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: Accepted)

import java.util.*;
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();
        }
        long res = 0;

        Arrays.sort(L);

        for(int i=N-1; i>1; i--){
            for(int j=0; j<i-1; j++){
                int ok=i;
                int ng=j;
                while(ok-ng>1){
                    int h=(ok+ng)/2;
                    if(L[i]<L[j]+L[h]){
                        ok = h;
                    }else{
                        ng = h;
                    }
                }
                res = res + i - ok;
            }
        }
        System.out.println(res);
        
        }
    }