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: Runtime Error)

#include<stdio.h>

int main(void) {

	long long int N, L[1000], i, u, o, m, answer = 0;

	scanf("%lld", &N);

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

	for(i = 0;i < N - 2;i++) {
		for(u = i + 1;u < N - 1;u++) {	
			for(o = u + 1;o < N;o++) {
				if(L[i] < L[u] + L[o]&&L[u] < L[i] + L[o]&&L[o] < L[u] + L[i]) {
				answer++;
				}
			}
		}
	}

	printf("%lld", answer);

	return 0;
}