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: Accepted)

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

#define N 2000

int compare(const void *a, const void *b) {
	int ia = *(int *) a;
	int ib = *(int *) b;

	return ia - ib;
}

int main() {
	static int ll[N];
	int n, i, j, k, ans;

	scanf("%d", &n);
	for (i = 0; i < n; i++)
		scanf("%d", &ll[i]);
	qsort(ll, n, sizeof *ll, compare);
	ans = 0;
	for (i = 0; i < n; i++)
		for (j = i + 1; j < n; j++)
			for (k = j + 1; k < n; k++) {
				int a, b, c;

				a = ll[i];
				b = ll[j];
				c = ll[k];
				if (c >= a + b)
					break;
				else if (b < c + a && a < b + c)
					ans++;
			}
	printf("%d\n", ans);
	return 0;
}