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 (2.7.1) (judge verdict: Accepted)

def ketashirabe(atai)
  kaisu=0
  k=atai
  loop{
    if(k/10!=0)
      k=k/10
    kaisu+=1
    else 
      return kaisu+1
    end 
  }
end

m=gets.to_i
result=[]
dasu=[]
ha=Array.new
for a in 1..m**(1/2.0)
  if(m%a==0&&a<=m/a)
  ha<<a
  ha<<m/a
  result.push(ha)
  ha=[]
  end
end

for sa in 0..result.length-1
  if(ketashirabe(result[sa][0])>=ketashirabe(result[sa][1]))
  dasu.push(ketashirabe(result[sa][0]))
  else
    dasu.push(ketashirabe(result[sa][1]))
  end
end

puts dasu.min