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-mcs 6.8.0.105) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

class Program
{
	static void Main()
	{
		int.Parse(Console.ReadLine());
		var t = Array.ConvertAll(Console.ReadLine().Split(new[] { ' ' }), number => int.Parse(number));

		var nums = new Dictionary<int, int>();
		foreach (var a in t) {
			if (nums.ContainsKey(a)) {
				nums[a] += 1;
			} else {
				nums.Add(a, 1);
			}
		}

		var maxNum = 0;
		var maxSum = 0;
		foreach (var num in nums) {
			var sum = num.Value;
			if (nums.ContainsKey(num.Key - 1)) {
				sum += nums[num.Key - 1];
			}

			if (nums.ContainsKey(num.Key + 1)) {
				sum += nums[num.Key + 1];
			}

			if (sum > maxSum) {
				maxNum = num.Key;
				maxSum = sum;
			}
		}

		Console.WriteLine(maxSum);

		//デバッグ実行での確認用。そのまま提出しても問題なし		
		Console.ReadKey();
	}
}