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 (Clang 3.8.0) (judge verdict: Runtime Error)

#include <stdio.h>
int main(void)
{
  int N = 0;
  scanf("%d", &N);
  int l[10000];
  for(int i = 0; i < N; i ++){ 
  scanf("%d", l[i]);
  }
  
  int ans = 0;
  for(int j = 0; j < N; j ++){ 
    for(int k = j; k < N; k ++){
       for(int m = k; m < N; m ++){
           if(l[m] < l[j] + l[k] && l[j] < l[k] + l[m] && l[k] < l[j] + l[m]){
             ans ++;
           }
       }
    }
  }
  printf("%d",ans);
  return 0;
}