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>
using namespace std;
typedef long long int ll;
const ll maxn=2e5+1;
void solve()
{
	ll N;
	cin>>N;
	ll a[maxn];
	for(ll i=0;i<N;i++)
	{
		cin>>a[i];
	}
	sort(a,a+N);
	ll ans=0;
	for(ll i=0;i<N;i++)
	{
		for(ll j=i+1;j<N;j++)
		{
			ll l=j;
			ll r=lower_bound(a,a+N,a[i]+a[j])-a;
			ans+=(r-l-1);
		}
	}
	cout<<ans<<"\n";
}
int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	ll T=1,p=0;
	//cin>>T;
	do
	{
		solve();
		p++;
	}while(p<T);
	return 0;
}