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<bits/stdc++.h>

#define fast ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define int long long int

using namespace std;

signed main()
{
	int n, p, q, r, ans = 0;
	cin >> n;
	int a[n];

	for (int i = 0; i < n; i++)
	{
		cin >> a[i];
	}

	for (int i = 0; i < n-2; i++)
	{
		for (int j = i+1; j < n-1; j++)
		{
			for (int k = j+1; k < n; k++)
			{
				p = a[i] + a[j];
  				q = a[j] + a[k];
  				r = a[i] + a[k];
  				if (a[k] < p && a[j] < r && a[i] < q)
  				{
  					ans++;
  				}
			}
		}
	}

	cout << ans;

	return 0;
}