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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
    var N = readLine()!!.toInt()

    var dp = Array(110000) {N}
    dp[0] = 0

    for (i in 1..N) {
        var pow6 = 1
        while (pow6 <= i && pow6 <= N) {
            dp[i] = Math.min(dp[i], 1 + dp[i - pow6])
            pow6 *= 6
        }

        var pow9 = 1
        while (pow9 <= i && pow9 <= N) {
            dp[i] = Math.min(dp[i], 1 + dp[i - pow9])
            pow9 *= 9
        }
    }

    println(dp[N])
}