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: Accepted)

#include<stdio.h>
#include<stdlib.h>
int cmp(const void *a,const void *b)
{
	return (*(int*)a - *(int*)b);
}
int main(void)
{
	int n,a[2005]={0},i,j,high=0,low=0,mid=0,X=0,ans,count=0;
		scanf("%d",&n);
		for(i=0;i<n;i++)
			scanf("%d",&a[i]);

		qsort(a,n,sizeof(int),cmp);

		for(i=0;i<n;i++)
		{
			for(j=i+1;j<n;j++)
			{
				X=a[i]+a[j];
				high=n-1;
				low=j;
				mid=low+(high-low)/2;
              ans = j;
				while(high>=low)
				{
					if(X>a[mid])
					{low=mid+1;ans=mid;}
					else
					{high=mid-1;}
					mid=low+(high-low)/2;
				}
				count+=(ans-j);
			}
		}
		printf("%d\n",count);
		count=0;
	return 0;
}