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>
#include<math.h>
int ju_trian(int a,int b,int c)
{
	if(a<b+c&&b<a+c&&c<a+b)
	{
		return 1;
	}
	else 
	{
		return 0;
	}
}
int main(void)
{
	int number=0;
	int sum=0;
	scanf("%d",&number);
	int tri[number];
	for(int i=0;i<number;i++)
	{
		tri[i]=0;
		
	}
	for(int i=0;i<number;i++)
	{
		scanf("%d",&tri[i]);
	}
	for(int i=0;i<number-2;i++)
	{
		for(int j=i+1;j<number-1;j++)
		{
			for(int k=j+1;k<number;k++)
			{
				sum=sum+ju_trian(tri[i],tri[j],tri[k]);
			}
		}
	}
	printf("%d",sum);
	return 0;
}