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>
long long int ar[10000000];
void sort(int a)
{
    int i,j,k;
    for(i=0; i<a-1; i++)
    {
        for(j=i+1; j<a; j++)
        {
            if(ar[i]>ar[j])
            {
                k=ar[i];
                ar[i]=ar[j];
                ar[j]=k;
            }
        }
    }
    return ;
}
int main()
{
    long long int a,b,c,i,j,k=0;
    scanf("%lld",&a);
    for(i=0; i<a; i++)
    {
        scanf("%lld",&ar[i]);
    }
    sort(a);
    for(i=0; i<a-2; i++)
    {
        for(j=i+1; j<a-1; j++)
        {
            for(c=j+1; c<a; c++)
            {
                if(ar[i]+ar[j]>ar[c] && ar[i]+ar[c]>ar[j] && ar[j]+ar[c]>ar[i])k++;
            }
        }
    }
    printf("%lld\n",k);
    return 0;
}