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 ll;
int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	cout.tie(NULL);
	ll n;
	cin>>n;
	ll a[n+5];
	for(ll i=0;i<n;i++)
	{
		cin>>a[i];
	}
	sort(a,a+n);
	ll ans = 0;
	for(ll i=2;i<n;i++)
	{
		for(ll j=0;j<i;j++)
		{
			ll val = a[i]-a[j];
			ll idx = upper_bound(a,a+n,val)-a;
			if (idx>=0)
			{
				ll m = max(0ll,i-idx);
				if(idx<=j)
					m--;
				ans+=m;
			}
		}
	}
	cout<<ans/2;
}