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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Main {

	public static void main(String[] args) throws Exception {
		// TODO 自動生成されたメソッド・スタブ
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		String W = in.readLine();
		int N = Integer.parseInt(W);

		W = in.readLine();
		String[] Ws = W.split(" ");
		long[] L = new long[Ws.length];
		for(int i=0;i<Ws.length;i++){
			L[i] = Long.parseLong(Ws[i]);
		}
		Arrays.sort(L);

		long ans =0;
		for(int a=0;a<N;a++){
			if(a!=0&&L[a-1]==L[a]){
				continue;
			}
			for(int b=a+1;b<N;b++){
				for(int c=b+1;c<N;c++){
//					if(L[a]-L[b] < L[c] && L[c] < L[a]+L[b]){
						if(L[a] < L[b]+L[c] && L[b] < L[c]+L[a] && L[c] <L[a]+L[b]){
							ans++;
						}
//					}else{
//						break;
//					}
				}
			}
		}

		System.out.println(ans);
	}
}