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 Julia (0.5.0) (judge verdict: Accepted)

if isfile("mystdin.txt");mystdin=open("mystdin.txt","r");redirect_stdin(mystdin);end
pI(x)=parse(Int,x)
pM(x::Array{SubString{String},1})=map(pI,x)
function mkdivisorpair(n::Int)
  divisors=[]
  for i=1:div(n^0.5,1)
    if n%i==0
      push!(divisors,(Int(i),Int(n/i)))
    end
  end
  sort!(divisors)
  return divisors
end
function main()
  d=mkdivisorpair(pI(readline()))
  ans=100000
  for i in d
    ans=min(ans,max(ndigits(i[1]),ndigits(i[2])))
  end
  println(ans)
end
main()
if isdefined(Base, :mystdin);close(mystdin);end