Bits Equalizer

You are given two non-empty strings $S$ and $T$ of equal lengths. $S$ contains the characters ‘0’, ‘1’ and ‘?’, whereas $T$ contains ‘0’ and ‘1’ only. Your task is to convert $S$ into $T$ in minimum number of moves. In each move, you can

  1. change a ‘0’ in $S$ to ‘1’,

  2. change a ‘?’ in $S$ to ‘0’ or ‘1’, or

  3. swap any two characters in $S$.

As an example, suppose $S =$01??00” and $T =$001010”. We can transform $S$ into $T$ in 3 moves:

  • Initially $S =$01??00

  • Move 1: change $S[2]$ to ‘1’. $S$ becomes “011?00”.

  • Move 2: change $S[3]$ to ‘0’. $S$ becomes “011000

  • Move 3: swap $S[1]$ with $S[4]$. $S$ becomes “001010

  • $S$ is now equal to $T$.

Input

The first line of input is an integer $C$ ($C \leq 200$) that indicates the number of test cases.

Each case consists of two lines. The first line is the string $S$ consisting of ‘0’, ‘1’ and ‘?’. The second line is the string $T$ consisting of ‘0’ and ‘1’. The lengths of the strings won’t be larger than $100$.

Output

For each case, output the case number first followed by the minimum number of moves required to convert $S$ into $T$. If the transition is impossible, output $-1$ instead.

Sample Input 1 Sample Output 1
3
01??00
001010
01
10
110001
000000
Case 1: 3
Case 2: 1
Case 3: -1