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 (GCC 9.2.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>

int cmp(const void *a, const void *b)
{ return *(int *)b - *(int *)a ;}

int if_tri(int a,int b, int c)
{
  if(a+b>c && b+c>a && c+a>b)
    return 1;
  else
    return 0;
}

int main()
{
  int n,i,j,k,count=0;
  int *l;

  scanf("%d", &n);
  l = calloc(n,sizeof(int));

  for(i=0; i<n; i++)
    scanf("%d",&l[i]);

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

  for(i=0; i<n-2; i++){
    for(k=i+1; k<n-1; k++){
      for(j=k+1; j<n; j++){
        if(if_tri(l[i],l[k],l[j]))
        count++;
      }
    }
  }

  printf("%d", count);
  free(l);
  return 0;
}