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;

fn main() {
    input! {
        n: usize,
    }

    let mut dp = vec![std::usize::MAX; n + 1];

    dp[0] = 0;

    for n in 1..=n {
        dp[n] = dp[n-1] + 1;
        let mut num6 = 6;
        while num6 <= n {
            dp[n] = std::cmp::min(dp[n], dp[n-num6] + 1);
            num6 *= 6;
        }
        let mut num9 = 9;
        while num9 <= n {
            dp[n] = std::cmp::min(dp[n], dp[n-num9] + 1);
            num9 *= 9;
        }
    }

    let ans = dp[n];

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