#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1 << 22;
struct CD {
  double r, i;
  CD(double r = 0, double i = 0) : r(r), i(i) {}
  double real() const { return r; }
  void operator/=(const int c) { r /= c, i /= c; }
};
CD operator*(const CD &a, const CD &b) {
  return CD(a.r * b.r - a.i * b.i, a.r * b.i + a.i * b.r);
}
CD operator+(const CD &a, const CD &b) { return CD(a.r + b.r, a.i + b.i); }
CD operator-(const CD &a, const CD &b) { return CD(a.r - b.r, a.i - b.i); }
const double pi = acos(-1);
CD cp1[MAXN + 9], cp2[MAXN + 9];
int R[MAXN + 9];
void dft(CD *a, int n, bool inv) {
  for (int i = 0, ThxDem = n; i < ThxDem; ++i)
    if (R[i] < i) swap(a[R[i]], a[i]);
  for (int m = 2; m <= n; m *= 2) {
    double z = 2 * pi / m * (inv ? -1 : 1);
    CD wi = CD(cos(z), sin(z));
    for (int j = 0; j < n; j += m) {
      CD w(1);
      for (int k = j, k2 = j + m / 2; k2 < j + m; k++, k2++) {
        CD u = a[k];
        CD v = a[k2] * w;
        a[k] = u + v;
        a[k2] = u - v;
        w = w * wi;
      }
    }
  }
  if (inv)
    for (int i = 0, ThxDem = n; i < ThxDem; ++i) a[i] /= n;
}
vector<int> multiply(vector<int> &p1, vector<int> &p2) {
  int n = int(p1.size()) + int(p2.size()) + 1;
  int m = 1, cnt = 0;
  while (m <= n) m += m, cnt++;
  for (int i = 0, ThxDem = m; i < ThxDem; ++i) {
    R[i] = 0;
    for (int j = 0, ThxDem = cnt; j < ThxDem; ++j)
      R[i] = (R[i] << 1) | ((i >> j) & 1);
  }
  for (int i = 0, ThxDem = m; i < ThxDem; ++i) cp1[i] = 0, cp2[i] = 0;
  for (int i = 0, ThxDem = p1.size(); i < ThxDem; ++i) cp1[i] = p1[i];
  for (int i = 0, ThxDem = p2.size(); i < ThxDem; ++i) cp2[i] = p2[i];
  dft(cp1, m, 0);
  dft(cp2, m, 0);
  for (int i = 0, ThxDem = m; i < ThxDem; ++i) cp1[i] = cp1[i] * cp2[i];
  dft(cp1, m, 1);
  n -= 2;
  vector<int> res;
  for (int i = 0, ThxDem = n; i < ThxDem; ++i)
    res.push_back((long long)floor(cp1[i].real() + .5));
  return res;
}
vector<int> mul(vector<int> &x, vector<int> &y) {
  auto ans = multiply(x, y);
  int carry = 0;
  int pos = 0;
  while (pos < int(ans.size())) {
    carry += ans[pos];
    ans[pos] = carry % 10;
    carry /= 10;
    if (carry && pos + 1 == int(ans.size())) ans.push_back(0);
    pos++;
  }
  return ans;
}
vector<int> pow3(long long exp) {
  vector<int> result = {1};
  vector<int> base = {3};
  while (exp) {
    if (exp & 1) result = mul(result, base);
    exp >>= 1;
    base = mul(base, base);
  }
  reverse(result.begin(), result.end());
  return result;
}
bool low(vector<int> &a, vector<int> &b) {
  if (int(a.size()) != int(b.size())) return int(a.size()) < int(b.size());
  for (int i = 0, ThxDem = int(a.size()); i < ThxDem; ++i)
    if (b[i] != a[i]) return a[i] < b[i];
  return 0;
}
void mul3(vector<int> &ans) {
  int carry = 0;
  int pos = 0;
  reverse(ans.begin(), ans.end());
  while (pos < int(ans.size())) {
    carry += ans[pos] * 3;
    ans[pos] = carry % 10;
    carry /= 10;
    if (carry && pos + 1 == int(ans.size())) ans.push_back(0);
    pos++;
  }
  reverse(ans.begin(), ans.end());
}
void sum(vector<int> &a, int asd) {
  int carry = asd;
  for (int i = int(a.size()) - 1; i >= 0; i--) {
    if (!carry) break;
    carry += a[i];
    a[i] = carry % 10;
    carry /= 10;
  }
}
vector<int> div2(vector<int> a) {
  vector<int> ans = a;
  int carry = 0;
  for (int i = 0, ThxDem = int(ans.size()); i < ThxDem; ++i) {
    carry = (10 * carry) + ans[i];
    ans[i] = carry / 2;
    carry = carry & 1;
  }
  if (carry) sum(ans, 1);
  if (int(ans.size()) > 1 && ans[0] == 0)
    ans = vector<int>(ans.begin() + 1, ans.end());
  return ans;
}
void print(vector<int> &a) {
  for (auto x : a) cout << x;
  cout << "\n";
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  string s;
  cin >> s;
  if (s == "1") cout << "1\n", exit(0);
  vector<int> n;
  for (auto x : s) n.push_back(x - '0');
  div2(n);
  auto n2 = div2(n);
  auto n4 = div2(n2);
  double lg10 = log(10) / log(3);
  int k = ceil((int(s.size()) - 1) * lg10);
  int mx = max(0, k - 4);
  auto ans = pow3(mx);
  while (low(ans, n4)) mul3(ans), mx++;
  int x4 = mx;
  while (low(ans, n2)) mul3(ans), mx++;
  int x2 = mx;
  while (low(ans, n)) mul3(ans), mx++;
  int x = mx;
  x = 3 * x;
  x2 = 3 * x2 + 2;
  x4 = 3 * x4 + 4;
  cout << min({x, x2, x4}) << "\n";
}

### Prompt

Your challenge is to write a Cpp solution to the following 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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1 << 22;
struct CD {
  double r, i;
  CD(double r = 0, double i = 0) : r(r), i(i) {}
  double real() const { return r; }
  void operator/=(const int c) { r /= c, i /= c; }
};
CD operator*(const CD &a, const CD &b) {
  return CD(a.r * b.r - a.i * b.i, a.r * b.i + a.i * b.r);
}
CD operator+(const CD &a, const CD &b) { return CD(a.r + b.r, a.i + b.i); }
CD operator-(const CD &a, const CD &b) { return CD(a.r - b.r, a.i - b.i); }
const double pi = acos(-1);
CD cp1[MAXN + 9], cp2[MAXN + 9];
int R[MAXN + 9];
void dft(CD *a, int n, bool inv) {
  for (int i = 0, ThxDem = n; i < ThxDem; ++i)
    if (R[i] < i) swap(a[R[i]], a[i]);
  for (int m = 2; m <= n; m *= 2) {
    double z = 2 * pi / m * (inv ? -1 : 1);
    CD wi = CD(cos(z), sin(z));
    for (int j = 0; j < n; j += m) {
      CD w(1);
      for (int k = j, k2 = j + m / 2; k2 < j + m; k++, k2++) {
        CD u = a[k];
        CD v = a[k2] * w;
        a[k] = u + v;
        a[k2] = u - v;
        w = w * wi;
      }
    }
  }
  if (inv)
    for (int i = 0, ThxDem = n; i < ThxDem; ++i) a[i] /= n;
}
vector<int> multiply(vector<int> &p1, vector<int> &p2) {
  int n = int(p1.size()) + int(p2.size()) + 1;
  int m = 1, cnt = 0;
  while (m <= n) m += m, cnt++;
  for (int i = 0, ThxDem = m; i < ThxDem; ++i) {
    R[i] = 0;
    for (int j = 0, ThxDem = cnt; j < ThxDem; ++j)
      R[i] = (R[i] << 1) | ((i >> j) & 1);
  }
  for (int i = 0, ThxDem = m; i < ThxDem; ++i) cp1[i] = 0, cp2[i] = 0;
  for (int i = 0, ThxDem = p1.size(); i < ThxDem; ++i) cp1[i] = p1[i];
  for (int i = 0, ThxDem = p2.size(); i < ThxDem; ++i) cp2[i] = p2[i];
  dft(cp1, m, 0);
  dft(cp2, m, 0);
  for (int i = 0, ThxDem = m; i < ThxDem; ++i) cp1[i] = cp1[i] * cp2[i];
  dft(cp1, m, 1);
  n -= 2;
  vector<int> res;
  for (int i = 0, ThxDem = n; i < ThxDem; ++i)
    res.push_back((long long)floor(cp1[i].real() + .5));
  return res;
}
vector<int> mul(vector<int> &x, vector<int> &y) {
  auto ans = multiply(x, y);
  int carry = 0;
  int pos = 0;
  while (pos < int(ans.size())) {
    carry += ans[pos];
    ans[pos] = carry % 10;
    carry /= 10;
    if (carry && pos + 1 == int(ans.size())) ans.push_back(0);
    pos++;
  }
  return ans;
}
vector<int> pow3(long long exp) {
  vector<int> result = {1};
  vector<int> base = {3};
  while (exp) {
    if (exp & 1) result = mul(result, base);
    exp >>= 1;
    base = mul(base, base);
  }
  reverse(result.begin(), result.end());
  return result;
}
bool low(vector<int> &a, vector<int> &b) {
  if (int(a.size()) != int(b.size())) return int(a.size()) < int(b.size());
  for (int i = 0, ThxDem = int(a.size()); i < ThxDem; ++i)
    if (b[i] != a[i]) return a[i] < b[i];
  return 0;
}
void mul3(vector<int> &ans) {
  int carry = 0;
  int pos = 0;
  reverse(ans.begin(), ans.end());
  while (pos < int(ans.size())) {
    carry += ans[pos] * 3;
    ans[pos] = carry % 10;
    carry /= 10;
    if (carry && pos + 1 == int(ans.size())) ans.push_back(0);
    pos++;
  }
  reverse(ans.begin(), ans.end());
}
void sum(vector<int> &a, int asd) {
  int carry = asd;
  for (int i = int(a.size()) - 1; i >= 0; i--) {
    if (!carry) break;
    carry += a[i];
    a[i] = carry % 10;
    carry /= 10;
  }
}
vector<int> div2(vector<int> a) {
  vector<int> ans = a;
  int carry = 0;
  for (int i = 0, ThxDem = int(ans.size()); i < ThxDem; ++i) {
    carry = (10 * carry) + ans[i];
    ans[i] = carry / 2;
    carry = carry & 1;
  }
  if (carry) sum(ans, 1);
  if (int(ans.size()) > 1 && ans[0] == 0)
    ans = vector<int>(ans.begin() + 1, ans.end());
  return ans;
}
void print(vector<int> &a) {
  for (auto x : a) cout << x;
  cout << "\n";
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  string s;
  cin >> s;
  if (s == "1") cout << "1\n", exit(0);
  vector<int> n;
  for (auto x : s) n.push_back(x - '0');
  div2(n);
  auto n2 = div2(n);
  auto n4 = div2(n2);
  double lg10 = log(10) / log(3);
  int k = ceil((int(s.size()) - 1) * lg10);
  int mx = max(0, k - 4);
  auto ans = pow3(mx);
  while (low(ans, n4)) mul3(ans), mx++;
  int x4 = mx;
  while (low(ans, n2)) mul3(ans), mx++;
  int x2 = mx;
  while (low(ans, n)) mul3(ans), mx++;
  int x = mx;
  x = 3 * x;
  x2 = 3 * x2 + 2;
  x4 = 3 * x4 + 4;
  cout << min({x, x2, x4}) << "\n";
}

```