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;
using System.Linq;
using System.Threading.Tasks;
using static System.Console;
using static System.Math;
class program{
  static void Main(string[] args){
    program p = new program();
    p.Run();
  }
  void Run(){
	int n = Readint()[0];
    int[] L = Readint();
    int count=0;
    
    for(int i=0;i<n-2;i++)
      for(int j=i+1;j<n-1;j++)
        for(int k=j+1;k<n;k++){
          if(i!=j && j!=k && k!=i)
          	if(L[i]+L[j]>L[k] && L[j]+L[k]>L[i] && L[k]+L[i]>L[j])
            	count++;
        }
    WriteLine(count.ToString());
  }

  int[] Readint(){
    string[] s = ReadLine().Split();
    int[] res=new int[s.Length];
    Parallel.For(0,s.Length,i=>{
      res[i]=int.Parse(s[i]);
    });
    return res;
  }
}