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: Wrong Answer)

use std::io;

fn main() {
    get_line();
    let mut ns: Vec<u64> = read_ints().into_iter().collect();
    ns.sort();
    println!("{}", together(&ns));
}
fn together(nums: &[u64]) -> usize {
    /// assumes nums is sorted.
    let mut groups = map_len_dot_group(nums);
    for _ in 0..2 {
        groups.push(0);
    }
    // zipWith3 (\x y z -> x+y+z) groups (tail groups) (tail tail groups)
    match groups
              .iter()
              .zip(&groups[1..])
              .map(|(x, y)| x + y)
              .zip(&groups[2..])
              .map(|(x, y)| x + y)
              .max() {
        Some(n) => n,
        None => groups[2],
    }
}

fn map_len_dot_group<T: PartialOrd>(xs: &[T]) -> Vec<usize> {
    let mut record = vec![];
    let mut current = xs.iter().next();
    let mut count = 0;
    for x in xs.iter() {
        if Some(x) == current {
            count = count + 1;
        } else {
            current = Some(x);
            record.push(count);
            count = 1;
        }
    }
    record.push(count);
    record
}

fn read_ints() -> Vec<u64> {
    get_line()
        .trim()
        .split_whitespace()
        .map(|n| n.parse().unwrap())
        .collect()
}

fn get_line() -> String {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).ok();
    buf
}