#10635Prince and Princess

★★★★

時間限制：2000 毫秒記憶體限制：64 MB

In an n × n chessboard, Prince and Princess plays a game. The squares in the chessboard are numbered 1, 2, 3, . . . , n ∗ n, as shown below:

n x n chessboard numbered in a spiral/boustrophedon pattern from 1 to n*n

Prince stands in square 1, make p jumps and finally reach square n ∗ n. He enters a square at most once. So if we use x to denote the p-th square he enters, then x, x, …, x are all different. Note that x = 1 and x = n ∗ n. Princess does the similar thing – stands in square 1, make q jumps and finally reach square n ∗ n. We use y, y, …, y to denote the sequence, and all q + 1 numbers are different.

範例輸入 1

1
3 6 7
1 7 5 4 8 3 9
1 4 3 5 6 2 8 9

範例輸出 1

Case 1: 4

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₁

₂

_p+1

₁

_p+1

₁

₂

_q+1

Figure 2 belows show a 3×3 square, a possible route for Prince and a different route for Princess.

Figure 2 and Figure 3: a 3x3 board with the Prince's and Princess's routes drawn as arrows, and their common route

The Prince moves along the sequence: 1 –> 7 –> 5 –> 4 –> 8 –> 3 –> 9 (Black arrows), while the Princess moves along this sequence: 1 –> 4 –> 3 –> 5 > 6 –> 2 –> 8 –> 9 (White arrow).

The King – their father, has just come. “Why move separately? You are brother and sister!” said the King, “Ignore some jumps and make sure that you’re always together.”

For example, if the Prince ignores his 2nd, 3rd, 6th jump, he’ll follow the route: 1 –> 4 –> 8 –> 9. If the Princess ignores her 3rd, 4th, 5th, 6th jump, she’ll follow the same route: 1 –> 4 –> 8 –> 9, (The common route is shown in figure 3) thus satisfies the King, shown above. The King wants to know the longest route they can move together, could you tell him?

Input

The first line of the input contains a single integer t (1 ≤ t ≤ 10), the number of test cases followed. For each case, the first line contains three integers n, p, q (2 ≤ n ≤ 250, 1 ≤ p, q < n ∗ n). The second line contains p + 1 different integers in the range [1 . . . n ∗ n], the sequence of the Prince. The third line contains q + 1 different integers in the range [1 . . . n ∗ n], the sequence of the Princess.

Output

For each test case, print the case number and the length of longest route. Look at the output for sample input for details.