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++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include<stdio.h>
int aa[2089];
main()
{
	int n;
	while(~scanf("%d",&n))
	{
		int i;
		for(i=0;i<n;i++)
			scanf("%d",&aa[i]);
		int a1=0,a2=1,a3=2,num=0;
		for(a1=0;a1<=n-3;a1++)
			for(a2=a1+1;a2<=n-2;a2++)
				for(a3=a2+1;a3<=n-1;a3++)
					if(aa[a1]+aa[a2]>aa[a3]&&aa[a1]+aa[a3]>aa[a2]&&aa[a2]+aa[a3]>aa[a1]&&aa[a1]-aa[a2]<aa[a3]&&aa[a1]-aa[a3]<aa[a2]&&aa[a2]-aa[a3]<aa[a1])
						num++;
						printf("%d\n",num);
	}
}