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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define all(x) begin(x), end(x)
#define dbg(x) cerr << #x << " = " << x << endl
#define _ << ' ' <<
using namespace std;
using ll = long long;
using vi = vector<int>;

int n;
int dp[100005];

int f(int x)
{
    if (x == 0)
        return 0;

    int& sol = dp[x];
    if (sol != -1)
        return sol;

    sol = 1 + f(x - 1);
    int a = 6;
    while (a <= x)
    {
        sol = min(sol, 1 + f(x - a));
        a *= 6;
    }
    int b = 9;
    while (b <= x)
    {
        sol = min(sol, 1 + f(x - b));
        b *= 9;
    }
    return sol;
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin >> n;
    memset(dp, -1, sizeof dp);
    cout << f(n);
}