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.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int L[] = new int[N];
		
		for(int i=0;i<N;i++) {
			L[i]=sc.nextInt();
		}
		
		Arrays.sort(L);
		//小さい順に並んでいる。
		
		
		//三角形ができない組み合わせを数える。
		long count=0;
		long count_memo=0;
		
		int sh =0;
		int mi =0;
		int sum=0;
		for(int i=0;i<N-2;i++) {
			sh=L[i];
			for(int j=i+1;j<N-1;j++) {
				mi=L[j];
				sum = sh + mi;
				int k=L.length;
				count_memo=count;
				while(sum<=L[k-1]) {
					count++;
					k--;
				}
				if(count_memo==count) {
					break;
				}
			}
		}
		
		//組み合わせの総数　
		long total = (N*(N-1)*(long)(N-2))/(3*2); 
		
		long ans = total-count;
		
		System.out.println(ans);
	}
}