Problem:
Score : 300 points

Problem Statement

To make it difficult to withdraw money, a certain bank allows its customers to withdraw only one of the following amounts in one operation:

1 yen (the currency of Japan)

6 yen, 6^2(=36) yen, 6^3(=216) yen, ...

9 yen, 9^2(=81) yen, 9^3(=729) yen, ...

At least how many operations are required to withdraw exactly N yen in total?

It is not allowed to re-deposit the money you withdrew.

Constraints

1 \leq N \leq 100000

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

If at least x operations are required to withdraw exactly N yen in total, print x.

Sample Input 1

127

Sample Output 1

4

By withdrawing 1 yen, 9 yen, 36(=6^2) yen and 81(=9^2) yen, we can withdraw 127 yen in four operations.

Sample Input 2

3

Sample Output 2

3

By withdrawing 1 yen three times, we can withdraw 3 yen in three operations.

Sample Input 3

44852

Sample Output 3

16

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::io::Read;
use std::cmp::min;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

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

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let n: usize = iterator.next().unwrap().parse().unwrap();

    const INF: usize = 100_001;
    let mut dp: Vec<usize> = vec![INF; n + 1];
    dp[0] = 0;
    for i in 0..n {
        dp[i + 1] = min(dp[i + 1], dp[i] + 1);
        let mut x: usize = 6;
        while i + x <= n {
            dp[i + x] = min(dp[i + x], dp[i] + 1);
            x *= 6;
        }
        let mut y: usize = 9;
        while i + y <= n {
            dp[i + y] = min(dp[i + y], dp[i] + 1);
            y *= 9;
        }
    }
    return dp[n].to_string();
}