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.Scanner;
import java.util.Arrays;

public class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int list[] = new int[n];
    
    for(int i = 0; i < n; i++)
      list[i] = sc.nextInt();
    Arrays.sort(list);
    
    int count = 0;
    int a,b,c;
    a: for(int ai = 0; ai < n-2; ai++){
      b: for(int bi = ai+1; bi < n-1; bi++){
        c: for(int ci = bi+1; ci < n; ci++){
    		a = list[ai];
     		b = list[bi];
      		c = list[ci];
    		if(a >= (b+c)){
				break a;
            }
          	if(b >= (c+a))
              continue a;
          	if(c >= (a+b)) 
              continue b;
          	count++; 	
        }
      }
    }
    System.out.println(count);
  }
}