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 (gfortran v4.8.4) (judge verdict: Accepted)

program digits_in_multiplication
  implicit none
  integer(8) :: n, m, h, l, i
  read(*,*) n
  m = int(ceiling(sqrt(real(n,8))),8)
  h = n/2_8
  l = 0_8
  do i = m, 1_8, -1_8
    if (mod(n,i).eq.0_8) then
      l = n/i
      exit
    end if
  end do
  if (l.eq.0_8) then
    write(*,'(i0)') int(log10(real(n,8))) + 1
  else
    write(*,'(i0)') int(log10(real(l,8))) + 1
  end if
end program digits_in_multiplication