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)

dividers::Int ->[Int]
dividers n = filter (\x-> (mod n x ) == 0 ) [1..(truncate (sqrt (fromIntegral n)))]

able::Int -> [(Int,Int)]
able n = [(i ,div n i)|i<-dividers n]

dig::Int -> Int
dig x = length (takeWhile (\y->x>=y) [ 10^i |i<-[0..]])

solver::Int -> Int
solver n =  minimum (map (\(x,y)-> dig (max x y)) (able n))

main::IO()
main=do
  nc<-getLine
  print (solver (read nc))