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: Accepted)

require 'pp'
require 'prime'
require 'set'

N=gets.chomp.split(' ').map{|n| n.to_i}.first
#
# if Prime.prime?(N)
#   puts N-1
#   exit
# end
#
# a=0
# b=0
#
# mini = 1_000_000_000_000_0
# source = Math.sqrt(N).to_i+1
# 1.upto(source) do |n|
#   next if N%n!=0
#   a=n
#   b=N/n
#   if ((a-1 + b-1) < mini)
#     mini = a-1 + b-1
#   end
# end
#
# puts mini
#
#
#

# a,b,x=gets.chomp.split(' ').map{|n| n.to_f}

def divisors(n)
  n.prime_division.inject([1]) do |ary, (p, e)|
    (0..e).map{ |e1| p ** e1 }.product(ary).map{ |a, b| a * b }
  end.sort
end

def arc057func(a,b)
  [a.to_s.size, b.to_s.size].max
end

ans = 10**10
divisors(N).each do |n|
  candidate = arc057func(n, N/n)
  if candidate < ans
    ans = candidate
  end
end

puts ans