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 C (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

/*
 * main.c
 *
 *  Created on: 2019/07/21
 *      Author: family
 */

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

int L[2001] = {0};

int main()
{
	int N = 0, ans = 0;
	int i = 0, j = 0, k = 0;
	scanf("%d", &N);
	for (i = 0; i < N; i++) {
		scanf("%d", &L[i]);
	}

//	int count = 0;
	for (i = 0; i < N-2; i++ ) {
		for (j = i+1; j < N-1; j++ ) {
			for (k = j+1; k < N; k++ ) {
				int ok = 0;
				if (L[i] < (L[j] + L[k])) {
					ok++;
				} else {
				}
				if (L[j] < (L[i] + L[k])) {
					ok++;
				} else {
				}
				if (L[k] < (L[i] + L[j])) {
					ok++;
				} else {
				}
				if (ok == 3) {
					ans++;
				}
//				count++;
			}
		}
	}
	printf("%d\n", ans);
//	printf("%d\n", count);
    return 0;
}