Home

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 $a_i=X$.

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

3

1
99999

1