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 (1.3.71) (judge verdict: Accepted)

fun main(args: Array<String>) {

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

    var result = Int.MAX_VALUE

    loop@ for (i in 1..n) {

        val b = n / i
        if (i > b) {
            break@loop
        }

        if (n % i == 0L) {
            // 約数でこのときのiと商をペアの配列として確保
            val ilen = cntDigits(i)
            val blen = cntDigits(b)

            val fResult = if (ilen < blen) blen else ilen
            // kotlinのデータ型変換はtoXXXで良いのか???
            if (result > fResult) result = fResult
        }
    }

    println(result)
}

// toString.lengthで桁数を求めてみたが、性能が間に合わず???
// kotlinでメソッドの引数を変更したときどうする???
// 桁数算出メソッドを作成したが -> NG 実行時間ほぼ同じ
fun cntDigits(num: Long): Int {

    var digits = 0
    var target = num

    while (target > 0) {
        target /= 10
        digits++
    }
    return digits
}