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.Arrays;
import java.util.Scanner;
public class Main{
    static Scanner sc = new Scanner(System.in);
    static int n = sc.nextInt();
    static int[] l = new int[n];
    public static void main(String[] args){
        for (int i=0; i<n; i++) l[i] = sc.nextInt();
        Arrays.sort(l);
        int ans = 0;
        for (int i=0; i<n-1; i++){
            for (int j=i+1; j<n; j++){
                int lower = j;
                int upper = n;
                while (upper-lower > 1){
                    int mid = (lower+upper)/2;
                    if (l[mid]<l[i]+l[j]){
                        lower = mid;
                    }else {
                        upper = mid;
                    }
                }
                ans += (lower-j);
            }
        }
        System.out.println(ans);
    }
}