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)

#include <stdio.h>
int main()
{
	int N;
	scanf("%d", &N);
	int a[2000];
	for(int i = 0; i < N; i++)
	{
		scanf("%d", &a[i]);
	}
	int sum = 0;
	for(int i = 0; i < N-2; i++)
	{
		for(int j = i + 1; j < N-1; j++)
		{
			for(int k = j+1; k < N; k++)
			{
				if((a[i] < a[j] + a[k]) && (a[j] < a[i] + a[k]) && (a[k] < a[i] + a[j]))
					sum++;
			}
		}
	}
	printf("%d", sum);
}