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 Fortran (GNU Fortran 9.2.1) (judge verdict: Wrong Answer)

integer,parameter :: p = 8
integer(p) :: n,i

do i = ceiling(sqrt(real(n))),1,-1
  if( mod(n,i)==0 ) exit
end do

print*,max(digit(i),digit(n/i))

contains
function digit( n ) result( i )
  integer(p) :: i,n
  i = 0
  do while( n/=0 )
    n = n / 10
    i = i + 1
  end do
end function
    

end