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<iostream>
#include<algorithm>
#include<vector>
#include<functional>
#include<string>
#include<cmath>
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<cstdio>
using namespace std;
using ll = long long;
int main(){
  int n;
  cin >> n;
  vector<int> dp(1000000, 1001001001);
  dp[0] = 0;
  for(int i = 0; i < n; i++) {
    for(int j = 0; i + pow(9, j) <= n; j++){
      dp[i + pow(9, j)] = min(dp[i + pow(9, j)], dp[i] + 1);
    }
    for(int j = 0; i + pow(6, j) <= n; j++){
      dp[i + pow(6, j)] = min(dp[i + pow(6, j)], dp[i] + 1);
    }
    for(int j = 0; j <= 6; j++){
      dp[i + 1] = min(dp[i + 1], dp[i] + 1);
    }
  }
  cout << dp[n] << "\n";
  return 0;
}