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.*;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
        int n = sc.nextInt(); 
        int ans = 0;
		int [] in = new int [n];
        for(int i=0;i<n;i++){in[i] = sc.nextInt();}
        Arrays.sort(in);
        for(int i=0;i<n-2;i++){
        for(int j=i+1;j<n-1;j++){
        int small = j;
        int big = n;
        int point = (small+big)/2;
        int size = point-small;               
        while(big-small>1){size = Math.max(size/2,1);
                         if(in[i]+in[j]>in[point]){small=point;point+=size;}
                         else{big=point;point-=size;}                
                        }
        ans+=small-j;
        }                              
                              }         
        System.out.println(ans);
	}
}