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 Ruby (2.3.3) (judge verdict: Wrong Answer)

include Math
define_method :max, -> (a,b) { a > b ? a : b }
define_method :min, -> (a,b) { a < b ?  a : b }
define_method :swap, -> (a,b) { a, b = b, a }
define_method :rep, -> (num, &block) { num.times do |i| block.call(i)  end }
define_method :repl, -> (st,en, &block) { st.upto en-1 do |i| block.call(i) end }
define_method :array, -> (size,init = nil) { Array.new(size){init} }
define_method :darray, -> (size1, size2, init = nil) { Array.new(size1){Array.new(size2){init}} }
define_method :gi, -> () { gets.split.map(&:to_i) }
define_method :gs, -> () { gets.chomp }
define_method :putall, -> (obj) { obj.each do |o| puts o end }



n = gi[0]
ans = Float::INFINITY

repl 1,sqrt(n) do |i|
	if n % i == 0
		a = (n / i).to_s.length
		b = i.to_s.length
		m = max(a,b)
		ans = m if m < ans
	end
end

puts ans