Problem:
Score : 300 points

Problem Statement

You are given an integer N.

For two positive integers A and B, we will define F(A,B) as the larger of the following: the number of digits in the decimal notation of A, and the number of digits in the decimal notation of B.

For example, F(3,11) = 2 since 3 has one digit and 11 has two digits.

Find the minimum value of F(A,B) as (A,B) ranges over all pairs of positive integers such that N = A \times B.

Constraints

1 \leq N \leq 10^{10}

N is an integer.

Input

The input is given from Standard Input in the following format:

N

Output

Print the minimum value of F(A,B) as (A,B) ranges over all pairs of positive integers such that N = A \times B.

Sample Input 1

10000

Sample Output 1

3

F(A,B) has a minimum value of 3 at (A,B)=(100,100).

Sample Input 2

1000003

Sample Output 2

7

There are two pairs (A,B) that satisfy the condition: (1,1000003) and (1000003,1). For these pairs, F(1,1000003)=F(1000003,1)=7.

Sample Input 3

9876543210

Sample Output 3

6

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

import qualified Data.ByteString.Char8 as BS
import Control.Monad
import Control.Monad.ST
import Data.List
import Data.Maybe (fromJust)

data Pair = Pair Integer Integer deriving Show


getDivisorPairs :: Integer -> Integer -> [Pair]
getDivisorPairs a b
    | a < b * b = []
    | a `mod` b == 0 = (Pair (a `div` b) b):(getDivisorPairs a (b + 1))
    | otherwise = getDivisorPairs a (b + 1)


getDigitCountPair :: Pair -> Integer
getDigitCountPair (Pair a b) = max (getDigitCount a) (getDigitCount b)


getDigitCount :: Integer -> Integer
getDigitCount 0 = 0
getDigitCount n = 1 + (getDigitCount (n `div` 10))


solve :: Integer -> Integer
solve n = minimum counts
    where
        pairs = getDivisorPairs n 1
        counts = map getDigitCountPair pairs


main :: IO ()
main = do
    n <- fst . fromJust . BS.readInteger <$> BS.getLine
    print $ solve n