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 <iostream>
#include <vector>
#include <string>
#include <algorithm>
using namespace std;

int main(){
	int n;
	cin >> n;
	vector<int> l(n);
	for(int i=0;i<n;i++){cin >> l[i];}
	sort(l.begin(),l.end());
	
	int ans =0;
	int tmp;
	
	for(int i=0;i<n-2;i++){
		for(int j=i+1;j<n-1;j++){
			tmp = l[i]+l[j];
			for(int k=j+1;k<n;k++){
				//cout << l[i] << " "<<l[j] <<" " <<l[k] << endl;
				if(tmp <= l[k]){
					//cout << "dame" << endl;
					break;
				}
				else{
					//cout << "ok" << endl;
					ans += 1;}
			}
		}
	}
	
	cout << ans << endl;
	
	return 0;
}