#include <bits/stdc++.h>
using namespace std;
namespace {
struct Complex {
  double x, y;
  Complex operator+(const Complex &b) const { return {x + b.x, y + b.y}; }
  Complex operator-(const Complex &b) const { return {x - b.x, y - b.y}; }
  Complex operator*(const Complex &b) const {
    return {x * b.x - y * b.y, x * b.y + y * b.x};
  }
  Complex MulR(double c) const { return {x * c, y * c}; }
  Complex MulI(double c) const { return {-y * c, x * c}; }
  Complex Conj(void) const { return {x, -y}; }
};
const int maxn = 1 << 21;
const double pi = acos(-1);
Complex root[maxn >> 1];
int rev[maxn];
void Init(int n) {
  rev[0] = 0;
  for (int i = 1; i < n; ++i) {
    rev[i] = i & 1 ? rev[i - 1] | n >> 1 : rev[i >> 1] >> 1;
  }
  for (int i = 0; i < n >> 1; ++i) {
    double alpha = 2 * pi * i / n;
    root[i] = {cos(alpha), sin(alpha)};
  }
}
void Dft(Complex *a, int n) {
  for (int i = 0; i < n; ++i) {
    if (i < rev[i]) {
      swap(a[i], a[rev[i]]);
    }
  }
  Complex *end = root + (n >> 1);
  for (int m = 1, step = n >> 1; m < n; m <<= 1, step >>= 1) {
    for (int i = 0; i < n; i += m << 1) {
      for (Complex *l = a + i, *r = l + m, *w = root; w < end; w += step) {
        Complex t = *r * *w;
        *r = *l - t;
        *l = *l + t;
        ++l;
        ++r;
      }
    }
  }
}
void Idft(Complex *a, int n) {
  reverse(a + 1, a + n);
  Dft(a, n);
  double inv = 1.0 / n;
  for (int i = 0; i < n; ++i) {
    a[i] = a[i].MulR(inv);
  }
}
}  // namespace
namespace {
void Transform(double &u, double &v, double &x, double &y) {
  double a = (u * u - v * v - x * x + y * y) * 0.25;
  u = x = (u * v + x * y) * 0.5;
  v = -a;
  y = a;
}
void Convolution(Complex *a, int n) {
  Init(n);
  Dft(a, n);
  for (int i = 0; i << 1 <= n; ++i) {
    int j = i ? n - i : 0;
    Transform(a[i].x, a[i].y, a[j].x, a[j].y);
  }
  Idft(a, n);
}
}  // namespace
const int maxlen = 1.5e6, base = 1e4;
int len;
vector<int> num, cur, tmp;
Complex com[maxn];
void GetMul(const vector<int> &a, const vector<int> &b, vector<int> &c) {
  int nn = 1;
  for (; nn < a.size() + b.size(); nn <<= 1)
    ;
  fill(com, com + nn, (Complex){0, 0});
  for (int i = 0; i < a.size(); ++i) {
    com[i].x = a[i];
  }
  for (int j = 0; j < b.size(); ++j) {
    com[j].y = b[j];
  }
  Convolution(com, nn);
  long long s = 0;
  c.clear();
  for (int i = 0; i < nn; ++i) {
    s += (long long)round(com[i].x);
    c.push_back(s % base);
    s /= base;
  }
  while (!c.empty() && c.back() == 0) {
    c.pop_back();
  }
}
void GetMul(const vector<int> &a, int b, vector<int> &c) {
  c.clear();
  long long s = 0;
  for (int i = 0; i < a.size() || s; ++i) {
    s += a[i] * b;
    c.push_back(s % base);
    s /= base;
  }
}
bool Less(const vector<int> &a, const vector<int> &b) {
  if (a.size() != b.size()) {
    return a.size() < b.size();
  }
  for (int i = (int)a.size() - 1; i >= 0; --i) {
    if (a[i] != b[i]) {
      return a[i] < b[i];
    }
  }
  return false;
}
void Read(vector<int> &a) {
  static char s[maxlen + 1];
  scanf("%s", s);
  len = strlen(s);
  a.clear();
  for (int r = len; r > 0; r -= 4) {
    int l = max(0, r - 4);
    int x = 0;
    for (int i = l; i < r; ++i) {
      x = 10 * x + s[i] - '0';
    }
    a.push_back(x);
  }
}
int main(void) {
  Read(num);
  int rest = floor(log(10) / log(3) * (len - 1));
  if (rest) {
    --rest;
  }
  int ans = rest * 3;
  tmp = {3};
  cur = {1};
  for (; rest; rest >>= 1) {
    if (rest & 1) GetMul(cur, tmp, cur);
    GetMul(tmp, tmp, tmp);
  }
  while (Less(cur, num)) {
    vector<int> t2, t3, t4;
    if (GetMul(cur, 2, t2), !Less(t2, num)) {
      ans += 2;
      break;
    } else if (GetMul(cur, 3, t3), !Less(t3, num)) {
      ans += 3;
      break;
    } else if (GetMul(cur, 4, t4), !Less(t4, num)) {
      ans += 4;
      break;
    } else {
      ans += 3;
      cur = t3;
    }
  }
  if (!ans) {
    ans = 1;
  }
  printf("%d\n", ans);
  return 0;
}

### Prompt

Generate 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;
namespace {
struct Complex {
  double x, y;
  Complex operator+(const Complex &b) const { return {x + b.x, y + b.y}; }
  Complex operator-(const Complex &b) const { return {x - b.x, y - b.y}; }
  Complex operator*(const Complex &b) const {
    return {x * b.x - y * b.y, x * b.y + y * b.x};
  }
  Complex MulR(double c) const { return {x * c, y * c}; }
  Complex MulI(double c) const { return {-y * c, x * c}; }
  Complex Conj(void) const { return {x, -y}; }
};
const int maxn = 1 << 21;
const double pi = acos(-1);
Complex root[maxn >> 1];
int rev[maxn];
void Init(int n) {
  rev[0] = 0;
  for (int i = 1; i < n; ++i) {
    rev[i] = i & 1 ? rev[i - 1] | n >> 1 : rev[i >> 1] >> 1;
  }
  for (int i = 0; i < n >> 1; ++i) {
    double alpha = 2 * pi * i / n;
    root[i] = {cos(alpha), sin(alpha)};
  }
}
void Dft(Complex *a, int n) {
  for (int i = 0; i < n; ++i) {
    if (i < rev[i]) {
      swap(a[i], a[rev[i]]);
    }
  }
  Complex *end = root + (n >> 1);
  for (int m = 1, step = n >> 1; m < n; m <<= 1, step >>= 1) {
    for (int i = 0; i < n; i += m << 1) {
      for (Complex *l = a + i, *r = l + m, *w = root; w < end; w += step) {
        Complex t = *r * *w;
        *r = *l - t;
        *l = *l + t;
        ++l;
        ++r;
      }
    }
  }
}
void Idft(Complex *a, int n) {
  reverse(a + 1, a + n);
  Dft(a, n);
  double inv = 1.0 / n;
  for (int i = 0; i < n; ++i) {
    a[i] = a[i].MulR(inv);
  }
}
}  // namespace
namespace {
void Transform(double &u, double &v, double &x, double &y) {
  double a = (u * u - v * v - x * x + y * y) * 0.25;
  u = x = (u * v + x * y) * 0.5;
  v = -a;
  y = a;
}
void Convolution(Complex *a, int n) {
  Init(n);
  Dft(a, n);
  for (int i = 0; i << 1 <= n; ++i) {
    int j = i ? n - i : 0;
    Transform(a[i].x, a[i].y, a[j].x, a[j].y);
  }
  Idft(a, n);
}
}  // namespace
const int maxlen = 1.5e6, base = 1e4;
int len;
vector<int> num, cur, tmp;
Complex com[maxn];
void GetMul(const vector<int> &a, const vector<int> &b, vector<int> &c) {
  int nn = 1;
  for (; nn < a.size() + b.size(); nn <<= 1)
    ;
  fill(com, com + nn, (Complex){0, 0});
  for (int i = 0; i < a.size(); ++i) {
    com[i].x = a[i];
  }
  for (int j = 0; j < b.size(); ++j) {
    com[j].y = b[j];
  }
  Convolution(com, nn);
  long long s = 0;
  c.clear();
  for (int i = 0; i < nn; ++i) {
    s += (long long)round(com[i].x);
    c.push_back(s % base);
    s /= base;
  }
  while (!c.empty() && c.back() == 0) {
    c.pop_back();
  }
}
void GetMul(const vector<int> &a, int b, vector<int> &c) {
  c.clear();
  long long s = 0;
  for (int i = 0; i < a.size() || s; ++i) {
    s += a[i] * b;
    c.push_back(s % base);
    s /= base;
  }
}
bool Less(const vector<int> &a, const vector<int> &b) {
  if (a.size() != b.size()) {
    return a.size() < b.size();
  }
  for (int i = (int)a.size() - 1; i >= 0; --i) {
    if (a[i] != b[i]) {
      return a[i] < b[i];
    }
  }
  return false;
}
void Read(vector<int> &a) {
  static char s[maxlen + 1];
  scanf("%s", s);
  len = strlen(s);
  a.clear();
  for (int r = len; r > 0; r -= 4) {
    int l = max(0, r - 4);
    int x = 0;
    for (int i = l; i < r; ++i) {
      x = 10 * x + s[i] - '0';
    }
    a.push_back(x);
  }
}
int main(void) {
  Read(num);
  int rest = floor(log(10) / log(3) * (len - 1));
  if (rest) {
    --rest;
  }
  int ans = rest * 3;
  tmp = {3};
  cur = {1};
  for (; rest; rest >>= 1) {
    if (rest & 1) GetMul(cur, tmp, cur);
    GetMul(tmp, tmp, tmp);
  }
  while (Less(cur, num)) {
    vector<int> t2, t3, t4;
    if (GetMul(cur, 2, t2), !Less(t2, num)) {
      ans += 2;
      break;
    } else if (GetMul(cur, 3, t3), !Less(t3, num)) {
      ans += 3;
      break;
    } else if (GetMul(cur, 4, t4), !Less(t4, num)) {
      ans += 4;
      break;
    } else {
      ans += 3;
      cur = t3;
    }
  }
  if (!ans) {
    ans = 1;
  }
  printf("%d\n", ans);
  return 0;
}

```