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::cmp;

fn main() {
    let mut sc = Scanner::new();
    let n = sc.usize_read();

    let mut dp = vec![std::usize::MAX; n + 1];
    dp[0] = 0;
    for i in 0..n {
        dp[i + 1] = cmp::min(dp[i] + 1, dp[i + 1]);

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

        let mut nine = 1;
        while i + nine * 9 <= n {
            dp[i + nine * 9] = cmp::min(dp[i + nine * 9], dp[i] + 1);
            nine *= 9;
        }
    }
    println!("{}", dp[n]);
}

struct Scanner {
    ptr: usize,
    length: usize,
    buf: Vec<u8>,
    small_cache: Vec<u8>,
}

#[allow(dead_code)]
impl Scanner {
    fn new() -> Scanner {
        Scanner {
            ptr: 0,
            length: 0,
            buf: vec![0; 1024],
            small_cache: vec![0; 1024],
        }
    }

    fn load(&mut self) {
        use std::io::Read;
        let mut s = std::io::stdin();
        self.length = s.read(&mut self.buf).unwrap();
    }

    fn byte(&mut self) -> u8 {
        if self.ptr >= self.length {
            self.ptr = 0;
            self.load();
            if self.length == 0 {
                self.buf[0] = b'\n';
                self.length = 1;
            }
        }

        self.ptr += 1;
        return self.buf[self.ptr - 1];
    }

    fn is_space(b: u8) -> bool {
        b == b'\n' || b == b'\r' || b == b'\t' || b == b' '
    }

    fn read_vec<T>(&mut self, n: usize) -> Vec<T>
    where
        T: std::str::FromStr,
        T::Err: std::fmt::Debug,
    {
        (0..n).map(|_| self.read()).collect()
    }

    fn usize_read(&mut self) -> usize {
        self.read()
    }

    fn read<T>(&mut self) -> T
    where
        T: std::str::FromStr,
        T::Err: std::fmt::Debug,
    {
        let mut b = self.byte();
        while Scanner::is_space(b) {
            b = self.byte();
        }

        for pos in 0..self.small_cache.len() {
            self.small_cache[pos] = b;
            b = self.byte();
            if Scanner::is_space(b) {
                return String::from_utf8_lossy(&self.small_cache[0..(pos + 1)])
                    .parse()
                    .unwrap();
            }
        }

        let mut v = self.small_cache.clone();
        while !Scanner::is_space(b) {
            v.push(b);
            b = self.byte();
        }
        return String::from_utf8_lossy(&v).parse().unwrap();
    }
}