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 Rust (1.15.1) (judge verdict: Accepted)

use std::io::prelude::*;

fn main() {
    let stdin = std::io::stdin();
    let mut reader = std::io::BufReader::new(stdin.lock());
    let mut s = String::new();
    reader.read_line(&mut s).unwrap();
    let _: usize = s.trim().parse().unwrap();

    let mut s = String::new();
    reader.read_line(&mut s).unwrap();
    let mut a = [0; 100000];

    for i in s.split_whitespace().map(|x| x.parse::<usize>().unwrap()) {
        a[i] += 1;
    }
    
    let mut max = 0;

    for i in 1..99999 {
        if a[i - 1] + a[i] + a[i + 1] > max {
            max = a[i - 1] + a[i] + a[i + 1];
        }
    }
    println!("{}", max);
}