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.Arrays;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner scn = new Scanner(System.in);
		int N = scn.nextInt();
		int[] L = new int[N];

		for(int i = 0;i < N;i++) {
			L[i] = scn.nextInt();
		}
		Arrays.sort(L);


		int ans = 0;
		for(int i = 0;i < N-1;i++) {
			for(int j = i+1;j < N;j++) {
				int l = L[i] + L[j];
				int lb = lowerbound(L,l);
				ans += lb - j - 1;
			}
		}

		System.out.println(ans);

	}



	public static int lowerbound(int[] A, int k) {//k<=Aiを満たす最小のi
		int lb = -1, ub = A.length;
		while(ub-lb > 1) {
			int mid = (lb + ub)/2;
			if(A[mid] >= k) {
				ub = mid;
			}else {
				lb = mid;
			}
		}
		return ub;
	}
}