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.*;
import static java.lang.Math.*;
import java.math.BigInteger;

public class Main {

	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		
		// 入力
		int n = sc.nextInt();
		int[] l = new int[n];
		for(int i = 0; i < n; i++){
		    l[i] = sc.nextInt();
		}

		// 計算
	    int result = 0;
	    Arrays.sort(l);
	    for(int i = 0; i < n; i++){
		    for(int j = i + 1; j < n; j++){
		        int index = lowerBound(l, l[i] + l[j]) - 1;
		        result += index - j;
		    }
		}

		// 出力
		System.out.println(result);
        
	}
	
	static int lowerBound(int[] array, int n){
	    Integer[] a = new Integer[array.length];
	    for(int i = 0; i < array.length; i++){
	        a[i] = array[i];
	    }
	    int index = ~Arrays.binarySearch(a, n, (x,y) -> x.compareTo(y) >= 0 ? 1 : -1);
	    return index;
	}
}