Hacker Cup contest strategy often involves a metagame, where choosing which problems to work on might just be an important decision. On a Quest to become more Pro, you encounter an oracle promising to teach you the contest meta if you play her own Meta-game.

The oracle presents a peg board with (2N) moving dots. The initial (y)-positions of the dots are given as two arrays (A_{1..N}) and (B_{1..N}). Each second, simultaneously, (A_1) will move to the end of (B), while (B_1) will move to the end of (A) (with all elements shifting left accordingly).

You can connect the dots to form a Meta-like logo if all of the following are true:

For the first half of both arrays, each dot in (A) is below the corresponding dot in (B).
For the last half of both arrays, each dot in (A) is above the corresponding dot in (B).
(A) equals the reverse of (B).

Formally:

(A_i < B_i) for every (i < (N+1)/2)
(A_i > B_i) for every (i > (N+1)/2)
(A_i = B_{N-i+1}) for every (i = 1..N)

Note that if (N) is odd, the arrays' middle elements are not subject to the first two constraints.

The following is a visualization of a Meta-like logo (corresponding to the first sample case), with dots in (A) shown in red and dots in (B) shown in blue.

You must answer the oracle: how many seconds must pass before the first time a Meta-like logo appears? If one never appears, output (-1).

Constraints

(1 \leq T \leq 135) (2 \leq N \leq 2{,}000{,}000) (0 \leq A_i, B_i \leq 1{,}000{,}000{,}000)

The sum of (N) across all test cases is at most (9{,}000{,}000).

Input Format

Input begins with an integer (T), the number of test cases. For each case, there is first a line containing a single integer (N). Then, there is a line containing integers (A_1, ..., A_N). Then, there is a line containing integers (B_1, ..., B_N).

Output Format

For the (i)th test case, print "Case #i: " followed by a single integer, the number of seconds that must pass before a Meta-like logo appears, or (-1) if that will never happen.

Sample Explanation

The first test case is shown above. (A) and (B) already form a Meta-like logo, so the answer is 0.

The second case is not initially a Meta-like logo, for several reasons. One reason is that it is not symmetric. Specifically, the ([3, 3, 2, 3, 5 ,6]) is not the reverse of ([4, 4, 6, 5, 3 ,2]). After (1) second though, this case turns into the case above and is Meta-like.

The third and fourth cases will never turn into a Meta-like logo, no matter how many seconds we wait.

In the fifth case, after 6 seconds we see the first Meta-like logo. In this case (A = [1, 1, 2, 2]) and (B = [2, 2, 1, 1]).