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 Haskell (GHC 8.8.3) (judge verdict: Accepted)


import qualified Data.Vector.Unboxed as U
import qualified Data.Vector as V
import qualified Data.ByteString.Char8 as C
import Debug.Trace
import Data.List
import Control.Monad
import Control.Arrow
import Data.Ord


r :: Int -> IO (U.Vector Int)
r n = U.unfoldrN n (C.readInt . C.dropWhile (==' ')) <$> C.getLine

r' :: IO [Int]
r'  =   unfoldr    (C.readInt . C.dropWhile (==' ')) <$> C.getLine



main :: IO ()
main = do
    x <- readLn :: IO Int
    print $ slv x 100 0

di :: Int -> Int
di x = floor (fromIntegral x * 1.01)

slv x am ac
    | am >= x = ac
    | otherwise = slv x (di am) (ac+1)