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 BASE_DIGITS = 9;
const int BASE = 1000000000;
struct BigInt {
  int sign;
  vector<int> a;
  BigInt() : sign(1) {}
  BigInt(long long v) { *this = v; }
  BigInt &operator=(long long v) {
    sign = 1;
    if (v < 0) {
      sign = -1;
      v = -v;
    }
    a.clear();
    for (; v > 0; v = v / BASE) a.push_back(v % BASE);
    return *this;
  }
  BigInt(const BigInt &other) {
    sign = other.sign;
    a = other.a;
  }
  friend void swap(BigInt &a, BigInt &b) {
    using std::swap;
    swap(a.sign, b.sign);
    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) {
    sign = 1;
    a.clear();
    int pos = 0;
    while (pos < (int)s.size() && (s[pos] == '-' || s[pos] == '+')) {
      if (s[pos] == '-') sign = -sign;
      ++pos;
    }
    for (int i = s.size() - 1; i >= pos; i -= BASE_DIGITS) {
      int x = 0;
      for (int j = max(pos, i - BASE_DIGITS + 1); j <= i; j++)
        x = x * 10 + s[j] - '0';
      a.push_back(x);
    }
    trim();
  }
  friend istream &operator>>(istream &stream, BigInt &v) {
    string s;
    stream >> s;
    v.read(s);
    return stream;
  }
  friend ostream &operator<<(ostream &stream, const BigInt &v) {
    if (v.sign == -1 && !v.isZero()) stream << '-';
    stream << (v.a.empty() ? 0 : v.a.back());
    for (int i = (int)v.a.size() - 2; i >= 0; --i)
      stream << setw(BASE_DIGITS) << setfill('0') << v.a[i];
    return stream;
  }
  bool operator<(const BigInt &v) const {
    if (sign != v.sign) return sign < v.sign;
    if (a.size() != v.a.size()) return a.size() * sign < v.a.size() * v.sign;
    for (int i = ((int)a.size()) - 1; i >= 0; i--)
      if (a[i] != v.a[i]) return a[i] * sign < v.a[i] * sign;
    return false;
  }
  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 __compare_abs(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 (isZero()) return res;
    res.sign = -sign;
    return res;
  }
  void __internal_add(const BigInt &v) {
    if (a.size() < v.a.size()) {
      a.resize(v.a.size(), 0);
    }
    for (int i = 0, carry = 0; i < (int)max(a.size(), v.a.size()) || carry;
         ++i) {
      if (i == (int)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 __internal_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 (sign == v.sign) {
      __internal_add(v);
    } else {
      if (__compare_abs(*this, v) >= 0) {
        __internal_sub(v);
      } else {
        BigInt vv = v;
        swap(*this, vv);
        __internal_sub(vv);
      }
    }
    return *this;
  }
  BigInt operator-=(const BigInt &v) {
    if (sign == v.sign) {
      if (__compare_abs(*this, v) >= 0) {
        __internal_sub(v);
      } else {
        BigInt vv = v;
        swap(*this, vv);
        __internal_sub(vv);
        this->sign = -this->sign;
      }
    } else {
      __internal_add(v);
    }
    return *this;
  }
  template <typename L, typename R>
  typename std::enable_if<std::is_convertible<L, BigInt>::value &&
                              std::is_convertible<R, BigInt>::value &&
                              std::is_lvalue_reference<R &&>::value,
                          BigInt>::type friend
  operator+(L &&l, R &&r) {
    BigInt result(std::forward<L>(l));
    result += r;
    return result;
  }
  template <typename L, typename R>
  typename std::enable_if<std::is_convertible<L, BigInt>::value &&
                              std::is_convertible<R, BigInt>::value &&
                              std::is_rvalue_reference<R &&>::value,
                          BigInt>::type friend
  operator+(L &&l, R &&r) {
    BigInt result(std::move(r));
    result += l;
    return result;
  }
  template <typename L, typename R>
  typename std::enable_if<std::is_convertible<L, BigInt>::value &&
                              std::is_convertible<R, BigInt>::value,
                          BigInt>::type friend
  operator-(L &&l, R &&r) {
    BigInt result(std::forward<L>(l));
    result -= r;
    return result;
  }
  friend pair<BigInt, BigInt> divmod(const BigInt &a1, const BigInt &b1) {
    assert(b1 > 0);
    long long norm = BASE / (b1.a.back() + 1);
    BigInt a = a1.abs() * norm;
    BigInt b = b1.abs() * norm;
    BigInt 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.sign = a1.sign * b1.sign;
    r.sign = a1.sign;
    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) {
    assert(v > 0);
    if (llabs(v) >= BASE) {
      *this /= BigInt(v);
      return;
    }
    if (v < 0) sign = -sign, 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 {
    assert(v > 0);
    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 > 0);
    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 * sign;
  }
  void operator*=(int v) {
    if (llabs(v) >= BASE) {
      *this *= BigInt(v);
      return;
    }
    if (v < 0) sign = -sign, v = -v;
    for (int i = 0, carry = 0; i < (int)a.size() || carry; ++i) {
      if (i == (int)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<complex<double> > &a, bool inv) const {
    int n = a.size(), j = 0;
    vector<complex<double> > roots(n / 2);
    for (int i = 1; i < n; i++) {
      int bit = (n >> 1);
      while (j >= bit) {
        j -= bit;
        bit >>= 1;
      }
      j += bit;
      if (i < j) swap(a[i], a[j]);
    }
    double ang = 2 * acos(-1) / n * (inv ? -1 : 1);
    for (int i = 0; i < n / 2; i++) {
      roots[i] = complex<double>(cos(ang * i), sin(ang * i));
    }
    for (int i = 2; i <= n; i <<= 1) {
      int step = n / i;
      for (int j = 0; j < n; j += i) {
        for (int k = 0; k < i / 2; k++) {
          complex<double> u = a[j + k], v = a[j + k + i / 2] * roots[step * k];
          a[j + k] = u + v;
          a[j + k + i / 2] = u - v;
        }
      }
    }
    if (inv)
      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<complex<double> > fa(a.begin(), a.end());
    vector<complex<double> > fb(b.begin(), b.end());
    int n = 1;
    while (n < (int)max(a.size(), b.size())) n <<= 1;
    n <<= 1;
    fa.resize(n);
    fb.resize(n);
    fft(fa, false);
    fft(fb, false);
    for (int i = 0; i < n; ++i) fa[i] *= fb[i];
    fft(fa, true);
    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 / 1000;
      res[i] = t % 1000;
    }
  }
  BigInt mul_simple(const BigInt &v) const {
    BigInt res;
    res.sign = sign * v.sign;
    res.a.resize(a.size() + v.a.size());
    for (int i = 0; i < (int)a.size(); ++i)
      if (a[i])
        for (int j = 0, carry = 0; j < (int)v.a.size() || carry; ++j) {
          long long cur = res.a[i + j] +
                          (long long)a[i] * (j < (int)v.a.size() ? v.a[j] : 0) +
                          carry;
          carry = (int)(cur / BASE);
          res.a[i + j] = (int)(cur % BASE);
        }
    res.trim();
    return res;
  }
  static vector<long long> karatsubaMultiply(const vector<long long> &a,
                                             const vector<long long> &b) {
    int n = a.size();
    vector<long long> res(n + n);
    if (n <= 32) {
      for (int i = 0; i < n; i++)
        for (int j = 0; j < n; j++) res[i + j] += a[i] * b[j];
      return res;
    }
    int k = n >> 1;
    vector<long long> a1(a.begin(), a.begin() + k);
    vector<long long> a2(a.begin() + k, a.end());
    vector<long long> b1(b.begin(), b.begin() + k);
    vector<long long> b2(b.begin() + k, b.end());
    vector<long long> a1b1 = karatsubaMultiply(a1, b1);
    vector<long long> a2b2 = karatsubaMultiply(a2, b2);
    for (int i = 0; i < k; i++) a2[i] += a1[i];
    for (int i = 0; i < k; i++) b2[i] += b1[i];
    vector<long long> r = karatsubaMultiply(a2, b2);
    for (int i = 0; i < (int)a1b1.size(); i++) r[i] -= a1b1[i];
    for (int i = 0; i < (int)a2b2.size(); i++) r[i] -= a2b2[i];
    for (int i = 0; i < (int)r.size(); i++) res[i + k] += r[i];
    for (int i = 0; i < (int)a1b1.size(); i++) res[i] += a1b1[i];
    for (int i = 0; i < (int)a2b2.size(); i++) res[i + n] += a2b2[i];
    return res;
  }
  BigInt mul_karatsuba(const BigInt &v) const {
    vector<int> a6 = convert_base(this->a, BASE_DIGITS, 6);
    vector<int> b6 = convert_base(v.a, BASE_DIGITS, 6);
    vector<long long> a(a6.begin(), a6.end());
    vector<long long> b(b6.begin(), b6.end());
    while (a.size() < b.size()) a.push_back(0);
    while (b.size() < a.size()) b.push_back(0);
    while (a.size() & (a.size() - 1)) a.push_back(0), b.push_back(0);
    vector<long long> c = karatsubaMultiply(a, b);
    BigInt res;
    res.sign = sign * v.sign;
    long long carry = 0;
    for (int i = 0; i < (int)c.size(); i++) {
      long long cur = c[i] + carry;
      res.a.push_back((int)(cur % 1000000));
      carry = cur / 1000000;
    }
    res.a = convert_base(res.a, 6, BASE_DIGITS);
    res.trim();
    return res;
  }
  void operator*=(const BigInt &v) { *this = *this * v; }
  BigInt operator*(const BigInt &v) const {
    if (a.size() <= 1 || v.a.size() <= 1) return mul_simple(v);
    return mul_fft(v);
  }
  BigInt mul_fft(const BigInt &v) const {
    BigInt res;
    res.sign = sign * v.sign;
    multiply_fft(convert_base(a, BASE_DIGITS, 3),
                 convert_base(v.a, BASE_DIGITS, 3), res.a);
    res.a = convert_base(res.a, 3, BASE_DIGITS);
    res.trim();
    return res;
  }
  BigInt abs() const {
    BigInt res = *this;
    res.sign *= res.sign;
    return res;
  }
  void trim() {
    while (!a.empty() && !a.back()) a.pop_back();
    if (a.empty()) sign = 1;
  }
  bool isZero() const { return a.empty() || (a.size() == 1 && !a[0]); }
  friend BigInt gcd(const BigInt &a, const BigInt &b) {
    return b.isZero() ? a : gcd(b, a % b);
  }
  friend BigInt lcm(const BigInt &a, const BigInt &b) {
    return a / gcd(a, b) * b;
  }
  friend BigInt sqrt(const BigInt &a1) {
    BigInt a = a1;
    while (a.a.empty() || a.a.size() % 2 == 1) a.a.push_back(0);
    int n = a.a.size();
    int firstDigit = (int)sqrt((double)a.a[n - 1] * BASE + a.a[n - 2]);
    int norm = BASE / (firstDigit + 1);
    a *= norm;
    a *= norm;
    while (a.a.empty() || a.a.size() % 2 == 1) a.a.push_back(0);
    BigInt r = (long long)a.a[n - 1] * BASE + a.a[n - 2];
    firstDigit = (int)sqrt((double)a.a[n - 1] * BASE + a.a[n - 2]);
    int q = firstDigit;
    BigInt res;
    for (int j = n / 2 - 1; j >= 0; j--) {
      for (;; --q) {
        BigInt r1 =
            (r - (res * 2 * BigInt(BASE) + q) * q) * BigInt(BASE) *
                BigInt(BASE) +
            (j > 0 ? (long long)a.a[2 * j - 1] * BASE + a.a[2 * j - 2] : 0);
        if (r1 >= 0) {
          r = r1;
          break;
        }
      }
      res *= BASE;
      res += q;
      if (j > 0) {
        int d1 = res.a.size() + 2 < r.a.size() ? r.a[res.a.size() + 2] : 0;
        int d2 = res.a.size() + 1 < r.a.size() ? r.a[res.a.size() + 1] : 0;
        int d3 = res.a.size() < r.a.size() ? r.a[res.a.size()] : 0;
        q = ((long long)d1 * BASE * BASE + (long long)d2 * BASE + d3) /
            (firstDigit * 2);
      }
    }
    res.trim();
    return res / norm;
  }
};
long double L2 = log10(2), L3 = log10(3);
long double calc(long long int n) {
  if (n == 1) return 0;
  if (n % 3 == 0) {
    return L3 * (n / 3);
  }
  if (n % 3 == 1) return L3 * (n / 3 - 1) + L2 * 2;
  return L3 * (n / 3) + L2;
}
long long int N = 1e7;
int p[10000005], q[10000005];
BigInt mu(int a, int n) {
  if (n == 0) return 1;
  BigInt Q = mu(a, n / 2);
  if (n % 2 == 0) return Q * Q;
  return Q * Q * a;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(NULL);
  srand(time(NULL));
  string S;
  cin >> S;
  int l = S.size();
  BigInt K(S);
  if (K <= 4) {
    cout << S;
    return 0;
  }
  long long int L = 1, R = N, mid;
  while (L < R) {
    mid = (L + R) / 2;
    if (calc(mid) + (1e-8) >= l - 1)
      R = mid;
    else
      L = mid + 1;
  }
  long long int A = L;
  L = 1;
  R = N;
  while (L < R) {
    mid = (L + R + 1) / 2;
    if (calc(mid) < l + (1e-8))
      L = mid;
    else
      R = mid - 1;
  }
  long long int B = R;
  L = A;
  R = B;
  B += 3;
  A -= 3;
  A = max(A, 2LL);
  B = min(B, N);
  int Mp = 1000000000, Mq = 1000000000;
  for (int i = A; i <= B; i++) {
    if (i % 3 == 0) {
      q[i] = i / 3;
    }
    if (i % 3 == 1) {
      q[i] = i / 3 - 1;
      p[i] = 2;
    }
    if (i % 3 == 2) {
      q[i] = i / 3;
      p[i] = 1;
    }
    Mp = min(Mp, p[i]);
    Mq = min(Mq, q[i]);
  }
  BigInt T = mu(3, Mq) * mu(2, Mp);
  L = A, R = B;
  while (L < R) {
    mid = (L + R) / 2;
    long long int T2 = 1, T3 = 1;
    for (int j = Mp + 1; j <= p[mid]; j++) {
      T2 *= 2;
    }
    for (int j = Mq + 1; j <= q[mid]; j++) {
      T3 *= 3;
    }
    T2 *= T3;
    BigInt Q = T * T2;
    if (Q >= K) {
      R = mid;
    } else
      L = mid + 1;
  }
  cout << L;
  return 0;
}