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>
#include <string.h>

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

long long not_n(long long a)
{
    if(a < 0)return 0;
    return a;
}

int binarySearch(int key,int n,int a[n],int left,int right)
{
    int mid;

    while ( -left + right > 1)
    {
        mid = (left + right) / 2;
        if(a[mid] > key)left = mid;
        else right = mid;
    }
    return left;
}

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

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

    qsort(l,n + 1,sizeof(int),asc);

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

    for (i = 0; i < n - 1; i++)
    {
        for (j = i + 1; j < n; j++)
        {
            if(l[j + 1] >= l[i] - l[j])
            {
                ans += binarySearch(l[i] - l[j],n + 1,l,0,n) - j;
            }
        }
    }
    
    printf("%lld",ans);
}