by the first, second, and third sticks.

Sample Input 2

3
1 1000 1

Sample Output 2

0

No triangles can be formed.

Sample Input 3

7
218 786 704 233 645 728 389

Sample Output 3

23

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

#include <stdio.h>
#include <string.h>
#include <stdbool.h>
#include <stdint.h>
#include <stdlib.h>
#include <limits.h>
#include <math.h>
int acs(const void *a, const void *b) { return *(int *)a - *(int *)b; }                            /* 1,2,3,4.. */
int des(const void *a, const void *b) { return *(int *)b - *(int *)a; }                            /* 8,7,6,5.. */
int cmp_char(const void *a, const void *b) { return *(char *)a - *(char *)b; }                     /* a,b,c,d.. */
int cmp_str(const void *a, const void *b) { return strcmp(*(const char **)a, *(const char **)b); } /* aaa,aab.. */
#define min(a, b) (a < b ? a : b)
#define max(a, b) (a > b ? a : b)
#define rep(i, n) for (int i = 0; i < n; i++)
#define MAX 100001
#define MOD 1000000007

typedef long long int lli;

int main(void)
{
  int n, l[2001];
  scanf("%d", &n);

  // int tmp, uni[1001] = {0}, times[1001] = {0};
  rep(i, n)
  {
    scanf("%d", &l[i]);
    // if (uni[tmp])
    //   times[tmp]++;
    // else
    //   uni[tmp] = 1;
  }

  qsort(l, n, sizeof(int), acs);

  int ans = 0;
  for (int i = 0; i < n; i++)
  {
    for (int j = i + 1; j < n; j++)
    {
      for (int k = j + 1; k < n && l[k] < l[i] + l[j]; k++)
      {
        if (l[k] < l[i] + l[j])
          ans++;
        else
          break;
      }
    }
  }
  printf("%d\n", ans);
  return 0;
}