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;

const INF: usize = 1_000_000;

struct Helper {
  pub n: usize,
  pub memo: Vec<usize>
}

impl Helper {
  pub fn new(n: usize) -> Helper {
    Helper {
      n: n,
      memo: vec![INF;n+1]
    }
  }
  
  pub fn traverse(&mut self, left: usize) -> usize {
    if left == 0 {
      return 0
    }

    if self.memo[left] != INF {
      return self.memo[left]
    }
    let mut res = INF;

    let mut nine = 1;
    while nine <= left {
      res = std::cmp::min(self.traverse(left - nine) + 1, res);
      nine *= 9;
    }
    
    let mut six = 1;
    while six <= left {
      res = std::cmp::min(self.traverse(left - six) + 1, res);
      six *= 6;
    }

    self.memo[left] = res;
    res
  }
}

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

  let mut helper = Helper::new(n);  
  println!("{}", helper.traverse(n));
}