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 <iostream>

using namespace std;

int main()
{
    int n;
    cin >> n;
    int l[n];
    for(int i=0; i<n; i++){
        cin >> l[i];
    }
    
    long long int cnt = 0;
    for(int i=0; i<n; i++){
        for(int j=i+1; j<n; j++){
            for(int k=j+1; k<n; k++){
                if((l[i] >= l[j]+l[k]) ||
                   (l[j] >= l[i]+l[k]) ||
                   (l[k] >= l[i]+l[j])){
                       //cout << l[i] << ", " << l[j] << ", " << l[k] << endl;
                       //cnt++;
                       continue;
                   }
                   cnt++;
            }
        }
    }
    cout << cnt << endl; 
    return 0;
}