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, 0);
    for(int i=0; i<N; i++){
        cin >> L.at(i);
    }

    int cnt=0;
    sort(L.begin(), L.end());

    if(N==3){
        if((L.at(0) + L.at(1) > L.at(2)) && (L.at(0) < L.at(1) + L.at(2)) && (L.at(0) + L.at(2) > L.at(0))){
            cnt++;
        }
        cout << cnt << endl;
        return 0;
    }

    for(int i=0; i<N; i++){
        for(int j=i; j<N; j++){
            for(int k=j; k<N; k++){
                if(i != j && j != k && i!= k){
                    if((L.at(i) + L.at(j)) - L.at(k) > 0){
                        cnt++;
                    }
                    else{
                        break;
                    }
                }
            }
        }
    }

    cout << cnt << endl;
}