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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.*;
import java.io.*;
import java.lang.*;
import java.math.*;
 
public class Main {

  static class Reader {

    final private int BUFFER_SIZE = 1 << 16; 
    private DataInputStream din; 
    private byte[] buffer; 
    private int bufferPointer, bytesRead; 

    public Reader() { 
      din = new DataInputStream(System.in); 
      buffer = new byte[BUFFER_SIZE]; 
      bufferPointer = bytesRead = 0; 
    } 

    public Reader(String file_name) throws IOException { 
      din = new DataInputStream(new FileInputStream(file_name)); 
      buffer = new byte[BUFFER_SIZE]; 
      bufferPointer = bytesRead = 0; 
    } 

    public String readLine() throws IOException { 
      byte[] buf = new byte[64]; // line length 
      int cnt = 0, c; 
      while ((c = read()) != -1) { 
        if (c == '\n') 
          break; 
        buf[cnt++] = (byte) c; 
      } 
      return new String(buf, 0, cnt); 
    } 

    public int nextInt() throws IOException { 
      int ret = 0; 
      byte c = read(); 
      while (c <= ' ') 
        c = read(); 
      boolean neg = (c == '-'); 
      if (neg) 
        c = read(); 
      do { 
        ret = ret * 10 + c - '0'; 
      } while ((c = read()) >= '0' && c <= '9'); 

      if (neg) 
        return -ret; 
      return ret; 
    } 

    public long nextLong() throws IOException { 
      long ret = 0; 
      byte c = read(); 
      while (c <= ' ') 
        c = read(); 
      boolean neg = (c == '-'); 
      if (neg) 
        c = read(); 
      do { 
        ret = ret * 10 + c - '0'; 
      } 
      while ((c = read()) >= '0' && c <= '9'); 
      if (neg) 
        return -ret; 
      return ret; 
    } 

    public double nextDouble() throws IOException { 
      double ret = 0, div = 1; 
      byte c = read(); 
      while (c <= ' ') 
        c = read(); 
      boolean neg = (c == '-'); 
      if (neg) 
        c = read(); 

      do { 
        ret = ret * 10 + c - '0'; 
      } 
      while ((c = read()) >= '0' && c <= '9'); 

      if (c == '.') { 
        while ((c = read()) >= '0' && c <= '9') { 
          ret += (c - '0') / (div *= 10); 
        } 
      } 

      if (neg) 
        return -ret; 
      return ret; 
    } 

    private void fillBuffer() throws IOException { 
      bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
      if (bytesRead == -1) 
        buffer[0] = -1; 
    } 

    private byte read() throws IOException { 
      if (bufferPointer == bytesRead) 
        fillBuffer(); 
      return buffer[bufferPointer++]; 
    } 

    public void close() throws IOException { 
      if (din == null) 
        return; 
      din.close(); 
    } 
  }

 
  public static void main(String args[]) throws IOException {
    // try {
    //   FileOutputStream output = new FileOutputStream("temp.out");
    //   PrintStream out = new PrintStream(output);
    //   //Diverting the output stream into file "temp.out".Comment the below line to use console
    //   System.setOut(out);
  
    //   InputStream input = new FileInputStream("temp.in");
    //   //Diverting the input stream into file "temp.in".Comment the below line to use console
    //   System.setIn(input);
    
    // } catch (FileNotFoundException e) {
    //   e.printStackTrace();
    // }
  
    // Scanner sc = new Scanner(System.in);
    Reader sc = new Reader();
    // BufferedReader sc = new BufferedReader(new InputStreamReader(System.in));
    PrintWriter wr = new PrintWriter(System.out);

    // int t = 1;
    // t = sc.nextInt();    //Comment this line if there is single test case
    
    // while((t--) != 0) {




    // }

    long x = sc.nextLong();

    long p = 100, step = 0;

    while(p < x){
      // wr.println(p / 100);
      p += p / 100;
      step++;
    } 

    wr.println(step);

    
    wr.flush();
    wr.close();
  }
}