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<vector>
#include<string>
#include<algorithm>
#include<cmath>
#include<functional>
#include<map>
#include<cstdlib>
#include<complex>
#include<numeric>
#include<set>
#include<deque>
#include<queue>

using namespace std;
using Int = long long;
Int INF = 1LL << 60;
const Int MOD = 1000000000 + 7;

int main() {

	cin.tie(nullptr);
	ios::sync_with_stdio(false);

	Int N;
	cin >> N;

	int L[2000];
	for (Int i = 0; i < N; i++) {
		cin >> L[i];
	}

	Int ans = 0;
	for (Int i = 0; i < N; i++) {
		for (Int j = i+1; j < N; j++) {
			for (Int k = j + 1; k < N; k++) {
              int tmp = L[j] - L[k];
				if ((tmp>0?tmp:-tmp) < L[i] && L[i] < L[j] + L[k]) {
						ans++;
					
				}

			}
		}
	}

	cout << ans << "\n";
}