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>
using namespace std;

typedef long long int ll;

int main () {


    ll n;
    cin >> n;

    ll a[n];

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

    ll ans=0;

    for (ll i=0 ; i<n ; i++) {
    	for (ll j=i+1 ; j<n ; j++) {
    		for (ll k=j+1 ; k<n ; k++) {
    			if (i!=j && j!=k && i!=k) {
    				if ((a[i]+a[j])>a[k] && (a[i]+a[k])>a[j] && (a[j]+a[k])>a[i]) {
    					ans++;
    				}
    			}
    		}
    	}
    }

    cout << ans << endl;
}