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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
$dummy = fgets(STDIN);
$a = explode(" ", fgets(STDIN));
$intRank = [];
foreach ($a as $val) {
    $val = intval($val);
    $box = [];
    $box[$val] = true;
    $valMax = $val + 1;
    if ($valMax > 99999) {
        $valMax = 99999;
    }
    $valMin = $val - 1;
    if ($valMin < 0) {
        $valMin = 0;
    }
    $box[$valMax] = true;
    $box[$valMin] = true;
    
    foreach (array_keys($box) as $value) {
        if (!isset($intRank[$value])) {
            $intRank[$value] = 0;
        }
        $intRank[$value] ++;
    }
}

arsort($intRank);
$intRank = array_keys($intRank);
$x = $intRank[0];
$cnt = 0;
foreach ($a as $val) {
    $val = intval($val);
    $valMax = $val + 1;
    if ($valMax > 99999) {
        $valMax = 99999;
    }
    $valMin = $val - 1;
    if ($valMin < 0) {
        $valMin = 0;
    }
    if ($val === $x || $valMin === $x || $valMax === $x) {
        $cnt ++;
    }
}

echo $cnt;
?>