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>
#define rep(i, n) for(int i=0; i<n; i++)
using namespace std;
int main(void){
    int n;
    int cnt =0;
    cin >> n;
    vector<int>L(n,0);
    rep(i, n) cin >> L[i];
    sort(L.begin(), L.end());
    //rep(i, n) cout << L[i];
    rep(i, n){
        rep(j, n){
            rep(k, n){
                if(i !=j and i !=k and j !=k){
                    if (i<j and j<k){
                        if(L[i]+L[j]>L[k]) cnt+=1;
                    }
                    
                }
                
            }
        }
    }
    cout << cnt;
}