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::fmt::{Debug, Display};
use std::io::{self, Read};
use std::str::{self, FromStr};
use std::cmp;


fn solve(a: Vec<usize>) -> u64 {
    let mut counter = [0; 100001];
    for x in a.into_iter() {
        counter[x] += 1;
    }
    let mut result = 0;
    for i in 1..100000 {
        result = cmp::max(result, counter[i - 1] + counter[i] + counter[i + 1]);
    }
    result
}


fn main() {
    let stdin = io::stdin();
    let mut sc = Scanner::new(stdin.lock().bytes());
    let n = sc.next();
    println!("{}", solve(sc.vec(n)));
}


struct Scanner<R: Read> {
    buf: Vec<u8>,
    bytes: io::Bytes<R>,
}

#[allow(dead_code)]
impl<R: Read> Scanner<R> {
    fn new(bytes: io::Bytes<R>) -> Self {
        Scanner {
            buf: Vec::with_capacity(256),
            bytes: bytes,
        }
    }

    fn next<T: FromStr>(&mut self) -> T
    where
        <T as FromStr>::Err: Debug,
    {
        self.buf.clear();
        for c in self.bytes
            .by_ref()
            .map(|c| c.unwrap())
            .skip_while(|&c| c == ' ' as u8 || c == '\n' as u8)
            .take_while(|&c| !(c == ' ' as u8 || c == '\n' as u8))
        {
            self.buf.push(c);
        }
        str::from_utf8(&self.buf).unwrap().parse().unwrap()
    }

    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T>
    where
        <T as FromStr>::Err: Debug,
    {
        (0..n).map(|_| self.next()).collect()
    }

    fn pairs<A: FromStr, B: FromStr>(&mut self, n: usize) -> Vec<(A, B)>
    where
        <A as FromStr>::Err: Debug,
        <B as FromStr>::Err: Debug,
    {
        (0..n).map(|_| (self.next(), self.next())).collect()
    }

    fn trios<A: FromStr, B: FromStr, C: FromStr>(&mut self, n: usize) -> Vec<(A, B, C)>
    where
        <A as FromStr>::Err: Debug,
        <B as FromStr>::Err: Debug,
        <C as FromStr>::Err: Debug,
    {
        (0..n)
            .map(|_| (self.next(), self.next(), self.next()))
            .collect()
    }

    fn mat<T: FromStr>(&mut self, m: usize, n: usize) -> Vec<Vec<T>>
    where
        <T as FromStr>::Err: Debug,
    {
        (0..n).map(|_| self.vec(m)).collect()
    }
}


#[allow(dead_code)]
fn print_foreach<T: Display>(answer: &[T]) {
    for x in answer {
        println!("{}", x);
    }
}


#[allow(dead_code)]
fn print_yn(answer: bool, yes: &str, no: &str) {
    println!("{}", if answer { yes } else { no });
}


#[allow(dead_code)]
fn print_or<T: Display>(answer: &Option<T>, or: &T) {
    match *answer {
        Some(ref x) => println!("{}", x),
        None => println!("{}", or),
    }
}