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 java.util.Scanner

import scala.collection.mutable.ArrayBuffer

object Main extends App {
  def solve: Unit = {
    val sc = new Scanner(System.in)
    val N = sc.next.toLong
    var divisor = new ArrayBuffer[Int]
    for (i <- 1 to 100000) {
      if (N % i == 0) {
        divisor += i
      }
    }
    var ans = 1000000
    for (i <- divisor) {
      ans = math.min(ans, math.max(i.toString.length, (N / i).toString.length))
    }
    println(ans)
  }

  solve
}