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::collections::HashMap;
use std::io::prelude::*;

fn main() {
    let stdin = std::io::stdin();
    let mut reader = std::io::BufReader::new(stdin.lock());
    let mut s = String::new();
    reader.read_line(&mut s).unwrap();
    let n: usize = s.trim().parse().unwrap();

    let mut s = String::new();
    reader.read_line(&mut s).unwrap();
    let mut map = HashMap::new();
    let an: Vec<i64> = s.split_whitespace().map(|x| x.parse().unwrap()).collect();
    for a in an {
        *map.entry(a).or_insert(0) += 1;
    }

    let mut max = 0;
    for i in -1..100002 {
        let tmp = match map.get(&(i - 1)) {
            Some(x) => *x,
            _ => 0
        } + match map.get(&i) {
            Some(x) => *x,
            _ => 0
        } + match map.get(&(i + 1)) {
            Some(x) => *x,
            _ => 0
        };
        max = std::cmp::max(max, tmp);
    }
    println!("{}", max);
}