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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.io.InputStreamReader
import java.io.BufferedReader

fun main(args: Array<String>) {
  val br = BufferedReader(InputStreamReader(System.`in`))

  val n = br.readLine().toLong()

  tailrec fun digit(acc: Int, i: Long):Int =
    if(i == 0L) acc else digit(acc+1, i/10)

  tailrec fun rec(a: Long): Int =
    if(n % a == 0L) {
      val b = n / a
      Math.max(digit(0, a), digit(0, b))
    }
    else rec(a-1)

  val nSqrt = Math.sqrt(n.toDouble()).toLong()
  val ans = rec(nSqrt)

  println(ans)
}