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 Perl (v5.18.2) (judge verdict: Accepted)

use strict;

my $n = <>;
my @input = split(/\s+/, <>);

my %cnt;
foreach my $key (@input){
    if ($cnt{$key}) {
        $cnt{$key}=$cnt{$key}+1;
    } else {
        $cnt{$key}=1;
    }
}

my $answer = 0;
foreach my $key (sort(keys(%cnt))){
    my $tmp = $cnt{$key} + $cnt{$key-1} + $cnt{$key+1};
    if ($answer < $tmp) {
        $answer = $tmp;
    }
}
print $answer;