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# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
public class Hello{
    public static void Main(){
        // Your code here!
        var N =long.Parse(Console.ReadLine());
        long n = 0;
        var Data = Console.ReadLine().Split();
        
        for(long i=0 ; i<N-2;i++)
        {
            var _i =int.Parse(Data[i]);
            for(long j=i+1;j<N-1;j++)
            {
                var _j =int.Parse(Data[j]);
                for(long k=j+1;k<N;k++)
                {
                    var _k =int.Parse(Data[k]);
                    if(_i < _k + _j && _j < _i + _k && _k < _i + _j)
                    {
                        n++;
                    }
                }
            }
            
        }
        Console.WriteLine(n);
        
    }
}