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C. Make a Square
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$y$$$.

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.

Examples
Input
8314
Output
2
Input
625
Output
0
Input
333
Output
-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.