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)

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

#define M 1000000007
#define MM 998244353 
#define ll long long 
#define pb push_back
#define mem0(a) memset(a,0,sizeof(a))
#define mem1(a) memset(a,-1,sizeof(a))
#define memf(a) memset(a,false,sizeof(a))
#define all(v) v.begin(),v.end()
#define sz(a) (ll)a.size()
#define F first
#define S second
#define PI 3.1415926536
#define INF 2000000000000000000
#define endl "\n"
#define _time_ 1.0 * clock() / CLOCKS_PER_SEC
#define popcount(x) __builtin_popcountll(x)
//RNG based on mersenne_twister 
mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
ll power(ll b,ll e,ll m)
{
	if(e==0) return 1;
	if(e&1) return b*power(b*b%m,e/2,m)%m;
	return power(b*b%m,e/2,m);
}
ll power( ll b, ll e)
{
	if(e==0) return 1;
	if(e&1) return b*power(b*b,e/2);
	return power(b*b,e/2);
}
template<typename T, typename U> static inline void amin(T &x, U y){ if(y<x) x=y; }
template<typename T, typename U> static inline void amax(T &x, U y){ if(x<y) x=y; }


int _runtimeTerror_()
{
	ll n;
	cin>>n;
	ll val2=0;
	ll ans=100;
	while(ans<n)
	{
		long double val=ans*1.01;
		ans=val;
		ans=floor(ans);
		++val2;
	}
	cout<<val2;
	return 0;
}

int main()
{
	ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	#ifdef runSieve
		sieve();
	#endif
	#ifdef NCR
		initialize();
	#endif
	int TESTS=1;
	//cin>>TESTS;
	while(TESTS--)
		_runtimeTerror_();
	cerr<<"\n"<<_time_;
	return 0;
}