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 <bits/stdc++.h>

using namespace std;
int a[2005],b[2005],c[5],n,ans;
void fun(int m,int cnt)
{
    if(cnt==3)
    {
        if(c[0]+c[1]>c[2] && c[0]+c[2]>c[1] && c[1]+c[2]>c[0])
        {
            ans++;
        }
        cnt=0;
        return;
    }
    for(int i=m;i<n;i++)
    {
        if(!b[i])
        {
            b[i]=1;
            c[cnt]=a[i];
            fun(i+1,cnt+1);
            b[i]=0;
        }
    }
}
int main()
{
    cin >> n;
    for(int i=0;i<n;i++)
    {
        scanf("%d",&a[i]);
    }
    sort(a,a+n);
    fun(0,0);
    cout << ans << endl;
    return 0;
}