A small sheet of thick paper laid on the table next to the vault. There were some kind of formulas with wiped out figures written on it. It’s likely that a long time ago these notes were quite easy to read, but the decades spent in the castle negatively affected the readability of some figures. By figuring out what figures were originally written, you’ll be able to find the correct combination for opening of the vault.

Your task is to create a function that as input receives an equation in a form of a string with digits, erased places ('#') and one of the three arithmetic operations (+, - or *), for example - "##*##=302#". As a result, your function...

Important note - none of the figures that already are in the equation cannot be in place of #. Also, if after the equal sign (=) there are 2 or more missing symbols, the answer cannot consist of zeros (00, 000, etc.).

Numbers in the format like #n, #nn and so on, where n - any digit, can't start with 0. For example, "#9+3=12" == -1.

In case there are several suitable digits - use the smallest of them.
The numbers in the formula can be both positive (for example, "1+1=#") and negative, with the "-" sign before them ("19--45=5#", "-1*-6=#").