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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

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=sc.nextInt(), count=0;
		int[] length = new int[n];
		for(int i=0;i<n;i++) length[i]=sc.nextInt();
		Arrays.sort(length);
		for(int i=0;i<n-2;i++) {
			for(int j=i+1;j<n-1;j++) {
				if(length[n-1]<length[i]+length[j]) count+=(n-j-1);
				else {
					int mid, left=j+1,right=n-1, tar=length[i]+length[j];
					while(true) {  //2分探索
						mid = (left+right)/2;
						if(length[mid]==tar || right<left) break;
						if(length[mid]<tar) left = mid+1;
						else right=mid-1;
					}
					if(length[mid]>=tar) mid--;
					count+=mid-j;
				}
			}
		}
		System.out.println(count);
	}
}