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 $N = A \times B$.