Make a Square
Description
You are given a positive integer $n$, written without leading zeroes (for example, the number 04 is incorrect).
In one operation you can delete any digit of the given integer so that the result remains a positive integer without leading zeros.
Determine the minimum number of operations that you need to consistently apply to the given integer $n$ to make from it the square of some positive integer or report that it is impossible.
An integer $x$ is the square of some positive integer if and only if $x=y^2$ for some positive integer $y$.
The first line contains a single integer $n$ ($1 \le n \le 2 \cdot 10^{9}$). The number is given without leading zeroes.
If it is impossible to make the square of some positive integer from $n$, print -1. In the other case, print the minimal number of operations required to do it.
Input
The first line contains a single integer $n$ ($1 \le n \le 2 \cdot 10^{9}$). The number is given without leading zeroes.
Output
If it is impossible to make the square of some positive integer from $n$, print -1. In the other case, print the minimal number of operations required to do it.
Samples
8314
2
625
0
333
-1
Note
In the first example we should delete from $8314$ the digits $3$ and $4$. After that $8314$ become equals to $81$, which is the square of the integer $9$.
In the second example the given $625$ is the square of the integer $25$, so you should not delete anything.
In the third example it is impossible to make the square from $333$, so the answer is -1.