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;

int main(){
    int n;
    cin >>n;
    vector<int> L(n);
    int i,j,k;
    for(i=0; i<n; i++){
        cin >> L.at(i);
    }
    
    int a,b,c;
    int ans=0;
    for(i=0; i<n-2; i++){
        for(j=i+1; j<n-1; j++){
            for(k=j+1; k<n; k++){
                if((L.at(i)<L.at(j)+L.at(k))&&(L.at(j)<L.at(i)+L.at(k))&&(L.at(k)<L.at(i)+L.at(j))){
                    ans++;
                }
            }
        }
    }
    cout << ans << endl;
    return 0;
}