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: Time Limit Exceeded)

import java.io.*;
import java.util.*;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int n = sc.nextInt();
        sc.nextLine();
        int[] L  = toArray(sc.nextLine());
        int res = 0;
        for (int i = 0; i < n; i++) {
            int a = L[i];
            for (int j = i+1; j < n; j++) {
                int b = L[j];
                for (int k = j+1; k < n; k++) {
                    int c = L[k];
                    if(a+b > c && a+c > b && b+c > a) res++;
                }
            }
        }
        System.out.println(res);
    }

    public static class Pair {
        int m1;
        int m2;

        public Pair(int m1, int m2) {
            this.m1 = m1;
            this.m2 = m2;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Pair pair = (Pair) o;
            return m1 == pair.m1 &&
                    m2 == pair.m2;
        }

        @Override
        public int hashCode() {
            return Objects.hash(m1, m2);
        }
    }

    private static int[] toArray(String text) {
        String[] vars = text.split("\\s+");
        int[] res = new int[vars.length];
        for (int i = 0; i < vars.length; i++) {
            res[i] = Integer.valueOf(vars[i]);
        }
        return res;
    }
}