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::{BufRead, Write};
use std::io;
use std::collections::HashMap;
use std::iter;

fn solve<R: BufRead, W: Write>(mut input: R, mut output: W) {
    let mut buf = String::new();
    input.read_line(&mut buf).unwrap();
    let _: usize = buf.trim_right().parse().unwrap();
    buf.clear();
    input.read_line(&mut buf).unwrap();
    let a: Vec<usize> = buf.split_whitespace().map(|x| x.parse().unwrap()).collect();
    let mut count: HashMap<usize, usize> = HashMap::new();
    for x in a {
        *count.entry(x).or_insert(0) += 1;
    }
    let result: usize = count
        .iter()
        .map(|(&k, &v)| {
            iter::once(v)
                .chain(count.get(&k.wrapping_sub(1)).cloned())
                .chain(count.get(&(k + 1)).cloned())
                .sum()
        })
        .max()
        .unwrap();
    writeln!(output, "{}", result).unwrap();
}

fn main() {
    let stdin = io::stdin();
    let stdout = io::stdout();
    solve(stdin.lock(), stdout.lock());
}

#[cfg(test)]
mod tests {
    fn test(input: &str, output: &str) {
        let mut v: Vec<u8> = Vec::new();
        ::solve(input.as_bytes(), &mut v);
        assert_eq!(String::from_utf8(v).unwrap(), output);
    }

    #[test]
    fn case1() {
        test(
            "7
3 1 4 1 5 9 2\n",
            "4\n",
        );
    }
    #[test]
    fn case2() {
        test(
            "10
0 1 2 3 4 5 6 7 8 9\n",
            "3\n",
        );
    }
    #[test]
    fn case3() {
        test(
            "1
99999\n",
            "1\n",
        );
    }
}