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 (Clang 3.8.0) (judge verdict: Accepted)

#include <stdio.h>

int main()
{
	int i, j, k, N, L[2000], sw = 0, sw2 = 0;

	scanf("%d", &N);

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

	for (i = 0; i < N - 2; i++) {
		for (j = i + 1; j < N - 1; j++) {
			for (k = j + 1; k < N; k++) {
				if (L[i] < L[j] + L[k]) {
					sw++;
				}
				if (L[j] < L[k] + L[i]) {
					sw++;
				}
				if (L[k] < L[i] + L[j]) {
					sw++;
				}

				if (sw == 3) {
					sw2++;
				}
				sw = 0;
			}
		}
	}

	printf("%d", sw2);
}