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++ (GCC 9.2.1) (judge verdict: Accepted)

//
//  triangle.cpp
//  my_programs
//
//  Created by Jiatuo Zou on 7/27/20.
//  Copyright © 2020 Jiatuo Zou. All rights reserved.
//

#include <iostream>
#include <algorithm>

int main()
{
    using namespace std;
    
    int n, l[2000], sum = 0;
    cin >> n;
    for(int i = 0; i < n; i++){
        cin >> l[i];
    }
    sort(l, l + n);
    for(int i = 0; i < n - 2; i++){
        for(int j = i + 1, k = i + 2; j < n - 1; ){
            if(k < n && l[k] < l[i] + l[j]){
                k++;
            } else{
                sum += (k - j - 1);
                j++;
            }
        }
    }
    cout << sum << endl;
    return 0;
}