Greatest Greatest Common Divisor

Time Limit: 4000/2000 MS (Java/Others)

Memory Limit: 65536/65536 K (Java/Others)

Description

Pick two numbers ${a}_{i},{a}_{j}(i\neq j)$ from a sequence to maximize the value of their greatest common divisor.

Input

Multiple test cases. In the first line there is an integer $T$, indicating the number of test cases. For each test cases, the first line contains an integer $n$, the size of the sequence. Next line contains $n$ numbers, from ${a}_{1}$ to ${a}_{n}$. $1\leq T\leq 100,2\leq n\leq {10}^{5},1\leq {a}_{i}\leq {10}^{5}$. The case for $n\geq {10}^{4}$ is no more than $10$.

Output

For each test case, output one line. The output format is Case #$x$: $ans$, $x$ is the case number, starting from $1$, $ans$ is the maximum value of greatest common divisor.

Sample Input

2 4 1 2 3 4 3 3 6 9

Sample Output

Case #1: 2 Case #2: 3

Hint

hujie

Source

BestCoder Round #38 ($)

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