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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.InteropServices;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using static Math2;
using static Output;

public class CP {
  public void Solve () {
    Input inp = new Input ();
    var n = inp.cin<int> ();
    var dp = Enumerable.Repeat (INF, n + 1).ToArray ();
    dp[0] = 0;
    for (int i = 0; i <= n; ++i) {
      for (int j = 0; Power2 (6, j) <= n; ++j) {
        if (i - Power2 (6, j) < 0) continue;
        dp[i] = Min (dp[i], dp[i - Power2 (6, j)] + 1);
      }
      for (int j = 0; Power2 (9, j) <= n; ++j) {
        if (i - Power2 (9, j) < 0) continue;
        dp[i] = Min (dp[i], dp[i - Power2 (9, j)] + 1);
      }
    }
    Put (dp[n]);
  }

}

public static class Math2 {
  public const int INF = 1 << 29;
  public const long INFL = 1L << 60;
  public const long MOD = 1000000007;
  public const long MOD2 = 998244353;

  public static long Power (long a, long b, long MOD = 1000000007) //i^N
  {
    long res = 1;
    while (b > 0) {
      if ((b & 1) != 0) res = res * a % MOD;
      a = a * a % MOD;
      b >>= 1;
    }
    return res;
  }
  public static long Power2 (long a, long b) //i^N
  {
    long res = 1;
    while (b > 0) {
      if ((b & 1) != 0) res = res * a;
      a = a * a;
      b >>= 1;
    }
    return res;
  }
  public static long GCD (long a, long b) {
    if (a == 0) return b;
    while (b > 0) {
      var r = a % b;
      a = b;
      b = r;
    }
    return a;
  }
  public static long LCM (long a, long b) => (b / GCD (a, b)) * a;
  public static long Comb (long n, long r, int MOD = 1000000007) {
    if (r > n - r) r = n - r;
    long Nume = 1;
    long Deno = 1;

    if (r > n - r) r = n - r;
    for (long i = 1; i <= r; ++i) {
      Deno = (Deno * i) % MOD;
      Nume = Nume * (n - i + 1) % MOD;
    }
    return (Nume * inv (Deno)) % MOD;
  }
  public static long Comb2 (long n, long r) {
    long Nume = 1;
    long Deno = 1;

    if (r > n - r) r = n - r;
    for (long i = 1; i <= r; ++i) {
      Deno *= i;
      Nume *= n - i + 1;
    }
    return Nume / Deno;
  }
  public static long inv (long x, int MOD = 1000000007) {
    return Power (x, MOD - 2, MOD);
  }
}
public static class Utils {
  public static void Swap<T> (ref T A, ref T B) {
    T x = A;
    A = B;
    B = x;
  }
  public static int DigitSum (string N) {

    int ret = 0;
    for (int i = 0; i < N.Length; ++i) ret += N[i] - '0';
    return ret;
  }
  public static string ConvertBase (long N, int K) {
    StringBuilder ret = new StringBuilder ();
    while (N > 0) {
      var r = N % K;
      N /= K;
      ret.Append (r);
    }
    return new string (ret.ToString ().ToCharArray ().Reverse ().ToArray ());
  }
  public static bool NextPermutation<T> (IList<T> lis, Comparison<T> cmp) {
    int n = lis.Count;
    int i = n - 1;
    while (i - 1 >= 0) {
      if (cmp (lis[i - 1], lis[i]) < 0) break;
      --i;
    }
    if (i == 0) return false;
    int j = i;
    while (j + 1 < n) {
      if (cmp (lis[i - 1], lis[j + 1]) > 0) break;
      ++j;
    }
    var _q = lis[j];
    lis[i - 1] = lis[j];
    lis[i - 1] = _q;
    int k = i;
    int l = n - 1;
    while (k < l) {
      var _p = lis[k];
      lis[l] = lis[k];
      lis[l] = _p;

      ++k;
      --l;
    }
    return true;
  }
  public static bool NextPermutation<T> (IList<T> lis) => NextPermutation (lis, Comparer<T>.Default.Compare);
}
public class PriorityQueue<T> {
  List<T> _item;
  public int Count { get { return _item.Count; } }
  bool _isascend { get; set; }
  public T Peek { get { return _item[0]; } }
  Comparison<T> Comp;
  public PriorityQueue (bool IsAscend = true, IEnumerable<T> list = null) : this (Comparer<T>.Default.Compare, IsAscend, list) { }
  public PriorityQueue (Comparison<T> cmp, bool IsAscend = true, IEnumerable<T> list = null) {
    _item = new List<T> ();
    _isascend = IsAscend;
    this.Comp = cmp;
    if (list != null) {
      _item.AddRange (list);
      Build ();
    }
  }

  private int Compare (int i, int j) => (_isascend ? -1 : 1) * Comp (_item[i], _item[j]);
  private void Swap (int i, int j) { var t = _item[i]; _item[i] = _item[j]; _item[j] = t; }
  private int Parent (int i) => (i - 1) >> 1;
  private int Left (int i) => (i << 1) + 1;
  public T Enqueue (T val) {
    int i = _item.Count;
    _item.Add (val);
    while (i > 0) {
      int p = Parent (i);
      if (Compare (i, p) > 0)
        Swap (i, p);
      i = p;
    }
    return val;
  }
  private void Heapify (int index) {
    for (int i = index, j;
      (j = Left (i)) < _item.Count; i = j) {
      if (j != _item.Count - 1 && Compare (j, j + 1) < 0) j++;
      if (Compare (i, j) < 0)
        Swap (i, j);
    }
  }
  public T Dequeue () {
    T val = _item[0];
    _item[0] = _item[_item.Count - 1];
    _item.RemoveAt (_item.Count - 1);
    Heapify (0);
    return val;
  }
  private void Build () {
    for (var i = (_item.Count >> 1) - 1; i >= 0; i--)
      Heapify (i);
  }
  public bool Any () => Count > 0;
}
class Program {
  static void Main (string[] args) {
    var CP = new CP ();
    CP.Solve ();
  }
}
public static class Output {

  public static void Put (string a) => Console.WriteLine (a);
  public static void Put (params object[] i) => Put (string.Join (" ", i));
  public static void Put<T> (IEnumerable<T> a) => Put (string.Join (" ", a));
  public static void PutV<T> (IEnumerable<T> a) { foreach (var z in a) Put (z); }
  public static void YN (bool i) {
    if (i) Put ("Yes");
    else Put ("No");
  }
}
public class Input {
  public static string Str => Console.ReadLine ();
  public static bool IsTypeEqual<T, U> () => typeof (T).Equals (typeof (U));
  public static T ConvertType<T, U> (U a) => (T) Convert.ChangeType (a, typeof (T));
  public static T Cast<T> (string s) {
    if (IsTypeEqual<T, int> ()) return ConvertType<T, int> (int.Parse (s));
    else if (IsTypeEqual<T, long> ()) return ConvertType<T, long> (long.Parse (s));
    else if (IsTypeEqual<T, double> ()) return ConvertType<T, double> (double.Parse (s));
    else if (IsTypeEqual<T, char> ()) return ConvertType<T, char> (char.Parse (s));
    else return ConvertType<T, string> (s);
  }
  public static T[] Castarr<T> (string[] s) {

    var ret = new T[s.Length];
    int i = 0;
    if (IsTypeEqual<T, char> ()) {
      var list = new List<T> ();
      foreach (var t in s) {
        foreach (var u in t) {
          list.Add (ConvertType<T, char> (char.Parse (u.ToString ())));
        }
      }
      return list.ToArray ();
    }
    foreach (var t in s) {
      if (IsTypeEqual<T, int> ()) ret[i++] = ConvertType<T, int> (int.Parse (t));
      else if (IsTypeEqual<T, long> ()) ret[i++] = ConvertType<T, long> (long.Parse (t));
      else if (IsTypeEqual<T, double> ()) ret[i++] = ConvertType<T, double> (double.Parse (t));
      else ret[i++] = ConvertType<T, string> (t);
    }
    return ret;
  }
  Queue<string> q = new Queue<string> ();
  void next () { var ss = Str.Split (' '); foreach (var item in ss) q.Enqueue (item); }
  public T cin<T> () { if (!q.Any ()) next (); return Cast<T> (q.Dequeue ()); }
  public void mul<T> (out T t) { t = cin<T> (); }
  public void mul<T, U> (out T t, out U u) { t = cin<T> (); u = cin<U> (); }
  public void mul<T, U, V> (out T t, out U u, out V v) { t = cin<T> (); u = cin<U> (); v = cin<V> (); }
  public void mul<T, U, V, W> (out T t, out U u, out V v, out W w) { t = cin<T> (); u = cin<U> (); v = cin<V> (); w = cin<W> (); }
  public void mul<T, U, V, W, X> (out T t, out U u, out V v, out W w, out X x) { t = cin<T> (); u = cin<U> (); v = cin<V> (); w = cin<W> (); x = cin<X> (); }
  public void mul<T, U, V, W, X, Y> (out T t, out U u, out V v, out W w, out X x, out Y y) { t = cin<T> (); u = cin<U> (); v = cin<V> (); w = cin<W> (); x = cin<X> (); y = cin<Y> (); }
  public void mul<T, U, V, W, X, Y, Z> (out T t, out U u, out V v, out W w, out X x, out Y y, out Z z) { t = cin<T> (); u = cin<U> (); v = cin<V> (); w = cin<W> (); x = cin<X> (); y = cin<Y> (); z = cin<Z> (); }
  public T[] cinarr<T> () { return Castarr<T> (Str.Split (' ')); }
}