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.Collections.Generic;
 
class program{
 
  static void Main(){
    int N;
    N = int.Parse(Console.ReadLine());
    int[] L= new int[N]; 
    string[] s = Console.ReadLine().Split(' ');
  for(int i=0;i<N;i++){
    L[i] = int.Parse(s[i]);
  }
  int sum=0;
  for(int i=0;i<N-1;i++){
    for(int j=i+1;j<N;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]))){
            sum++;
          }
        }
      }
    }
  }
  Console.WriteLine(sum);
  }
}