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.math.*

fun main(args: Array<String>) {
    val N = readInputLine().toLong()

    var ans = Int.MAX_VALUE

    for (i in LongRange(1L, Math.ceil(Math.sqrt(N.toDouble())).toLong())) {
        if (N % i != 0L) {
            continue
        }
        ans = Math.min(ans, countDigits(N / i))
    }

    println(ans)
}

fun readInputLine(): String {
    return readLine()!!
}

fun countDigits(i: Long): Int {
    var ans = 0
    var tmp = i
    while (tmp != 0L) {
        ans++
        tmp /= 10L
    }
    
    return ans
}