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;
const int MOD = 1e9 + 7;
template <class T>
struct cplx {
  T x, y;
  cplx() {
    x = 0.0;
    y = 0.0;
  }
  cplx(T nx, T ny = 0) {
    x = nx;
    y = ny;
  }
  cplx operator+(const cplx &c) const { return {x + c.x, y + c.y}; }
  cplx operator-(const cplx &c) const { return {x - c.x, y - c.y}; }
  cplx operator*(const cplx &c) const {
    return {x * c.x - y * c.y, x * c.y + y * c.x};
  }
  cplx &operator*=(const cplx &c) {
    return *this = {x * c.x - y * c.y, x * c.y + y * c.x};
  }
  inline T real() const { return x; }
  inline T imag() const { return y; }
  template <class U>
  cplx operator*(const U &c) const {
    return {x * c, y * c};
  }
  template <class U>
  cplx operator/(const U &c) const {
    return {x / c, y / c};
  }
  template <class U>
  void operator/=(const U &c) {
    x /= c;
    y /= c;
  }
};
const int DIG = 9, FDIG = 3;
const int BASE = 1e9, FBASE = 1e3;
struct BigInt {
  int sgn;
  vector<int> a;
  BigInt() : sgn(1) {}
  BigInt(long long v) { *this = v; }
  BigInt &operator=(long long v) {
    sgn = 1;
    if (v < 0) sgn = -1, v = -v;
    a.clear();
    for (; v > 0; v /= BASE) a.push_back(v % BASE);
    return *this;
  }
  BigInt(const BigInt &other) {
    sgn = other.sgn;
    a = other.a;
  }
  friend void swap(BigInt &a, BigInt &b) {
    swap(a.sgn, b.sgn);
    swap(a.a, b.a);
  }
  BigInt &operator=(BigInt other) {
    swap(*this, other);
    return *this;
  }
  BigInt(BigInt &&other) : BigInt() { swap(*this, other); }
  BigInt(const string &s) { read(s); }
  void read(const string &s) {
    sgn = 1;
    a.clear();
    int k = 0;
    for (; k < s.size() && (s[k] == '-' || s[k] == '+'); k++)
      if (s[k] == '-') sgn = -sgn;
    for (int i = s.size() - 1; i >= k; i -= DIG) {
      int x = 0;
      for (int j = max(k, i - DIG + 1); j <= i; j++) x = x * 10 + s[j] - '0';
      a.push_back(x);
    }
    trim();
  }
  friend istream &operator>>(istream &in, BigInt &v) {
    string s;
    in >> s;
    v.read(s);
    return in;
  }
  friend ostream &operator<<(ostream &out, const BigInt &v) {
    if (v.sgn == -1 && !v.zero()) out << '-';
    out << (v.a.empty() ? 0 : v.a.back());
    for (int i = (int)v.a.size() - 2; i >= 0; --i)
      out << setw(DIG) << setfill('0') << v.a[i];
    return out;
  }
  bool operator<(const BigInt &v) const {
    if (sgn != v.sgn) return sgn < v.sgn;
    if (a.size() != v.a.size()) return a.size() * sgn < v.a.size() * v.sgn;
    for (int i = (int)a.size() - 1; i >= 0; i--)
      if (a[i] != v.a[i]) return a[i] * sgn < v.a[i] * sgn;
    return 0;
  }
  bool operator>(const BigInt &v) const { return v < *this; }
  bool operator<=(const BigInt &v) const { return !(v < *this); }
  bool operator>=(const BigInt &v) const { return !(*this < v); }
  bool operator==(const BigInt &v) const {
    return !(*this < v) && !(v < *this);
  }
  bool operator!=(const BigInt &v) const { return *this < v || v < *this; }
  friend int __cmp(const BigInt &x, const BigInt &y) {
    if (x.a.size() != y.a.size()) return x.a.size() < y.a.size() ? -1 : 1;
    for (int i = (int)x.a.size() - 1; i >= 0; --i)
      if (x.a[i] != y.a[i]) return x.a[i] < y.a[i] ? -1 : 1;
    return 0;
  }
  BigInt operator-() const {
    BigInt res = *this;
    if (zero()) return res;
    res.sgn = -sgn;
    return res;
  }
  void __add(const BigInt &v) {
    if (a.size() < v.a.size()) a.resize(v.a.size(), 0);
    for (int i = 0, carry = 0; i < max(a.size(), v.a.size()) || carry; ++i) {
      if (i == a.size()) a.push_back(0);
      a[i] += carry + (i < (int)v.a.size() ? v.a[i] : 0);
      carry = a[i] >= BASE;
      if (carry) a[i] -= BASE;
    }
  }
  void __sub(const BigInt &v) {
    for (int i = 0, carry = 0; i < (int)v.a.size() || carry; ++i) {
      a[i] -= carry + (i < (int)v.a.size() ? v.a[i] : 0);
      carry = a[i] < 0;
      if (carry) a[i] += BASE;
    }
    this->trim();
  }
  BigInt operator+=(const BigInt &v) {
    if (sgn == v.sgn)
      __add(v);
    else if (__cmp(*this, v) >= 0)
      __sub(v);
    else {
      BigInt vv = v;
      swap(*this, vv);
      __sub(vv);
    }
    return *this;
  }
  BigInt operator-=(const BigInt &v) {
    if (sgn == v.sgn) {
      if (__cmp(*this, v) >= 0)
        __sub(v);
      else {
        BigInt vv = v;
        swap(*this, vv);
        __sub(vv);
        sgn = -sgn;
      }
    } else
      __add(v);
    return *this;
  }
  template <typename L, typename R>
  typename enable_if<is_convertible<L, BigInt>::value &&
                         is_convertible<R, BigInt>::value &&
                         is_lvalue_reference<R &&>::value,
                     BigInt>::type friend
  operator+(L &&l, R &&r) {
    BigInt result(forward<L>(l));
    result += r;
    return result;
  }
  template <typename L, typename R>
  typename enable_if<is_convertible<L, BigInt>::value &&
                         is_convertible<R, BigInt>::value &&
                         is_rvalue_reference<R &&>::value,
                     BigInt>::type friend
  operator+(L &&l, R &&r) {
    BigInt result(move(r));
    result += l;
    return result;
  }
  template <typename L, typename R>
  typename enable_if<is_convertible<L, BigInt>::value &&
                         is_convertible<R, BigInt>::value,
                     BigInt>::type friend
  operator-(L &&l, R &&r) {
    BigInt result(forward<L>(l));
    result -= r;
    return result;
  }
  friend pair<BigInt, BigInt> divmod(const BigInt &a1, const BigInt &b1) {
    long long norm = BASE / (b1.a.back() + 1);
    BigInt a = a1.abs() * norm, b = b1.abs() * norm, q = 0, r = 0;
    q.a.resize(a.a.size());
    for (int i = a.a.size() - 1; i >= 0; i--) {
      r *= BASE;
      r += a.a[i];
      long long s1 = r.a.size() <= b.a.size() ? 0 : r.a[b.a.size()];
      long long s2 = r.a.size() <= b.a.size() - 1 ? 0 : r.a[b.a.size() - 1];
      long long d = ((long long)BASE * s1 + s2) / b.a.back();
      r -= b * d;
      while (r < 0) r += b, --d;
      q.a[i] = d;
    }
    q.sgn = a1.sgn * b1.sgn;
    r.sgn = a1.sgn;
    q.trim();
    r.trim();
    auto res = make_pair(q, r / norm);
    if (res.second < 0) res.second += b1;
    return res;
  }
  BigInt operator/(const BigInt &v) const { return divmod(*this, v).first; }
  BigInt operator%(const BigInt &v) const { return divmod(*this, v).second; }
  void operator/=(int v) {
    if (llabs(v) >= BASE) {
      *this /= BigInt(v);
      return;
    }
    if (v < 0) sgn = -sgn, v = -v;
    for (int i = (int)a.size() - 1, rem = 0; i >= 0; --i) {
      long long cur = a[i] + rem * (long long)BASE;
      a[i] = (int)(cur / v);
      rem = (int)(cur % v);
    }
    trim();
  }
  BigInt operator/(int v) const {
    if (llabs(v) >= BASE) return *this / BigInt(v);
    BigInt res = *this;
    res /= v;
    return res;
  }
  void operator/=(const BigInt &v) { *this = *this / v; }
  long long operator%(long long v) const {
    assert(v < BASE);
    int m = 0;
    for (int i = a.size() - 1; i >= 0; --i)
      m = (a[i] + m * (long long)BASE) % v;
    return m * sgn;
  }
  void operator*=(int v) {
    if (llabs(v) >= BASE) {
      *this *= BigInt(v);
      return;
    }
    if (v < 0) sgn = -sgn, v = -v;
    for (int i = 0, carry = 0; i < a.size() || carry; ++i) {
      if (i == a.size()) a.push_back(0);
      long long cur = a[i] * (long long)v + carry;
      carry = (int)(cur / BASE);
      a[i] = (int)(cur % BASE);
    }
    trim();
  }
  BigInt operator*(int v) const {
    if (llabs(v) >= BASE) return *this * BigInt(v);
    BigInt res = *this;
    res *= v;
    return res;
  }
  static vector<int> convert_base(const vector<int> &a, int old_digits,
                                  int new_digits) {
    vector<long long> p(max(old_digits, new_digits) + 1);
    p[0] = 1;
    for (int i = 1; i < (int)p.size(); i++) p[i] = p[i - 1] * 10;
    vector<int> res;
    long long cur = 0;
    int cur_digits = 0;
    for (int i = 0; i < (int)a.size(); i++) {
      cur += a[i] * p[cur_digits];
      cur_digits += old_digits;
      while (cur_digits >= new_digits) {
        res.push_back((long long)(cur % p[new_digits]));
        cur /= p[new_digits];
        cur_digits -= new_digits;
      }
    }
    res.push_back((int)cur);
    while (!res.empty() && !res.back()) res.pop_back();
    return res;
  }
  void fft(vector<cplx<long double> > &a, bool invert) const {
    int n = a.size();
    for (int i = 1, j = 0; i < n; ++i) {
      int bit = n / 2;
      for (; j >= bit; bit /= 2) j -= bit;
      j += bit;
      if (i < j) swap(a[i], a[j]);
    }
    for (int len = 2; len <= n; len *= 2) {
      long double ang = 2 * 3.14159265358979323846L / len * (invert ? -1 : 1);
      cplx<long double> wlen(cos(ang), sin(ang));
      for (int i = 0; i < n; i += len) {
        cplx<long double> w(1);
        for (int j = 0; j < len / 2; ++j) {
          cplx<long double> u = a[i + j], v = a[i + j + len / 2] * w;
          a[i + j] = u + v;
          a[i + j + len / 2] = u - v;
          w *= wlen;
        }
      }
    }
    if (invert)
      for (int i = 0; i < n; ++i) a[i] /= n;
  }
  void multiply_fft(const vector<int> &a, const vector<int> &b,
                    vector<int> &res) const {
    vector<cplx<long double> > fa(a.begin(), a.end()), fb(b.begin(), b.end());
    int n = 1;
    while (n < max(a.size(), b.size())) n *= 2;
    n *= 2;
    fa.resize(n);
    fb.resize(n);
    fft(fa, 0);
    fft(fb, 0);
    for (int i = 0; i < n; ++i) fa[i] *= fb[i];
    fft(fa, 1);
    res.resize(n);
    long long carry = 0;
    for (int i = 0; i < n; i++) {
      long long t = (long long)(fa[i].real() + 0.5) + carry;
      carry = t / FBASE;
      res[i] = t % FBASE;
    }
  }
  BigInt mul_simple(const BigInt &v) const {
    BigInt res;
    res.sgn = sgn * v.sgn;
    res.a.resize(a.size() + v.a.size());
    for (int i = 0; i < a.size(); i++)
      if (a[i])
        for (int j = 0, carry = 0; j < v.a.size() || carry; j++) {
          long long cur = res.a[i + j] +
                          (long long)a[i] * (j < v.a.size() ? v.a[j] : 0) +
                          carry;
          carry = (int)(cur / BASE);
          res.a[i + j] = (int)(cur % BASE);
        }
    res.trim();
    return res;
  }
  BigInt mul_fft(const BigInt &v) const {
    BigInt res;
    multiply_fft(convert_base(a, DIG, FDIG), convert_base(v.a, DIG, FDIG),
                 res.a);
    res.a = convert_base(res.a, FDIG, DIG);
    res.trim();
    return res;
  }
  void operator*=(const BigInt &v) { *this = *this * v; }
  BigInt operator*(const BigInt &v) const {
    if (a.size() * v.a.size() <= 100111) return mul_simple(v);
    return mul_fft(v);
  }
  BigInt abs() const {
    BigInt res = *this;
    res.sgn *= res.sgn;
    return res;
  }
  void trim() {
    while (!a.empty() && !a.back()) a.pop_back();
  }
  bool zero() const { return a.empty() || (a.size() == 1 && !a[0]); }
  friend BigInt gcd(const BigInt &a, const BigInt &b) {
    return b.zero() ? a : gcd(b, a % b);
  }
};
const int N = 1.7e5;
BigInt pow(int b, int e) {
  BigInt ans = 1, cur = b;
  ans.a.reserve(N);
  cur.a.reserve(N);
  int i = 0;
  while (e) {
    if (e % 2) ans *= cur;
    cur *= cur;
    e /= 2;
  }
  return ans;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  string s;
  cin >> s;
  BigInt n = BigInt(s);
  int e = s.size() / log10(3);
  BigInt k = pow(3, max(0, e - 6));
  long long ans = 3 * max(0, e - 6);
  while (k < n) {
    if (k * 2 >= n) {
      ans += 2;
      break;
    }
    if (k * 4 >= n && k * 3 < n) {
      ans += 4;
      break;
    }
    k *= 3;
    ans += 3;
  }
  cout << max(1LL, ans) << '\n';
  return 0;
}