Problem:
Score : 200 points

Problem Statement

Takahashi has a deposit of 100 yen (the currency of Japan) in AtCoder Bank.

The bank pays an annual interest rate of 1 % compounded annually. (A fraction of less than one yen is discarded.)

Assuming that nothing other than the interest affects Takahashi's balance, in how many years does the balance reach X yen or above for the first time?

Constraints

101 \le X \le 10^{18}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X

Output

Print the number of years it takes for Takahashi's balance to reach X yen or above for the first time.

Sample Input 1

103

Sample Output 1

3

The balance after one year is 101 yen.

The balance after two years is 102 yen.

The balance after three years is 103 yen.

Thus, it takes three years for the balance to reach 103 yen or above.

Sample Input 2

1000000000000000000

Sample Output 2

3760

Sample Input 3

1333333333

Sample Output 3

1706

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

//#define NDEBUG
#include "bits/stdc++.h"
#include <iostream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <array>
#include <random>
#ifdef _MSC_VER
#include <ppl.h>
//#include <boost/multiprecision/cpp_dec_float.hpp>
//#include <boost/multiprecision/cpp_int.hpp>
//#include <boost/rational.hpp>
//#include <opencv2/core.hpp>
//#include <opencv2/imgproc.hpp>
//#include <opencv2/highgui.hpp>
//#else
//#include <omp.h>
#endif


using namespace std;

#define DUMPOUT cerr
#define dump(...) DUMPOUT<<"  ";DUMPOUT<<#__VA_ARGS__<<" :["<<__LINE__<<":"<<__FUNCTION__<<"]"<<endl;DUMPOUT<<"    ";dump_func(__VA_ARGS__)

using uint = unsigned; using ll = long long; using ull = unsigned long long; using pii = pair<int, int>; using pll = pair<ll, ll>; using pdd = pair<double, double>; using pss = pair<string, string>;
template <typename _KTy, typename _Ty> ostream& operator << (ostream& o, const pair<_KTy, _Ty>& m) { o << "{" << m.first << ", " << m.second << "}"; return o; }
template <typename _KTy, typename _Ty> ostream& operator << (ostream& o, const map<_KTy, _Ty>& m) { if (m.empty()) { o << "{ }"; return o; } o << "{" << *m.begin(); for (auto itr = ++m.begin(); itr != m.end(); itr++) { o << ", " << *itr; } o << "}"; return o; }
template <typename _KTy, typename _Ty> ostream& operator << (ostream& o, const unordered_map<_KTy, _Ty>& m) { if (m.empty()) { o << "{ }"; return o; } o << "{" << *m.begin(); for (auto itr = ++m.begin(); itr != m.end(); itr++) { o << ", " << *itr; } o << "}"; return o; }
template <typename _Ty> ostream& operator << (ostream& o, const vector<_Ty>& v) { if (v.empty()) { o << "{ }"; return o; } o << "{" << v.front(); for (auto itr = ++v.begin(); itr != v.end(); itr++) { o << ", " << *itr; } o << "}"; return o; }
template <typename _Ty> ostream& operator << (ostream& o, const deque<_Ty>& v) { if (v.empty()) { o << "{ }"; return o; } o << "{" << v.front(); for (auto itr = ++v.begin(); itr != v.end(); itr++) { o << ", " << *itr; } o << "}"; return o; }
template <typename _Ty> ostream& operator << (ostream& o, const set<_Ty>& s) { if (s.empty()) { o << "{ }"; return o; } o << "{" << *(s.begin()); for (auto itr = ++s.begin(); itr != s.end(); itr++) { o << ", " << *itr; } o << "}"; return o; }
template <typename _Ty> ostream& operator << (ostream& o, const unordered_set<_Ty>& s) { if (s.empty()) { o << "{ }"; return o; } o << "{" << *(s.begin()); for (auto itr = ++s.begin(); itr != s.end(); itr++) { o << ", " << *itr; }	o << "}"; return o; }
template <typename _Ty> ostream& operator << (ostream& o, const stack<_Ty>& s) { if (s.empty()) { o << "{ }"; return o; } stack<_Ty> t(s); o << "{" << t.top(); t.pop(); while (!t.empty()) { o << ", " << t.top(); t.pop(); } o << "}";	return o; }
template <typename _Ty> ostream& operator << (ostream& o, const list<_Ty>& l) { if (l.empty()) { o << "{ }"; return o; } o << "{" << l.front(); for (auto itr = ++l.begin(); itr != l.end(); ++itr) { o << ", " << *itr; } o << "}"; return o; }
template <typename _KTy, typename _Ty> istream& operator >> (istream& is, pair<_KTy, _Ty>& m) { is >> m.first >> m.second; return is; }
template <typename _Ty> istream& operator >> (istream& is, vector<_Ty>& v) { for (size_t t = 0; t < v.size(); t++) is >> v[t]; return is; }
template <typename _Ty> istream& operator >> (istream& is, deque<_Ty>& v) { for (size_t t = 0; t < v.size(); t++) is >> v[t]; return is; }
namespace aux { // print tuple
  template<typename Ty, unsigned N, unsigned L> struct tp { static void print(ostream& os, const Ty& v) { os << get<N>(v) << ", "; tp<Ty, N + 1, L>::print(os, v); } };
  template<typename Ty, unsigned N> struct tp<Ty, N, N> { static void print(ostream& os, const Ty& v) { os << get<N>(v); } };
}

template<typename... Tys> ostream& operator<<(ostream& os, const tuple<Tys...>& t) { os << "{"; aux::tp<tuple<Tys...>, 0, sizeof...(Tys) - 1>::print(os, t); os << "}"; return os; }

template<typename A, size_t N, typename T> inline void Fill(A(&array)[N], const T& val) { fill((T*)array, (T*)(array + N), val); }

void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail> void dump_func(Head&& head, Tail&&... tail) { DUMPOUT << head; if (sizeof...(Tail) == 0) { DUMPOUT << " "; } else { DUMPOUT << ", "; } dump_func(move(tail)...); }

#define PI 3.14159265358979323846
#define EPS 1e-8
#define rep(t,n) for(int t=0;t<(n);++t)
#define all(j) (j).begin(), (j).end()
#define SZ(j) ((int)(j).size())
#define fake false

class Timer {
public:
  double t = 0;
  Timer() {}
  static double time() {
#ifdef _MSC_VER
    return __rdtsc() / 2.8e9;
#else
    unsigned long long a, d;
    __asm__ volatile("rdtsc"
      : "=a"(a), "=d"(d));
    return (d << 32 | a) / 2.8e9;
#endif
  }
  void measure() { t = time() - t; }
  double elapsedMs() { return (time() - t) * 1000.0; }
} timer;

struct Xorshift {
  uint64_t x = 88172645463325252LL;
  unsigned next_int() {
    x = x ^ (x << 7);
    return x = x ^ (x >> 9);
  }
  unsigned next_int(unsigned mod) {
    x = x ^ (x << 7);
    x = x ^ (x >> 9);
    return x % mod;
  }
  unsigned next_int(unsigned l, unsigned r) {
    x = x ^ (x << 7);
    x = x ^ (x >> 9);
    return x % (r - l + 1) + l;
  }
  double next_double() {
    return double(next_int()) / UINT_MAX;
  }
} rnd;

template<typename T>
void shuffle_vector(vector<T>& v, Xorshift& rnd) {
  int n = v.size();
  for (int i = n - 1; i >= 1; i--) {
    int r = rnd.next_int(i);
    swap(v[i], v[r]);
  }
}



int main() {
  timer.measure();

  std::ios::sync_with_stdio(false);
  std::cin.tie(0);

  ll X;
  cin >> X;
  
  int ans = 0;
  ll a = 100;
  while (a < X) {
    a = a + a / 100;
    ans++;
  }

  cout << ans << endl;

  return 0;
}