Problem:
Score : 300 points

Problem Statement

You are given an integer sequence of length N, a_1,a_2,...,a_N.

For each 1≤i≤N, you have three choices: add 1 to a_i, subtract 1 from a_i or do nothing.

After these operations, you select an integer X and count the number of i such that a_i=X.

Maximize this count by making optimal choices.

Constraints

1≤N≤10^5

0≤a_i<10^5 (1≤i≤N)

a_i is an integer.

Input

The input is given from Standard Input in the following format:

N
a_1 a_2 .. a_N

Output

Print the maximum possible number of i such that a_i=X.

Sample Input 1

7
3 1 4 1 5 9 2

Sample Output 1

4

For example, turn the sequence into 2,2,3,2,6,9,2 and select X=2 to obtain 4, the maximum possible count.

Sample Input 2

10
0 1 2 3 4 5 6 7 8 9

Sample Output 2

3

Sample Input 3

1
99999

Sample Output 3

1

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;

class Program {
  const int BUCKET_SIZE = 100010;
  static void Main(string[] args) {
    int N = int.Parse(Console.ReadLine());
    string[] A = Console.ReadLine().Split();
    int[] B = new int[BUCKET_SIZE];

    for (int i = 0; i < N; ++i) {
      ++B[int.Parse(A[i])];
    }

    int ans = 0;
    for (int i = 1; i < BUCKET_SIZE - 1; ++i) {
      ans = Math.Max(ans, B[i-1] + B[i] + B[i + 1]);
    }
    Console.WriteLine(ans);
  }
}