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.util.*;

public class Main {

    /* チェックリスト
     * intの範囲を超えていないか
     * TLEしそうな処理の有無
     */
    public static void main(String args[]){
        Scanner sc = new Scanner(System.in);
        int n = Integer.parseInt(sc.nextLine());
        String[] in = sc.nextLine().split(" ");
        List<Integer> ints = new ArrayList<Integer>();
        for(String str : in){
            ints.add(Integer.parseInt(str));
        }
        ints.sort(Comparator.reverseOrder());
        long r = 0;
        for(int ia = 0;ia < n;ia++){
            int a = ints.get(ia);
            for(int ib = ia + 1;ib < n;ib++) {
                int b = ints.get(ib);
                for (int ic = ib + 1; ic < n; ic++) {
                    int c = ints.get(ic);
                    if (a < b + c) {
                        if (b < c + a) {
                            if (c < a + b) {
                                r++;
                            }else{
                                break;
                            }
                        }else{
                            break;
                        }
                    }else{
                        break;
                    }
                }
            }
        }
        System.out.println(r);
    }
}