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 {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N;
		N = sc.nextInt();
		int L[] = new int[N];
		for (int i=0;i<N;i++) {
			L[i] = sc.nextInt();
		}
//		int a[][] = new int[N][N];
//		for (int i=0;i<N;i++) {
//			for (int j=i+1;j<N;j++) {
//				a[i][j] = L[i] +L[j];
//			}
//		}
		Arrays.sort(L);
		int count =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[k]>=L[j]+L[i]) {
						break;
					}
					if (L[i]<L[j]+L[k]&&L[j]<L[i]+L[k]) {
						count ++;
					}
				}
			}
		}
		System.out.println(count);
	}
}