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>
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;
  if(memo[n] != -1) return memo[n];
  
  int res = n;
  
  for(int i=1; i<=n; i*=6) res = min(res, rec(n-i)+1);
  for(int j=1; j<=n; j*=9) res = min(res, rec(n-j)+1);
  
  return memo[n] = res;
}
 
int main(){
  int N; cin >> N;
  for(int i=0; i<MAX_N; i++) memo[i] = -1;
  cout << rec(N) << endl;
}