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 C++ (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
using namespace std;

const int MAX_N = 110000;

int memo[MAX_N]; // memo[i] が i についての答え
int rec(int n) {
    if (n == 0) return 0; // 終端条件
    if (memo[n] != -1) return memo[n]; // すでに探索済みならリターン

    int res = n; // INF の気持ち

    // 1, 6, 6^2, ..., を試す (n を超えない範囲で)
    for (int pow6 = 1; pow6 <= n; pow6 *= 6) res = min(res, rec(n - pow6) + 1);

    // 1, 9, 9^2, ..., を試す (n を超えない範囲で)
    for (int pow9 = 1; pow9 <= n; pow9 *= 9) res = min(res, rec(n - pow9) + 1);

    // メモしながらリターン
    return memo[n] = res;
}

int main() {
    int N; cin >> N;

    // テーブルを -1 で初期化
    for (int i = 0; i < MAX_N; ++i) memo[i] = -1;
    cout << rec(N) << endl;
}