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;
const MAX_N: usize = 100000;

fn main() {
    get_line();
    let ns: Vec<u64> = read_ints();
    println!("{}", together(&ns));
}
fn together(nums: &[u64]) -> usize {
    let mut counter: Vec<usize> = vec![0;MAX_N+2];
    for &n in nums {
        counter[n as usize] += 1;
        counter[n as usize + 1] += 1;
        counter[n as usize + 2] += 1;
    }
    *counter.iter().max().expect("no such thing!")
}

fn read_ints() -> Vec<u64> {
    get_line()
        .trim()
        .split_whitespace()
        .map(|n| n.parse().unwrap())
        .collect()
}

fn get_line() -> String {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).ok();
    buf
}