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)

import scala.annotation.tailrec
import scala.io.StdIn

object Main extends App {

  def f(a:Long, b:Long):Long = {
    @tailrec
    def rec(acc:Long, num:Long):Long = {
      if(num == 0L) acc
      else rec(acc+1L, num/10L)
    }
    math.max(rec(0L,a), rec(0L,b))
  }

  val n =StdIn.readLong
  val r = math.sqrt(n).toLong
  val ans = (2L to r)./:(f(n, 1))((acc,i) => {
    if(n % i == 0) math.min(acc, f(n/i, i))
    else acc
  })
  println(ans)
}