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: Accepted)

#include<bits/stdc++.h>
#define ll long long
using namespace std;
const int N=1e6+10;
int a[N],n,b;
char c[N];
int main()
{cin>>n;
	for(int i=1;i<=n;i++)scanf("%d",&a[i]);
	sort(a+1,a+n+1);
	for(int i=1;i<=n-2;i++)
	{
		int k=i+1;if(a[i]+a[k]<=a[i+2])k++;
		for(int j=i+2;j<=n;j++)
		{
			b+=j-k;
			while(a[i]+a[k]<=a[j+1])k++;
		}
	}cout<<b;
}