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.Scanner;
public class Main {
@SuppressWarnings("resource")
public static void main(String[] args) {
	Scanner sc =new Scanner(System.in);
	int N=sc.nextInt();
	int[] L=new int[N];
	int[] L2=new int[N];
	for(int i=0;i<N;i++) {
		L[i]=sc.nextInt();
	}
	Arrays.sort(L);
	for(int i=0;i<N;i++) {
		L2[i]=L[N-1-i];
	}
	int ans=0;
	for(int i=0;i<N-2;i++) {
		for(int j=i+1;j<N-1;j++) {
			for(int z=j+1;z<N;z++) {
				if(L2[i]<L2[j]+L2[z]) {
					ans++;
				}
			}
		}
	}
	System.out.println(ans);
}
}