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 <math.h>
#include <stdio.h>
#include <stdlib.h>
int cmpint(const void *a, const void *b) { return *(int *)b - *(int *)a; }
int main() {
	int n, ans = 0;
	int l[2000];
	scanf("%d", &n);
	for (int i = 0; i < n; i++) {
		scanf("%d", &l[i]);
	}
	qsort(l, n, sizeof(int), cmpint);
	for (int i = 0; i < n; i++) {
		for (int j = i + 1; j < n; j++) {
			for (int k = j + 1; k < n; k++) {
				if (l[i] < l[j] + l[k]) {
					ans++;
				}
			}
		}
	}
	printf("%d\n", ans);
	return 0;
}