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)

fun main(args: Array<String>) {
    val N = nextLong()
    val max = Math.sqrt(N.toDouble()).toLong()
    var ans = Int.MAX_VALUE
    var a = 1L
    while (a <= max) {
        try {
            if (N % a != 0L) continue
            val b = N / a
            ans = Math.min(ans, Math.max(D(a), D(b)))
        } finally {
            a += 1
        }
    }
    println(ans)
}
fun D(d: Long) =
    if (d > 999999999L) 10 else
    if (d > 99999999L) 9 else
    if (d > 9999999L) 8 else
    if (d > 999999L) 7 else
    if (d > 99999L) 6 else
    if (d > 9999L) 5 else
    if (d > 999L) 4 else
    if (d > 99L) 3 else
    if (d > 9L) 2 else 1
fun next() = readLine()!!
fun nextInt(delta: Int = 0) = Integer.parseInt(next()) + delta
fun nextLong() = next().toLong()
fun listOfString() = next().split(" ")
fun listOfLong() = listOfString().map(String::toLong)