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;
class Program{
  static void Main(){
    int N=int.Parse(Console.ReadLine());
    string[] l=Console.ReadLine().Split(' ');
    int[] L=new int[N];
    for(int I=0;I<N;I++){
      L[I]=int.Parse(l[I]);
    }
    int V=0;
    for(int n1=0;n1<N;n1++){
      for(int n2=0;n2<N;n2++){
        for(int n3=0;n3<N;n3++){
          if(n1!=n2&&n2!=n3&&n1!=n3){
            if(L[n1]<L[n2]+L[n3]&&L[n2]<L[n1]+L[n3]&&L[n3]<L[n1]+L[n2])V++;
          }
    }
    }
    }
    Console.WriteLine(V/6);
  }
}