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::stdin;
use std::collections::HashMap;

#[allow(dead_code)]
fn input_strs() -> Vec<String> {
    let mut s = String::new();
    match stdin().read_line(&mut s) {
        Ok(_) => s.split_whitespace().map(|s| s.to_string()).collect(),
        Err(_) => panic!("err"),
    }
}

#[allow(dead_code)]
fn input_ints() -> Vec<i32> {
    let mut s = String::new();
    match stdin().read_line(&mut s) {
        Ok(_) => s.split_whitespace().map(|s| s.parse().unwrap()).collect(),
        Err(_) => panic!("err"),
    }
}

#[allow(unused_variables)]
fn solve() {
    let l = input_ints();
    let n = l[0] as usize;
    let a = input_ints();

    let mut h = HashMap::<i32, u32>::new();

    for num in &a {
        let current = h.entry(*num).or_insert(0);
        *current += 1;
    }

    let mut x_num = 0;

    for (x, v) in &h {
        let mut total = *v;

        if let Some(num) = h.get(&(*x - 1)) {
            total += *num;
        }
        if let Some(num) = h.get(&(*x + 1)) {
            total += *num;
        }

        x_num = std::cmp::max(total, x_num);
    }

    println!("{}", x_num);
}

fn main() {
    solve();
}