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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;
class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        Integer d[] = new Integer[N];
        for(int i = 0; i<N; i++){
            d[i] = sc.nextInt();
        }
        int sum = 0;
        for(int j = 0; j<N-2; j++){
            for(int k = j+1; k<N-1; k++){
                for(int h = k+1; h<N; h++){
                    int A = d[j];
                    int B = d[k];
                    int C = d[h];
                    if(((A < B+C) && (B < C+A)) && (C < A+B)){
                        sum = sum+1;
                    }
                }
            }
        }
        System.out.println(sum);
    }
}