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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
typedef  long long int ll;
const ll mod = 1e9+7;
const ll mod1 = 998244353;
const ll inf = 9e18+5;
#define rep(i,a,b) for(ll i=a;i<b;i++)

void swap(ll &a , ll &b){
    ll t = a;
    a = b;
    b = t;
}

ll min(ll a, ll b){
    if(a<b)return a;
    return b;
}

ll max(ll a, ll b){
    if(a>b)return a;
    return b;
}

 ll pow(ll a, ll b) {
    a %= mod;
    ll ans = 1;
    while (b > 0) {
        if (b & 1)
            ans = ans * a % mod;
        a = a * a % mod;
        b /= 2;
    }
    return ans;
}


//*********Debugger template starts***********************//
#ifndef ONLINE_JUDGE
vector<string> vec_splitter(string s) {
	s += ',';
	vector<string> res;
	while(!s.empty()) {
		res.push_back(s.substr(0, s.find(',')));
		s = s.substr(s.find(',') + 1);
	}
	return res;
}
void debug_out(
vector<string> __attribute__ ((unused)) args,
__attribute__ ((unused)) int idx,
__attribute__ ((unused)) int LINE_NUM) { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(vector<string> args, int idx, int LINE_NUM, Head H, Tail... T) {

	if(idx == 0) {
        cerr << "Line(" << LINE_NUM << ") ";
	}
	stringstream ss; ss << H;
	cerr << " [" << args[idx] << " = " << ss.str() <<"] ";
	debug_out(args, idx + 1, LINE_NUM, T...);

}
#define debug(...) debug_out(vec_splitter(#__VA_ARGS__), 0, __LINE__, __VA_ARGS__)
#else
#define debug(...)
#endif

#ifndef ONLINE_JUDGE
#define n_l '\n'
#define dbg(...) cerr <<"Line("<<__LINE__<<") " "[" << #__VA_ARGS__ << "]: "; cerr << to_string(__VA_ARGS__) << endl
template <typename T, size_t N> int SIZE(const T (&t)[N]){ return N; } template<typename T> int SIZE(const T &t){ return t.size(); } string to_string(const string s, int x1=0, int x2=1e9){ return '"' + ((x1 < s.size()) ? s.substr(x1, x2-x1+1) : "") + '"'; } string to_string(const char* s) { return to_string((string) s); } string to_string(const bool b) { return (b ? "true" : "false"); } string to_string(const char c){ return string({c}); } template<size_t N> string to_string(const bitset<N> &b, int x1=0, int x2=1e9){ string t = ""; for(int __iii__ = min(x1,SIZE(b)),  __jjj__ = min(x2, SIZE(b)-1); __iii__ <= __jjj__; ++__iii__){ t += b[__iii__] + '0'; } return '"' + t + '"'; } template <typename A, typename... C> string to_string(const A (&v), int x1=0, int x2=1e9, C... coords); int l_v_l_v_l = 0, t_a_b_s = 0; template <typename A, typename B> string to_string(const pair<A, B> &p) { l_v_l_v_l++; string res = "(" + to_string(p.first) + ", " + to_string(p.second) + ")"; l_v_l_v_l--; return res; } template <typename A, typename... C> string to_string(const A (&v), int x1, int x2, C... coords) { int rnk = rank<A>::value; string tab(t_a_b_s, ' '); string res = ""; bool first = true; if(l_v_l_v_l == 0) res += n_l; res += tab + "["; x1 = min(x1, SIZE(v)), x2 = min(x2, SIZE(v)); auto l = begin(v); advance(l, x1); auto r = l; advance(r, (x2-x1) + (x2 < SIZE(v))); for (auto e = l; e != r; e = next(e)) { if (!first) { res += ", "; } first = false; l_v_l_v_l++; if(e != l){ if(rnk > 1) { res += n_l; t_a_b_s = l_v_l_v_l; }; } else{ t_a_b_s = 0; } res += to_string(*e, coords...); l_v_l_v_l--; } res += "]"; if(l_v_l_v_l == 0) res += n_l; return res; } void dbgm(){;} template<typename Heads, typename... Tails> void dbgm(Heads H, Tails... T){ cerr << to_string(H) << " | "; dbgm(T...); }
#else
    #define dbg(...)
#endif


//*********Debugger template ends ***********************//


int main() {


  ios_base :: sync_with_stdio(0);
  cin.tie(0);
  ll X;
  ll st;
  cin>>X;
  st = X;
  ll ans = 0;
  ll temp;
  X = 100;
  while(1){
    temp = X/100;
    X += temp;
    ans++;
    if(X >=st)break;
  }
  cout<<ans;





  return 0;
}