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;
use std::collections::HashMap;


/// https://beta.atcoder.jp/contests/arc082/tasks/arc082_a
fn main() {
    let _ = read_one::<usize>();
    let an = read::<isize>();
    let mut hm = HashMap::new();
    let am = an.clone().iter().map(|i| i - 1).collect::<Vec<_>>();
    let ap = an.clone().iter().map(|i| i + 1).collect::<Vec<_>>();

    for a in an {
        *hm.entry(a).or_insert(0) += 1;
    }

    for a in am {
        *hm.entry(a).or_insert(0) += 1;
    }

    for a in ap {
        *hm.entry(a).or_insert(0) += 1;
    }

    let mut v = hm.iter().collect::<Vec<_>>();
    v.sort_by_key(|&(_, v)| -v);

    println!("{:?}", v[0].1);
}


#[allow(dead_code)]
fn read<T>() -> Vec<T>
where T:
    std::str::FromStr,
    T::Err: std::fmt::Debug {

    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    buf.split_whitespace()
        .map(|s| s.trim().parse().unwrap())
        .collect()
}

#[allow(dead_code)]
fn read_one<T>() -> T
where T:
    std::str::FromStr,
    T::Err: std::fmt::Debug {

    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    buf.trim().parse().unwrap()
}