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 {

    Scanner sc = new Scanner(System.in);

    public static void main(String[] args) {
        new Main().run();
    }

    void run() {
        int n = sc.nextInt();
        int[] arr = new int[n];
        for (int i=0; i<n; i++) arr[i] = sc.nextInt();

        Arrays.sort(arr);

        long ans = 0;

        for (int i=0; i<n-2; i++) {
            for (int j=i+1; j<n-1; j++) {
                int a = arr[i];
                int b = arr[j];
                int left = j+1;
                int right = n;
                while (left<right) {
                    int mid = (left+right)/2;
                    if (arr[mid]<a+b) {
                        left = mid+1;
                    } else {
                        right = mid;
                    }
                }                 
                ans += (left-j-1);

            }
        }

        System.out.println(ans);
    }

}