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 Scala (2.11.7) (judge verdict: Runtime Error)


object Main extends App {
	def Ndigits(x: Int): Int = {
		var z = x;
		var i = 1
		while(z > 1){
			z = z / 10;
			i = i + 1;
		}
		i
	}

	val N = io.StdIn.readLine.toInt
	var result = N;

	for(i <- 1 to N/2){
		if(N%i == 0){
			val temp = math.max(Ndigits(i), Ndigits(N/i))
			if(result > temp){
				result = temp;
			}
		}
	}

	println(result)
}