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::*;
use std::str::*;

// const MOD: i32 = 1000000007;

fn read<T: FromStr>() -> Option<T> {
    let stdin = stdin();
    let s = stdin
        .bytes()
        .map(|c| c.unwrap() as char)
        .take_while(|c| !c.is_whitespace())
        .collect::<String>();
    s.parse::<T>().ok()
}

fn main() {
    let n: usize = read().unwrap();

    // 0 initialize
    let mut a: [u32; 100001] = [0; 100001];

    for _ in 0..n {
        let tmp: usize = read().unwrap();
        a[tmp] += 1;
    }


    let mut ans = 0;
    for i in 1..100000 {
        let cnt = a[i - 1] + a[i] + a[i + 1];
        ans = std::cmp::max(cnt, ans);
    }
    ans = std::cmp::max(ans, a[0] + a[1]);
    ans = std::cmp::max(ans, a[100000] + a[99999]);
    println!("{}", ans);

}