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: Wrong Answer)

import java.util.Arrays;
import java.util.Scanner;
public class Main {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		Integer[] len = new Integer[n];
		for ( int i = 0; i < n; i++ ) {
			len[i] = in.nextInt()*2; // 2倍して（偶数にして）受け取る
		}
		Arrays.sort(len);

		int cnt = 0;		
		for ( int e1 = 0; e1 < n - 2; e1++ ) {
			for ( int e2 = e1 + 1; e2 < n - 1; e2++ ) {				
				// LowerBoundを取りたい // 奇数は存在しないので一意な値が返ってくる
				int d = len[e1] + len[e2] - 1;				
				int i = ~Arrays.binarySearch(len, d);
				cnt += i - e2;
			}
		}
		System.out.println(cnt);
		in.close();
	}
}