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: Time Limit Exceeded)

#include<stdio.h>

int main(void)
{
int a,c,i,j,k;
  
scanf("%d",&a);
  int num[a];
  
  for(i=0;i<a;++i)
  {
  scanf("%d",&num[i]);
  }
    
  for(i=2;i<a;i++)
  {
   for(j=1;j<i;j++)
   {
    for(k=0;k<j;k++)
    {
    if(num[i]+num[k]>num[j] && num[i]+num[j]>num[k] && num[j]+num[k]>num[i]) c++;
    }
   }
  }
  printf("%d",c);

return 0;
}