Problem: You are working as an analyst in a company working on a new system for big data storage. This system will store n different objects. Each object should have a unique ID.

To create the system, you choose the parameters of the system — integers m ≥ 1 and b_{1}, b_{2}, …, b_{m}. With these parameters an ID of some object in the system is an array of integers [a_{1}, a_{2}, …, a_{m}] where 1 ≤ a_{i} ≤ b_{i} holds for every 1 ≤ i ≤ m.

Developers say that production costs are proportional to ∑_{i=1}^{m} b_{i}. You are asked to choose parameters m and b_{i} so that the system will be able to assign unique IDs to n different objects and production costs are minimized. Note that you don't have to use all available IDs.

Input

In the only line of input there is one positive integer n. The length of the decimal representation of n is no greater than 1.5 ⋅ 10^{6}. The integer does not contain leading zeros.

Output

Print one number — minimal value of ∑_{i=1}^{m} b_{i}.

Examples

Input

36


Output

10


Input

37


Output

11


Input

12345678901234567890123456789


Output

177

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
constexpr int power(int x, int e) { return e ? x * power(x, e - 1) : 1; }
template <typename T>
void transpose(std::vector<std::vector<T>>& M) {
  auto tmp = M;
  M.resize(tmp[0].size());
  for (auto& row : M) row.resize(tmp.size());
  for (int i = 0; i < (int)M.size(); i++) {
    for (int j = 0; j < (int)M[0].size(); j++) {
      M[i][j] = tmp[j][i];
    }
  }
}
class FFT {
 public:
  FFT(int max_degree) {
    int lg = get_lg(max_degree + 1);
    reverse.resize(lg + 1);
    int size = 1 << lg;
    ws.resize(lg);
    ws[lg - 1].resize(size >> 1);
    for (int i = 0; i < (size >> 1); i++) {
      double ang = 2 * PI * i / size;
      ws[lg - 1][i] = {cos(ang), sin(ang)};
    }
    for (int j = lg - 2; j >= 0; j--) {
      int sz_level = ws[j + 1].size() >> 1;
      ws[j].resize(sz_level);
      for (int i = 0; i < sz_level; i++) ws[j][i] = ws[j + 1][i << 1];
    }
  }
  int get_lg(int x) { return x ? 32 - __builtin_clz(x - 1) : 0; }
  void precompute_reverse(int lg) {
    int size = 1 << lg;
    reverse[lg].assign(size, 0);
    for (int i = 1, j = 0; i < size; i++) {
      int bit = size >> 1;
      for (; j & bit; bit >>= 1) j ^= bit;
      j ^= bit;
      reverse[lg][i] = j;
    }
  }
  using cd = std::complex<double>;
  using vcd = std::vector<cd>;
  using vvcd = std::vector<vcd>;
  void fft(vcd& a, bool inv) {
    int lg = get_lg(a.size());
    if (reverse[lg].empty()) precompute_reverse(lg);
    int size = 1 << lg;
    auto& rev = reverse[lg];
    for (int i = 0; i < size; i++) {
      if (i < rev[i]) swap(a[i], a[rev[i]]);
    }
    for (int k = 0; k < lg; k++) {
      int len = 1 << k;
      auto& w = ws[k];
      for (int i = 0; i < size; i += 2 * len) {
        for (int j = 0; j < len; j++) {
          cd u = a[i + j], v = a[i + j + len] * w[j];
          a[i + j] = u + v;
          a[i + j + len] = u - v;
        }
      }
    }
    if (inv) {
      for (cd& x : a) x /= size;
      std::reverse(a.begin() + 1, a.end());
    }
  }
  void multiply(vcd& fa, vcd& fb) {
    int result_size = fa.size() + fb.size() - 1;
    int size = 1 << get_lg(result_size);
    fa.resize(size);
    fb.resize(size);
    fft(fa, false);
    fft(fb, false);
    for (int i = 0; i < size; i++) fa[i] *= fb[i];
    fft(fa, true);
    fa.resize(result_size);
  }
  template <typename T>
  std::vector<long long> multiply_brute_force(std::vector<T> const& a,
                                              std::vector<T> const& b) {
    vector<long long> result(a.size() + b.size() + 1, 0);
    for (auto i = 0u; i < a.size(); i++) {
      for (auto j = 0u; j < b.size(); j++) {
        result[i + j] += a[i] * b[j];
      }
    }
    return result;
  }
  template <typename T>
  std::vector<long long> multiply(std::vector<T> const& a,
                                  std::vector<T> const& b) {
    vector<long long> result;
    int result_size = a.size() + b.size() + 1;
    if (result_size <= 200) {
      result = multiply_brute_force(a, b);
    } else {
      vcd fa(a.begin(), a.end()), fb(b.begin(), b.end());
      multiply(fa, fb);
      result.resize(result_size);
      for (int i = 0; i < result_size; i++)
        result[i] = std::llround(fa[i].real());
    }
    return result;
  }

 private:
  std::vector<std::vector<int>> reverse;
  std::vector<vcd> ws;
  const double PI = std::acos(-1);
};
class BigInteger {
 public:
  BigInteger(long long x = 0) {
    if (x > 0)
      sign = 1;
    else if (x == 0)
      sign = 0;
    else
      sign = -1;
    x *= sign;
    while (x) {
      data.push_back(x % BASE);
      x /= BASE;
    }
  }
  BigInteger& operator+=(BigInteger const& o) {
    data.resize(max(data.size(), o.data.size()) + 1, 0);
    int carry = 0;
    for (auto i = 0u; i < o.data.size() || carry; i++) {
      if (i < o.data.size()) carry += o.data[i];
      if (i < data.size()) carry += data[i];
      data[i] = carry % BASE;
      carry /= BASE;
    }
    pop_zeros();
    return *this;
  }
  BigInteger& operator*=(int o) {
    if (o == 0) {
      sign = 0;
      data.clear();
    } else {
      if (o < 0) {
        sign *= -1;
        o = std::abs(o);
      }
      int n = data.size();
      data.resize(n + 9, 0);
      long long carry = 0;
      for (int i = 0; i < n || carry; i++) {
        carry += (long long)data[i] * o;
        data[i] = carry % BASE;
        carry /= BASE;
      }
      pop_zeros();
    }
    return *this;
  }
  BigInteger& operator*=(BigInteger const& o) {
    sign *= o.sign;
    if (sign == 0) {
      data.clear();
    } else {
      FFT fft(data.size() + o.data.size() + 1);
      auto result = fft.multiply(data, o.data);
      data.resize(result.size());
      long long carry = 0;
      for (auto i = 0u; i < result.size(); i++) {
        carry += result[i];
        data[i] = carry % BASE;
        carry /= BASE;
      }
      pop_zeros();
    }
    return *this;
  }
  void pop_zeros() {
    while (!data.empty() && data.back() == 0) data.pop_back();
  }
  friend std::ostream& operator<<(std::ostream& stream, BigInteger const& b) {
    if (b.data.empty()) {
      stream << 0;
    } else {
      if (b.sign == -1) stream << '-';
      stream << b.data.back();
      for (int i = b.data.size() - 2; i >= 0; i--) {
        stream.width(DIGITS);
        stream.fill('0');
        stream << b.data[i];
      }
    }
    return stream;
  }
  friend std::istream& operator>>(std::istream& is, BigInteger& b) {
    std::string s;
    is >> s;
    int start = 0;
    if (s == "0") {
      b.sign = 0;
      b.data.clear();
    } else {
      if (s[0] == '-') {
        b.sign = -1;
        start++;
      } else {
        b.sign = 1;
      }
      b.data.resize((s.size() - start + DIGITS - 1) / DIGITS);
      for (int i = 0, idx = s.size() - 1; i < (int)b.data.size();
           i++, idx -= DIGITS) {
        int value = 0;
        for (int j = max(start, idx - DIGITS + 1); j <= idx; j++)
          value = value * 10 + s[j] - '0';
        b.data[i] = value;
      }
    }
    return is;
  }
  unsigned int digits() const {
    if (data.empty()) return 0;
    unsigned int d = (data.size() - 1) * DIGITS;
    int x = data.back();
    while (x > 0) {
      d++;
      x /= 10;
    }
    return d;
  }
  int compare(BigInteger const& o) const {
    if (sign < o.sign) return -1;
    if (sign > o.sign) return 1;
    if (data.size() != o.data.size())
      return (data.size() < o.data.size()) == (sign == 1) ? -1 : 1;
    for (int i = data.size() - 1; i >= 0; i--) {
      if (data[i] != o.data[i])
        return (data[i] < o.data[i]) == (sign == 1) ? -1 : 1;
    }
    return 0;
  }
  bool operator==(BigInteger const& o) const { return compare(o) == 0; }
  bool operator!=(BigInteger const& o) const { return compare(o) != 0; }
  bool operator<(BigInteger const& o) const { return compare(o) == -1; }
  bool operator<=(BigInteger const& o) const { return compare(o) <= 0; }
  bool operator>(BigInteger const& o) const { return compare(o) == 1; }
  bool operator>=(BigInteger const& o) const { return compare(o) >= 0; }
  static const int DIGITS = 4;
  static const int BASE = power(10, DIGITS);
  int sign;
  vector<int> data;
};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  BigInteger a;
  cin >> a;
  if (a < 5) {
    cout << a << '\n';
    return 0;
  }
  int p = max(0, (int)(a.digits() * log(10) / log(3) - 3));
  int sum = p * 3;
  BigInteger x = 1;
  BigInteger base = 3;
  while (p) {
    if (p & 1) x *= base;
    base *= base;
    p >>= 1;
  }
  int best = std::numeric_limits<int>::max();
  for (int twos = 0; twos < 3; twos++) {
    int sum_cur = sum;
    BigInteger y = x;
    for (int i = 0; i < twos; i++) {
      sum_cur += 2;
      y *= 2;
    }
    while (y < a) {
      sum_cur += 3;
      y *= 3;
    }
    best = min(best, sum_cur);
  }
  cout << best << '\n';
}