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: Time Limit Exceeded)

#include <bits/stdc++.h>
#define repr(i,a,b) for(int i=a;i<b;i++)
#define rep(i,n) for(int i=0;i<n;i++)
#define reprrev(i,a,b) for(int i=b-1;i>=a;i--) // [a, b)
#define reprev(i,n) reprrev(i,0,n)
#define _GLIBCXX_DEBUG

using ll = long long;
using ull = unsigned long long;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }
const ll mod = 1e9+7;
void chmod(ll &M){
  if(M >= mod) M %= mod;
  else if(M < 0){
     M += (abs(M)/mod + 1)*mod;
    M %= mod;
}
}
ll modpow(ll x, ll n){
   if(n==0) return 1;
  ll res=modpow(x, n/2);
 if(n%2==0) return res*res%mod;
else return res*res%mod*x%mod;
}
int getl(int i, int N) { return i==0? N-1:i-1; };
int getr(int i, int N) { return i==N-1? 0:i+1; };
long long GCD(long long a, long long b) {
  if (b == 0) return a;
  else return GCD(b, a % b);
}

using namespace std;
/* <-----------------------------------------------------------------------------------> */
/* <-----------------------------------------------------------------------------------> */
/* <-----------------------------------------------------------------------------------> */
/* <-----------------------------------------------------------------------------------> */
int main()
{
    ull X;
    cin >> X;
    ull sum = 100; 
    ull year = 0;
    while(sum < X) {
        sum *= 101/100;
        year++;
    }
cout << year << "\n";
}