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.

Samples

8
??
?
0
9
03
1??7
?5?
9??99

90
9
0
1
0
100
90
100