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)


// Problem : B - 1%
// Contest : AtCoder - AtCoder Beginner Contest 165
// URL : https://atcoder.jp/contests/abc165/tasks/abc165_b
// Memory Limit : 1024 MB
// Time Limit : 2000 ms
// Powered by CP Editor (https://github.com/cpeditor/cpeditor)

#include<bits/stdc++.h>
using namespace std;

#define ff first
#define fs second
#define lb lower_bound
#define ub upper_bound

#define int long long
#define pii pair<int, int>
#define vi vector<int>
#define vvi vector< vi >
#define vpii vector< pii >
#define vb vector<bool>
#define si set<int>
#define mii map<int, int>
#define mci map<char, int>
#define md 1000000007
#define pb push_back
#define eb emplace_back
#define fio ios_base::sync_with_stdio (false); cin.tie (NULL);  cout.tie (NULL);
#define qw1(x) cerr<<#x<<": "<<x<<" "<<endl
#define qw2(x, y) cerr<<#x<<": "<<x<<" | "<<#y<<": "<<y<<endl
#define qw3(x, y, z) cerr<<#x<<":" <<x<<" | "<<#y<<": "<<y<<" | "<<#z<<": "<<z<<endl
#define qw4(a, b, c, d) cerr<<#a<<": "<<a<<" | "<<#b<<": "<<b<<" | "<<#c<<": "<<c<<" | "<<#d<<": "<<d<<endl


#define f(i,a,b) for(int i=(int)a;i<=(int)b;i++)
#define rl(i,a,b) for(int i=(int)a;i>=(int)b;i--)
#define all(x) x.begin(),x.end()
#define endl '\n'
void printv(vector<int>  v){ for(int i=0;i<v.size();i++) cout<<v[i]<<' '; cout<<endl;   }
int bem(int m , int n, int mod) { int res=1; while(n){
	     			        if(n%2!=0) { res*=m; res%=mod; }
	    			        m*=m;   m%=mod;   n/=2;
			                          }
				return res;	}
int be(int a, int b) { int res=1; 	while(b){
				if(b%2!=0) res*=a;
				a*=a; b/=2;
				}
			return res;	}
void sieve(int n, vb &prime){
    prime[0]=false;     prime[1]=false;
    for(int i=2;i*i<=n;i++){
         if(prime[i]==true){
              for(int j=i*i;j<=n;j+=i)    prime[j]=false;
             	  }
    	 }
	}

void solve()
  {
int z=100;
int x; cin>>x;
int cnt=0;
while(z<x)
{
	z= z + (z/100);
	cnt++;
}
cout<<cnt<<endl;

  }

int32_t main ()
{
//fio
int t=1; 
//cin>>t; 
while(t--){
	solve();
}
 
}