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::collections::HashMap;
use std::ops::{Deref, DerefMut};

fn main() {
    let mut buffer = String::new();
    io::stdin().read_line(&mut buffer).unwrap();
    buffer.clear();
    io::stdin().read_line(&mut buffer).unwrap();
    let mut xs: CountedData = CountedData(
        buffer
        .split_whitespace()
        .map(|x| x.parse().unwrap())
        .collect()
    );
    
    xs.sort();
    let mut counter = HashMap::new();
    while !xs.is_empty() {
        let (key, c) = xs.count_and_drain();
        counter.insert(key, c);
    }

    let m: i32 = counter.keys().map(
        |key| {
            [-1, 0, 1]
                .iter()
                .map(|x| {
                    match counter.get(&(key + x)) {
                        None => 0,
                        Some(i) => *i,
                    }
                })
                .sum()
        }).max().unwrap();
    
    println!("{}", m);
}

struct CountedData(Vec<i32>);

impl CountedData {
    fn count_and_drain(&mut self) -> (i32, i32) {
        let key = self[0].clone();
        let cnt = self.iter()
            .take_while(|&&x| x == key)
            .count();
        self.drain(..cnt);
        (key, cnt as i32)        
    }
}

impl Deref for CountedData {
    type Target = Vec<i32>;

    fn deref(&self) -> &Vec<i32> {
        &self.0
    }
}

impl DerefMut for CountedData {
    fn deref_mut(&mut self) -> &mut Vec<i32> {
        &mut self.0
    }
}