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Problems

A + B Problem

A + B Problem

Time limit 1 second
Memory limit 64 MiB

Do you know the famous Fibonacci sequence? It is defined by the recurrence

F_0 = 0, F_1 = 1 and F_n = F_{n-1} + F_{n-2} for n2.

The Fibonacci numbers have many interesting properties. One of them is that the Fibonacci numbers can be used to represent integers. Every positive integer has a unique representation of the form

n = F_k1 + F_k2 + … + F_km, k_ik_{i-1} + 2 for 2im and k_12

For example, 6 can be represented as F_2+F_5 and 12 can be represented as F_2+F_4+F_6.

Now you know how to represent positive integers with the Fibonacci numbers, can you add them? Given two Fibonacci formed integers, you should calculate the sum of them.

Input data

The first line contains a single integer T, indicating the number of test cases.

Each test case contains two lines; each line contains a single integer m followed by m integers k_1, k_2, …, k_m indicate a Fibonacci formed integer F_k1+F_k2+…+F_km.

The input will be always correct. 1T100, 1m100, 2k_i1000000.

Output data

For each test case, output the case number first, then a single line indicates the sum of the two Fibonacci formed integer. The sum should be Fibonacci formed like the input.

Examples

Input example #1
2
1 2
2 2 4
3 2 4 6
2 2 5
Output example #1
Case 1:
1 5
Case 2:
2 5 7