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 <bits/stdc++.h>

using namespace std;

int main() {

	long n;
	cin >> n;

	vector<long> L(n);
	for (long i = 0; i < n; i++) {
		cin >> L[i];
	}
	sort(L.begin(), L.end());

	//for (long i = n-2; i >=0; i--) {
	//	if (L[i] == L[i + 1]) {
	//		L.erase(L.begin() + i+1);
	//	}
	//}
	
	n = L.size();

	long long counter = 0;
	for (long i = 0; i < n-2; i++) {
		for (long j = i+1; j<n-1 ; j++) {
			for (long k = j+1; k < n; k++) {

				if (L[i] + L[j] > L[k]) { counter++; }
				else { break; }

			}
		}
	}

	cout << counter << endl;
}