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::{self};
use std::collections::HashMap;

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: Vec<i32> = buffer
        .split_whitespace()
        .map(|x| x.parse().unwrap())
        .collect();
    
    xs.sort();
    let mut counter = HashMap::new();
    loop {
        let (key, c) = count_and_truncate(&mut xs);
        counter.insert(key, c);
        if xs.is_empty() {break;}
    }
    let m = counter.keys().map(
        |key| {
            get_default(&counter, *key-1)
            + get_default(&counter, *key)
            + get_default(&counter, *key+1)
        }).max().unwrap();
    println!("{}", m);
}


fn count_and_truncate(xs: &mut Vec<i32>) -> (i32, i32) {
    let mut cnt = 0;
    let key = &xs[0].clone();
    for x in xs.iter() {
        if x != key {
            break;
        }
        cnt += 1;
    }
    xs.drain(..cnt as usize);
    // println!("{:?}", xs);
    (*key, cnt)
}

fn get_default(hashmap: &HashMap<i32, i32>, key: i32) -> i32 {
    match hashmap.get(&key) {
        None => 0,
        Some(x) => *x,
    }
}