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.*;

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();

        Arrays.sort(l);
        int ans=0;

        for(int i=0;i<n-2;i++){
            for(int j=i+1;j<n-1;j++){
                int max = l[i]+l[j]-1;
                int min = Math.abs(l[i]-l[j])+1;

                int indexMax= Arrays.binarySearch(l,max);
                int indexMin = Arrays.binarySearch(l,min);

                if(indexMin<0)indexMin = -(indexMin+1);
                if(indexMax<0)indexMax=-(indexMax+1);

                if(indexMax<0)indexMax*=-1;

                indexMin = Math.max(j + 1, indexMin);
                indexMax = Math.min(indexMax,l.length);

                if(indexMax>=indexMin)ans+=indexMax-indexMin;
                if(indexMax==indexMin)ans++;

            }
        }

        System.out.println(ans);


    }




}