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>

void quicksort(int number[],int first,int last);

int main()
{
    int n,l[2000],i,j,k;
    long long ans = 0;

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

    quicksort(l,0,n - 1);

    for (i = 0; i < n - 1; i++)
    {
        for (j = i + 1; j < n; j++)
        {
            k = j + 1;
            while (l[i] + l[j] <= l[k])
            {
                k++;
            }
            ans += n - k;
        }
    }
    
    printf("%d",ans);
}


void quicksort(int number[],int first,int last)
{
   int i, j, pivot, temp;

   if(first < last){
      pivot = first;
      i = first;
      j = last;

      while(i < j){
         while((number[pivot] >= number[i]) && (i < last))
         {
            i++;
         }
         while(number[pivot] < number[j])
         {
            j--;
         }
         if(i < j){
            temp = number[i];
            number[i] = number[j];
            number[j] = temp;
         }
      }

      temp = number[pivot];
      number[pivot] = number[j];
      number[j] = temp;
      quicksort(number,first,j - 1);
      quicksort(number,j+1,last);

   }
}