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: Time Limit Exceeded)

#include<iostream>
#include<algorithm>
#include<string>
#include<vector>
using namespace std;
#define long long int
int main()
{
    int n;
    cin>>n;
    vector<int> v;
    for(int i=0;i<n;i++)
    {
        int a;
        cin>>a;
        v.push_back(a);
    }
    int count=0;
    for(int i=0;i<n;i++)
    {
        for(int j=i+1;j<n;j++)
        {
            for(int k=j+1;k<n;k++)
            {
                //cout<<v[i]<<" "<<v[j]<<" "<<v[k]<<endl;
                if(((v[i]+v[j])>v[k]) && ((v[i]+v[k])>v[j]) && ((v[j]+v[k])>v[i]))
                {
                count+=1;
                //cout<<v[i]<<" "<<v[j]<<" "<<v[k]<<endl;
                }
            }

        }
    }
    cout<<count<<endl;
    return 0;


}