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 Go (1.6) (judge verdict: Accepted)

package main

import (
	. "fmt"
)

func Min(a, b int) int {
	if a < b {
		return a
	} else {
		return b
	}
}

func main() {
	var n int
	Scan(&n)
	dp := make([]int, n + 1)
	for i := 0; i < n; i++ {
		dp[i + 1] = 1000000000
	}

	for i := 0; i < n; i++ {
		for j := 1; i + j <= n; j *= 6 {
			dp[i + j] = Min(dp[i + j], dp[i] + 1)
		}

		for j := 1; i + j <= n; j *= 9 {
			dp[i + j] = Min(dp[i + j], dp[i] + 1)
		}
	}

	Println(dp[n])
}