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::prelude::*;

fn input<T>() -> T
where
    T: std::str::FromStr,
{
    let stdin = std::io::stdin();
    let token: String = stdin
        .lock()
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}

fn main() {
    let n: usize = input();
    let mut a: Vec<i64> = (0..n).map(|_| input()).collect();
    a.sort();
    let mut b = a.clone();
    b.dedup();

    let mut ans = 0;
    for x in b {
        let y = x - 1;
        ans = std::cmp::max(ans, bsearch(&a, y + 2) - bsearch(&a, y - 1));
        let y = x;
        ans = std::cmp::max(ans, bsearch(&a, y + 2) - bsearch(&a, y - 1));
        let y = x + 1;
        ans = std::cmp::max(ans, bsearch(&a, y + 2) - bsearch(&a, y - 1));
    }
    println!("{}", ans);
}

fn bsearch(v: &Vec<i64>, k: i64) -> usize {
    let mut l = -1;
    let mut r = v.len() as i64;
    while r - l > 1 {
        let m = (l + r) / 2;
        if v[m as usize] >= k {
            r = m;
        } else {
            l = m;
        }
    }
    r as usize
}