Migrated from Lutece 836 Kia's Calculation

All parts of this problem, including description, images, samples, data and checker, might be broken. If you find bugs in this problem, please contact the admins.

Description

Doctor Ghee is teaching Kia how to calculate the sum of two integers. But Kia is so careless and alway forget to carry a number when the sum of two digits exceeds $9$. For example, when she calculates $4567+5789$, she will get $9246$, and for $1234+9876$, she will get $0$. Ghee is angry about this, and makes a hard problem for her to solve:

Now Kia has two integers $A$ and $B$, she can shuffle the digits in each number as she like, but leading zeros are not allowed. That is to say, for $A = 11024$, she can rearrange the number as $10124$, or $41102$, or many other, but $02411$ is not allowed.

After she shuffles $A$ and $B$, she will add them together, in her own way. And what will be the maximum possible sum of $A$ + $B$?

Input

The first line has a number $T$ ($T \leq 25$) , indicating the number of test cases.

For each test case there are two lines. First line has the number $A$, and the second line has the number $B$.

Both $A$ and $B$ will have same number of digits, which is no larger than $10^6$, and without leading zeros.

Output

For test case $X$, output Case #X: first, then output the maximum possible sum without leading zeros.

Samples

1
5958
3036

Case #1: 8984

Resources

2013 ACM-ICPC China Chengdu Provincial Programming Contest