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.readLine().toLong

  def solve(): Long = {
    val sqrtN = Math.floor(Math.sqrt(n)).toInt
    (1 to sqrtN).foldLeft(Int.MaxValue) { case (acc, a) =>
      if(n % a == 0) {
        val b = n / a
        val tmpMax = maxDigit(a, b)
        Math.min(acc, tmpMax)
      } else acc
    }
  }

  def maxDigit(a: Long, b: Long) = {
    Math.max(a.toString.length, b.toString.length)
  }

  println(solve)

}