100572: [AtCoder]ABC057 C - Digits in Multiplication

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