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.

Input

The first line contains one integer $$$t$$$ ($$$1 \le t \le 2 \cdot 10^4$$$) — the number of test cases.

Each test case consists of one line containing the string $$$s$$$ ($$$1 \le |s| \le 5$$$) consisting of digits and/or question marks — the integer template for the corresponding test case.

Output

For each test case, print one integer — the number of positive (strictly greater than $$$0$$$) integers that match the template.

Matching

Examples