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 main() {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    let a: Vec<usize> = s.trim().split_whitespace().map(|x| x.parse().unwrap()).collect();

    let mut h: HashMap<usize, usize> = HashMap::new();
    let mut p = std::usize::MAX;
    let mut q = 0;
    for i in &a {
        let x = match h.get(i) {Some(x) => *x, None => 0};
        h.insert(*i, x+1);
        if *i < p {p = *i;}
        if *i > q {q = *i;}
    }

    let mut x = 0;
    if p < std::usize::MAX {p += 1;}
    if q > 0 {q -= 1;}
    for i in std::cmp::min(p, q)..std::cmp::max(p, q)+1 {
        let mut y = 0;
        y += match h.get(&i) {Some(x) => *x, None => 0};
        y += match h.get(&(i-1)) {Some(x) => *x, None => 0};
        y += match h.get(&(i+1)) {Some(x) => *x, None => 0};
        if y > x {x = y;}
    }

    println!("{}", x);
}