Matching

An integer template is a string consisting of digits and/or question marks.

A positive (strictly greater than $$$0$$$) integer matches the integer template if it is possible to replace every question mark in the template with a digit in such a way that we get the decimal representation of that integer without any leading zeroes.

For example:

• $$$42$$$ matches 4?;
• $$$1337$$$ matches ????;
• $$$1337$$$ matches 1?3?;
• $$$1337$$$ matches 1337;
• $$$3$$$ does not match ??;
• $$$8$$$ does not match ???8;
• $$$1337$$$ does not match 1?7.

You are given an integer template consisting of at most $$$5$$$ characters. Calculate the number of positive (strictly greater than $$$0$$$) integers that match it.