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 (1.42.0) (judge verdict: Accepted)

use proconio::input;
use std::cmp;

fn main() {
    input! {
        n: usize,
    }
    let inf = 10usize.pow(10);
    let mut dp = vec![inf; n + 1];

    dp[0] = 0;
    for i in 1..=n {
        dp[i] = cmp::min(dp[i], dp[i - 1] + 1);

        let mut power_6 = 6;
        while power_6 <= i {
            dp[i] = cmp::min(dp[i], dp[i - power_6] + 1);
            power_6 *= 6;
        }

        let mut power_9 = 9;
        while power_9 <= i {
            dp[i] = cmp::min(dp[i], dp[i - power_9] + 1);
            power_9 *= 9;
        }
    }

    println!("{}", dp[n]);
}