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: Accepted)

#include <iostream>
#include <string>
#include <algorithm>
#include <cstdio>
#include <vector>
#include <map>
#include <functional>
#include <cmath>
using namespace std;

int main()
{
	ios::sync_with_stdio(false);
	cin.tie(0);

	int n, l[3000];
	int cnt = 0;
	int i, j, k;

	cin >> n;
	for (i = 0; i < n; i++)
		cin >> l[i];

	sort(l, l + n);

	for (i = 0; i < n - 2; i++)
	{
		for (j = i + 1; j < n - 1; j++)
		{
			for (k = j + 1; k < n; k++)
			{
				if (l[i] < l[j] + l[k] && l[j] < l[i] + l[k] && l[k] < l[j] + l[i])
					cnt++;
			}
		}
	}
	cout << cnt << endl;
	return 0;
}