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 5.4.1) (judge verdict: Wrong Answer)

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

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

int main(int argc, char const *argv[]) {
  int n;
  int i,j,k;
  int *lens;
  int sum;
  int a,b,c;

  scanf("%d", &n);
  lens = (int*)(malloc(sizeof(int) * n));
  for(i = 0; i < n; i++){
    scanf("%d", &lens[i]);
  }
  qsort(lens, n, sizeof(int), compare_int);
  sum = 0;
  i = 0;
  while(i <= n - 2){
    a = lens[i];
    for(j = i+1; j < n-1; j++){
      b = lens[i];
      for(k = j+1; k < n; k++){
        c = lens[j];
        if(c < a + b){
          if(b < c + a){
            if(a < b + c){
              sum++;
            }
          }
        }
      }
    }
    i++;
  }
  printf("%d\n", sum);
  return 0;
}