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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        final int N = sc.nextInt();
        int[] sticks = scanSticks(sc, N);
        Arrays.sort(sticks);

        long answer = 0;

        for (int iLeft = 0; iLeft < N - 2; iLeft++) {
            int left = sticks[iLeft];
            
            for (int iMiddle = iLeft + 1; iMiddle < N - 1; iMiddle++) {
                int middle = sticks[iMiddle];
                
                for (int iRight = iMiddle + 1; iRight < N; iRight++) {
                    int right = sticks[iRight];
                    
                    if (isSatisfied(left, middle, right))
                        answer++;
                }
            }
        }

        System.out.println(answer);
    }

    private static int[] scanSticks(Scanner sc, final int N) {
        int[] sticks = new int[N];

        for (int i = 0; i < N; i++)
            sticks[i] = sc.nextInt();

        return sticks;
    }

    private static boolean isSatisfied(int left, int middle, int right) {
        return left + middle > right;
    }
}