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: Wrong Answer)

function dig(n)
	k = 0
	while 10^k <= n
		k += 1
	end
	k
end

function main()
	n = parse(Int, readline())
	if n == 1
		println(1)
	else
		m = n
		k = 2
		s = Int[]
		while k <= sqrt(n)
			if m % k == 0
				push!(s,k)
				m = div(m,k)
			else
				k += 1
			end
		end
		if m > sqrt(n)
			push!(s,m)
		end
		if length(s) == 1
			print(dig(s[1]))
		else
			l = s[length(s)-1]
			r = s[length(s)]
			for i in 2:length(s)-1
				if l > r
					r = r*s[length(s)-i]
				else
					l = l*s[length(s)-i]
				end
			end
			print(max(dig(l),dig(r)))
		end
	end
end

main()