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++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include<iostream>
#include<algorithm>
#include<string>
#include<vector>
#include<queue>
#include<cmath>
#include<utility>
#define mod 998244853 
using namespace std;
int main()
{
    ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
    int n, nb;
    cin >> n;
    int a[n];
    //cout << n << '\n';
    for(int i = 0; i < n; i++)
        cin >> a[i];
    nb=0;
    for(int i = 0; i < n; i++)
    {
        for(int j = i+1; j < n; j++)
        {
            for(int k = j+1; k < n; k++)
            {
                if(a[i] < a[j]+a[k] && a[j] < a[i]+a[k] && a[k] < a[j]+a[i])
                {
                    //cout << nb << '\n';
                    nb++;
                }
            }
        }
    }
    cout << nb << '\n';
}