题目描述

I have written down a large perfect square in binary, and then replaced some of the digits with question marks. Can you figure out what my original number was?

输入格式

The first line of the input gives the number of test cases, $T$. $T$ test cases follow, one per line. Each line contains $S$: a perfect square written in binary, but with some of the digits replaced by question marks.

输出格式

For each test case, output one line containing "Case #$x$: $N$", where $x$ is the case number (starting from 1) and $N$ is a perfect square written in binary, obtained by replacing each '?' character in $S$ with either a '0' character or a '1' character.

3
1???
1
10??110??00??1000??

Case #1: 1001
Case #2: 1
Case #3: 1011110110000100001

提示

Limits

• $1 \leq T \leq 25$.
• $S$ begins with '1'.
• $S$ contains only the characters '0', '1', and '?'.
• In every test case, there is exactly one possible choice for $N$.

Small dataset (10 Pts, Test set 1 - Visible)

• $S$ is at most $60$ characters long.
• $S$ contains at most $20$ '?' characters.
• Time limit: 30 6 seconds.

Large dataset (31 Pts, Test set 2 - Hidden)

• $S$ is at most $125$ characters long.
• $S$ contains at most $40$ '?' characters.
• Time limit: 60 20 seconds.