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::cmp;
use std::cmp::Ordering;


// read a line(without line feed)
fn read_line() -> String {
    let mut in_str = String::new();
    io::stdin().read_line(&mut in_str).unwrap();
    return in_str.trim().to_string();
}

// read wods on a line
pub fn read_words_in_line() -> Vec<String> {
    let s = read_line();
    return s.split_whitespace().map(|x| x.to_string()).collect::<Vec<String>>()
}

// read type t on a line
pub fn read_t_in_line<T : std::str::FromStr>() -> Vec<T> {
    let mut v : Vec<T> = Vec::new();
    for e in read_words_in_line().iter().map(|x| x.parse::<T>()) {
        if let Ok(r) = e {
            v.push(r);
        }
        else{
            return Vec::new();
        }
    }
    return v;
}

// sort slice
pub fn sort<T : std::cmp::Ord>(slice : &mut [T]) {
    slice.sort();
}
// sort slice by reverse order
pub fn sort_rev<T : std::cmp::Ord>(slice : &mut [T]) {
    slice.sort_by(|x, y| y.cmp(x));
}

pub fn min<T : std::cmp::Ord>(a : T, b : T) -> T{
    return cmp::min(a, b);
}

pub fn max<T : std::cmp::Ord>(a : T, b : T) -> T{
    return cmp::max(a, b);
}

#[derive(Copy, Clone, Eq, PartialEq, Debug)]
struct State {
    cost     : i32,
    node     : i32,
    vismask  : i32
}

impl Ord for State {
    fn cmp(&self, other: &State) -> Ordering {
        other.cost.cmp(&self.cost)
    }
}

impl PartialOrd for State {
    fn partial_cmp(&self, other : &State) -> Option<Ordering> {
        Some(self.cmp(other))
    }
}


fn main() {
    
    let n = read_t_in_line::<i32>()[0];
    let a = read_t_in_line::<i32>();
    let mut f = vec![0 ; 101000];

    for i in 0..n {
        let ai = a[i as usize];
        let v = vec![ai, ai + 1, ai - 1];
        for j in v {
            f[(j + 1) as usize] += 1;
        }
    }
    
    let mut res = -1;
    for i in 0..f.len() {
        res = max(res, f[i]);
    }

    println!("{}", res);


}