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: Wrong Answer)

import java.util.*;
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 count=0;
    int a,b;
    int highid=N-1;
    int lowid,mid;
    for(int i=0;i<N-2;i++){
      for(int j=i+1;j<N-1;j++){
        a=L[i];
        b=L[j];
        lowid=j+1;
        highid=N-1;
        if(a+b>L[lowid]&&a+b<L[highid]){
          while(highid-lowid<=1){
            mid=(highid+lowid)/2;
            if(a+b<L[lowid]){
              lowid=mid;
            }
            if(a+b>L[highid]){
              highid=mid;
            }
          }
          count+=(N-1)-highid+1;
        }
        else if(a+b>L[highid]&&a+b>L[lowid]){
          count+=highid-lowid+1;
        }
        else if(a+b<L[highid]&&a+b<L[lowid]){
          count+=0;
        }
      }
    }
    System.out.println(count);
  }
}