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: Accepted)

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

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

int main() {
  int N;
  int L[5000];
  int a,b,c,a_b;
  int s=0;
  scanf("%d", &N);
  for (int i=0; i<N; i++) scanf("%d", &L[i]);
  qsort(L, N, sizeof(int), asc);

  for (int i=0; i<N-2; i++) {
    a = L[i];
    for (int j=i+1; j<N-1; j++) {
      b = L[j];
      c = L[j+1];
      a_b = a - b;
      //printf("%d %d %d\n", a, b, c);
      if (a_b < c) {
        s++;
        for (int k=j+2; k<N; k++) {
          c = L[k];
          //printf("%d %d %d\n", a, b, c);
          if (a_b < c) s++;
          else break;
        }
      } else {
        break;
      }      
    }
  }
  printf("%d\n", s);

}