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;

class Assignment {
  static void Main() {
    var N = int.Parse(Console.ReadLine().Trim());
    var L = Console.ReadLine().Trim().Split(' ').Select(x => int.Parse(x.Trim())).ToArray();
    //N = L.Length;
    var answer = 0;
    //var prev_i = 0;
    //ソート
    Array.Sort(L);
    //Console.WriteLine(string.Join(" ", L));
    
    for(var i = 0; i < N - 2; i++) {   
      /*
      var prev_j = 0;
      if(L[i] == prev_i) {
        continue;
      }
      */
      for(var j = i + 1; j < N - 1; j++) {
        /*
        var prev_k = 0;
        if(L[j] == prev_j) {
          continue;
        }
        */
        /*
        if(L[j] == L[i]) {
          continue;
        }
        */
        for(var k = j + 1; k < N; k++) {
          //Console.WriteLine(i + ", " + j + ", " + k + ", " + answer);
          //if(L[k] != prev_k) {
            if(L[i] + L[j] > L[k]) {
              answer++;   
              /*
              prev_i = L[i];
              prev_j = L[j];
              prev_k = L[k];
              */
            } else {
              break;
            }
          //}
        }
      }
    }
    Console.WriteLine(answer);
    
  }
}