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: Accepted)

import java.util.Arrays;
import java.util.Comparator;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = Integer.parseInt(sc.next());
        Integer[] l = new Integer[n];
        for(int i=0; i<n; i++) {
            l[i] = Integer.parseInt(sc.next());
        }

        Arrays.sort(l,Comparator.reverseOrder());

        //l[i] >= l[j] >= l[k]
        int cnt = 0;
        for(int i=0; i<n-2; i++) {
            for(int j=i+1; j<n-1; j++) {
                for(int k=j+1; k<n; k++) {
                    if(l[j]-l[k]<l[i] && l[i]<l[j]+l[k]) cnt++;
                    else break;
                }
            }
        }
        System.out.println(cnt);
    }
}