#include <bits/stdc++.h>
using namespace std;
struct cpx {
  double r, i;
  cpx(double real = 0.0, double image = 0.0) {
    r = real;
    i = image;
  }
  cpx operator+(cpx a) { return cpx(r + a.r, i + a.i); }
  cpx operator-(cpx a) { return cpx(r - a.r, i - a.i); }
  cpx operator*(cpx a) { return cpx(r * a.r - i * a.i, i * a.r + r * a.i); }
} a[2000005], wn[2000005];
int c1[600005], s1;
int c2[600005], s2;
int res[600005];
long long tp[600005];
char s[1500005];
const double pi = acos(-1.0);
const int mod = 1000;
inline int max(int a, int b) { return a > b ? a : b; }
inline int min(int a, int b) { return a < b ? a : b; }
inline void change(cpx y[], int len) {
  int i, j, k;
  for (i = 1, j = (len >> 1); i < len - 1; i++) {
    if (i < j) swap(y[i], y[j]);
    k = (len >> 1);
    while (j >= k) {
      j -= k;
      k >>= 1;
    }
    j += k;
  }
}
inline void fft(cpx y[], int len, int f) {
  int h, i, j;
  wn[0] = cpx(1, 0);
  change(y, len);
  for (h = 2; h <= len; h <<= 1) {
    cpx wo(cos(-2.0 * pi / h), sin(-2.0 * pi / h));
    for (j = 1; j < (h >> 1); j++) wn[j] = wn[j - 1] * wo;
    for (i = 0; i < len; i += h) {
      cpx *a = y + i, *b = y + i + (h >> 1);
      for (j = 0; j < (h >> 1); j++) {
        cpx u = a[j], v = b[j] * wn[j];
        a[j] = u + v;
        b[j] = u - v;
      }
    }
  }
  if (f == -1) {
    for (i = 1; i < (len >> 1); i++) swap(y[i], y[len - i]);
    double o = 1.0 / len;
    for (i = 0; i < len; i++) y[i].r *= o;
  }
}
inline void mul_poly() {
  int sz = s2, len = 1, i, pos = 0;
  while (len < sz + sz) len <<= 1;
  for (i = 0; i < len; i++) a[i] = cpx(c2[i], 0);
  fft(a, len, 1);
  for (i = 0; i < len; i++) a[i] = a[i] * a[i];
  fft(a, len, -1);
  for (i = 0; i < len; i++) tp[i] = ((long long)(a[i].r + 0.5));
  while (len && (!tp[len - 1])) len--;
  while (pos < len || tp[pos]) {
    tp[pos + 1] += tp[pos] / mod;
    c2[pos] = tp[pos] % mod;
    pos++;
  }
  s2 = pos;
}
inline int mul_num(int p) {
  int i, pos = 0;
  res[s2] = 0;
  for (i = 0; i < s2; i++) res[i] = c2[i] * p;
  while (pos < s2 || res[pos]) {
    res[pos + 1] += res[pos] / mod;
    res[pos] %= mod;
    pos++;
  }
  return pos;
}
inline bool cmp(int a[], int b[], int p1, int p2) {
  if (p1 > p2) return true;
  if (p1 < p2) return false;
  for (int i = p1 - 1; i >= 0; i--) {
    if (a[i] > b[i]) return true;
    if (a[i] < b[i]) return false;
  }
  return false;
}
int main() {
  scanf("%s", s + 1);
  int n = strlen(s + 1), i, j, o = 1, ans = 233333333, x;
  int pw = (int)(1.0 * n * log(10) / log(3) - 6.0);
  pw = max(pw, 0);
  for (i = n; i >= 1; i -= 3) {
    for (x = 0, j = max(1, i - 2); j <= i; j++) x = x * 10 + (s[j] - '0');
    c1[s1++] = x;
  }
  c2[s2++] = 1;
  while ((1 << (o + 1)) <= pw) o++;
  for (i = o; i >= 0; i--) {
    mul_poly();
    if (pw & (1 << i)) {
      s2 = mul_num(3);
      for (j = 0; j < s2; j++) c2[j] = res[j];
    }
  }
  while (cmp(c1, c2, s1, s2)) {
    int ss = mul_num(2);
    if (!cmp(c1, res, s1, ss)) ans = min(ans, 3 * pw + 2);
    int sk = mul_num(4);
    if (!cmp(c1, res, s1, sk)) ans = min(ans, 3 * pw + 4);
    pw++;
    s2 = mul_num(3);
    for (j = 0; j < s2; j++) c2[j] = res[j];
  }
  ans = min(ans, 3 * pw);
  ans = max(ans, 1);
  printf("%d\n", ans);
  return 0;
}

### Prompt

In Cpp, your task is to solve 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;
struct cpx {
  double r, i;
  cpx(double real = 0.0, double image = 0.0) {
    r = real;
    i = image;
  }
  cpx operator+(cpx a) { return cpx(r + a.r, i + a.i); }
  cpx operator-(cpx a) { return cpx(r - a.r, i - a.i); }
  cpx operator*(cpx a) { return cpx(r * a.r - i * a.i, i * a.r + r * a.i); }
} a[2000005], wn[2000005];
int c1[600005], s1;
int c2[600005], s2;
int res[600005];
long long tp[600005];
char s[1500005];
const double pi = acos(-1.0);
const int mod = 1000;
inline int max(int a, int b) { return a > b ? a : b; }
inline int min(int a, int b) { return a < b ? a : b; }
inline void change(cpx y[], int len) {
  int i, j, k;
  for (i = 1, j = (len >> 1); i < len - 1; i++) {
    if (i < j) swap(y[i], y[j]);
    k = (len >> 1);
    while (j >= k) {
      j -= k;
      k >>= 1;
    }
    j += k;
  }
}
inline void fft(cpx y[], int len, int f) {
  int h, i, j;
  wn[0] = cpx(1, 0);
  change(y, len);
  for (h = 2; h <= len; h <<= 1) {
    cpx wo(cos(-2.0 * pi / h), sin(-2.0 * pi / h));
    for (j = 1; j < (h >> 1); j++) wn[j] = wn[j - 1] * wo;
    for (i = 0; i < len; i += h) {
      cpx *a = y + i, *b = y + i + (h >> 1);
      for (j = 0; j < (h >> 1); j++) {
        cpx u = a[j], v = b[j] * wn[j];
        a[j] = u + v;
        b[j] = u - v;
      }
    }
  }
  if (f == -1) {
    for (i = 1; i < (len >> 1); i++) swap(y[i], y[len - i]);
    double o = 1.0 / len;
    for (i = 0; i < len; i++) y[i].r *= o;
  }
}
inline void mul_poly() {
  int sz = s2, len = 1, i, pos = 0;
  while (len < sz + sz) len <<= 1;
  for (i = 0; i < len; i++) a[i] = cpx(c2[i], 0);
  fft(a, len, 1);
  for (i = 0; i < len; i++) a[i] = a[i] * a[i];
  fft(a, len, -1);
  for (i = 0; i < len; i++) tp[i] = ((long long)(a[i].r + 0.5));
  while (len && (!tp[len - 1])) len--;
  while (pos < len || tp[pos]) {
    tp[pos + 1] += tp[pos] / mod;
    c2[pos] = tp[pos] % mod;
    pos++;
  }
  s2 = pos;
}
inline int mul_num(int p) {
  int i, pos = 0;
  res[s2] = 0;
  for (i = 0; i < s2; i++) res[i] = c2[i] * p;
  while (pos < s2 || res[pos]) {
    res[pos + 1] += res[pos] / mod;
    res[pos] %= mod;
    pos++;
  }
  return pos;
}
inline bool cmp(int a[], int b[], int p1, int p2) {
  if (p1 > p2) return true;
  if (p1 < p2) return false;
  for (int i = p1 - 1; i >= 0; i--) {
    if (a[i] > b[i]) return true;
    if (a[i] < b[i]) return false;
  }
  return false;
}
int main() {
  scanf("%s", s + 1);
  int n = strlen(s + 1), i, j, o = 1, ans = 233333333, x;
  int pw = (int)(1.0 * n * log(10) / log(3) - 6.0);
  pw = max(pw, 0);
  for (i = n; i >= 1; i -= 3) {
    for (x = 0, j = max(1, i - 2); j <= i; j++) x = x * 10 + (s[j] - '0');
    c1[s1++] = x;
  }
  c2[s2++] = 1;
  while ((1 << (o + 1)) <= pw) o++;
  for (i = o; i >= 0; i--) {
    mul_poly();
    if (pw & (1 << i)) {
      s2 = mul_num(3);
      for (j = 0; j < s2; j++) c2[j] = res[j];
    }
  }
  while (cmp(c1, c2, s1, s2)) {
    int ss = mul_num(2);
    if (!cmp(c1, res, s1, ss)) ans = min(ans, 3 * pw + 2);
    int sk = mul_num(4);
    if (!cmp(c1, res, s1, sk)) ans = min(ans, 3 * pw + 4);
    pw++;
    s2 = mul_num(3);
    for (j = 0; j < s2; j++) c2[j] = res[j];
  }
  ans = min(ans, 3 * pw);
  ans = max(ans, 1);
  printf("%d\n", ans);
  return 0;
}

```