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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

from collections import Counter



def main()->None:
    # a_iに１を足すか、１引くか、何もしないかの操作を行って、ある整数個数最大化をする
    # x を決めるとgreedyに決まる。
    # 最後の一つのサンプルがTLEになる。jit の使い方もよくわからん
    N = int(input())
    a = list(map(int, input().split()))
    a_dict = Counter(a)
    keys = a_dict.keys()
    max_count = 0
    for key in keys:
        tmp_count = a_dict[key]
        for i in keys:
            if key - 1 == i or key + 1 == i:
                tmp_count += a_dict[i]
        if tmp_count > max_count:
            max_count = tmp_count
    print(max_count)

if __name__ == "__main__":
    main()