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;

fn getline() -> String {
    let mut __ret = String::new();
    std::io::stdin().read_line(&mut __ret).ok();
    return __ret;
}

fn main() {
    let n: usize = getline().trim().parse().unwrap();
    let s = getline();
    let vec: Vec<_> = s.trim().split(' ').collect();

    let mut num_cnt = HashMap::new();
    for i in 0..n {
        let a: i32 = vec[i].parse().unwrap();
        if num_cnt.contains_key(&a) {
            let old = *num_cnt.get(&a).unwrap();
            num_cnt.insert(a, old + 1);
        } else {
            num_cnt.insert(a, 1);
        }
    }

    let mut ans = 0;

    for x in 0..100001 {
        let mut cand = 0;
        if num_cnt.contains_key(&(x - 1)) {
            cand += *num_cnt.get(&(x - 1)).unwrap();
        }

        if num_cnt.contains_key(&x) {
            cand += *num_cnt.get(&x).unwrap();
        }

        if num_cnt.contains_key(&(x + 1)) {
            cand += *num_cnt.get(&(x + 1)).unwrap();
        }

        if cand > ans {
            ans = cand;
        }
    }
    println!("{}", ans);
}