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;
#define INF 1LL<<62
#define inf 1000000007

vector<ll>a;
int main() {
	ll n;
	cin>>n;
	for(ll i=0;i<n;i++){
		ll x;
		cin>>x;
		a.push_back(x);
	}
	ll ans=0;
	sort(a.begin(),a.end());
	for(ll i=n-1;i>=0;i--){
		for(ll j=i-1;j>=0;j--){
			ll now=a[i]-a[j]+1;
			auto itr=lower_bound(a.begin(),a.end(),now);
			ll k=itr-a.begin();
			if(k<j){
				ans+=j-k;
				//cout << i<<j<<k<<*itr<<endl;
			}
		}
	}
	cout <<ans;
	// your code goes here
	return 0;
}