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 scan = new Scanner(System.in);
    int N = scan.nextInt();
    int[] L = new int[N];
    
    for(int i=0; i<N; i++) {
      L[i] = scan.nextInt();
    }
    Arrays.sort(L);
    
    int ans = 0;
    for(int start=0; start<N; start++) {
      for(int end=N-1; start<end; end--) {
        for(int target = end-1; target>start; target--) {
          if(L[start]+L[target] > L[end]) {
            ans++;
          } else {
            break;
          }
        }
      }
    }
    System.out.println(ans);
  }
}