Migrated from Lutece 491 Tricks in Bits

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Description

Given $N$ unsigned $64$-bit integers, you can bitwise NOT each or not. Then you need to add operations selected from bitwise XOR, bitwise OR and bitwise AND, between any two successive integers and calculate the result. Your job is to make the result as small as possible.

Input

The first line of the input is $T$ (no more than $1000$), which stands for the number of test cases you need to solve.

Then $T$ blocks follow. The first line of each block contains a single number $N$ ($1 \leq N \leq 100$) indicating the number of unsigned $64$-bit integers. Then $n$ integers follow in the next line.

Output

For every test case, you should output Case #k: first, where $k$ indicates the case number and counts from $1$. Then output the answer.

Samples

2
3
1 2 3
2
3 6

Case #1: 0
Case #2: 1

Note

• Case #$1$: 1|2^3 = 0
• Case #$2$: 3&(~6) = 1

The bitwise NOT, is a unary operation that performs logical negation on each bit, forming the ones' complement of the given binary value. Digits which were $0$ become $1$, and vice versa.

The bitwise OR takes two bit patterns of equal length, and produces another one of the same length by matching up corresponding bits (the first of each; the second of each; and so on) and performing the logical inclusive or operation on each pair of corresponding bits. In each pair, the result is $1$ if the first bit is $1$ or the second bit is $1$ or both bits are $1$; otherwise, the result is $0$.

The bitwise XOR takes two bit patterns of equal length and performs the logical XOR operation on each pair of corresponding bits. The result in each position is $1$ if the two bits are different, and $0$ if they are the same.

Resources

Sichuan State Programming Contest 2011