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: Time Limit Exceeded)

//Triangles
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();
    }

    int count=0;

    for (int i=0;i<n-2;i++) {
      for (int j=i+1;j<n-1;j++) {
        for (int t=j+1;t<n;t++) {
          if (l[i]<l[j]+l[t] && l[j]<l[i]+l[t] && l[t]<l[i]+l[j]) {
            count=count+1;
          }
        }
      }
    }

    System.out.println(count);

  }
}