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: Accepted)

object Main extends App {
	val N = scala.io.StdIn.readLong
	val T = math.sqrt(N).toLong

	@inline def check(x: Long): Int = {
		var ans = 1
		var tp1 = x
		var tp2 = 10L
		while(tp1/tp2 != 0){
			ans += 1
			tp2 *= 10L
		}
		return ans
	}

	var ans = Int.MaxValue

	for(x<-1L to T){
		if(N%x == 0){
			val y = N/x
			val p = math.max(check(x), check(y))
			ans = math.min(ans, p)
		}
	}

	println(ans)

	
}