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<algorithm>
#include<string>
#include<cstdlib>
#include<vector>
#include<queue>
#include<map>
#include<set>
#include<math.h>

using namespace std;

typedef long long ll;

#define rep(i, n) for (ll i = 0; i < n; i++)

const ll INF = 1LL << 60;


signed main() {

	ll n;
	cin >> n;

	vector<ll>a(n);

	rep(i, n)cin >> a[i];
	sort(a.begin(), a.end());
	ll ans = 0;
	rep(i, n - 2) {
		for (int j = i + 1; j < n - 1; 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[i] + a[j]) {
					ans++;
				}
				else {
					break;
				}
			}
		}
	}
	cout << ans;
}