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 sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[n];
        int[] b = new int[1001];
        for (int i = 0; i < n; i++) {
            int x = sc.nextInt();
            a[i] = x;
            b[x]++;
        }
        Arrays.sort(a);
        int ans = 0;
        for (int i = 0; i < n; i++) {
            for (int j = i+1; j < n; j++) {
                int s = a[i] + a[j];
                int l = 0, r = n;
                while(1 < r - l){
                    int m = (l+r)/2;
                    if(s <= a[m]) r = m;
                    else l = m;
                }
                ans += l - j;
            }
        }
        System.out.println(ans);
        sc.close();

    }

}