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 rep(i,n) for(int i=0;i<(int)(n);i++)
using namespace std;

int main(void){
  int n; cin >> n;
  int INF = 1001001;
  vector<int> dp(n+1,INF);
  dp[0]=0;
  dp[1]=1;
  
  for(int i=0;i<=n;i++){
    int power = 1;
    rep(j,10){
      if(i-power>=0) dp[i] = min(dp[i],dp[i-power]+1);
      power *= 6;
    }
  }
  for(int i=0;i<=n;i++){
    int power = 1;
    rep(j,10){
      if(i-power>=0) dp[i] = min(dp[i],dp[i-power]+1);
      power *= 9;
    }
  }

  cout << dp[n] << endl;
  
  return 0;
}