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"
	"math"
)

const (
	MAX_INF = math.MaxInt64 / 2
)

func main() {
	var N int
	fmt.Scan(&N)
	count := make([]int, N+1)
	count[0] = 0
	count[1] = 1
	for i := 2; i <= N; i++ {
		min := MAX_INF
		c := count[i-1] + 1
		if c < min {
			min = c
		}
		pay := 6
		for i-pay >= 0 {
			c = count[i-pay] + 1
			if c < min {
				min = c
			}
			pay *= 6
		}
		pay = 9
		for i-pay >= 0 {
			c = count[i-pay] + 1
			if c < min {
				min = c
			}
			pay *= 9
		}
		count[i] = min
	}
	fmt.Println(count[N])
}