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Contest: Task: Related: TaskA TaskC

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