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: Time Limit Exceeded)

package main

import (
	"fmt"
)

const MaxN = 110000

var memo [MaxN]int

func main() {
	var N int
	fmt.Scan(&N)
	for i := 0; i < MaxN; i++ {
		memo[i] = -1
	}
	fmt.Println(rec(N))
}
func rec(n int) int {
	if n == 0 {
		return 0
	}
	if memo[n] != -1 {
		return memo[n]
	}
	res := n
	for x := 1; x <= n; x++ {
		res = Min(res, rec(n-1)+1)
	}

	for x := 1; x <= n; x *= 6 {
		res = Min(res, rec(n-x)+1)
	}
	for x := 1; x <= n; x *= 9 {
		res = Min(res, rec(n-x)+1)
	}
	memo[n] = res
	return res
}
func Min(a, b int) int {
	if b < a {
		return b
	}
	return a
}