Problem C

2-D Nim

Input: standard input
Output: standard output

TimeLimit: 1 second

The 2D-Nim board game is played on a grid, withpieces on the grid points. On each move, a player may remove any positive numberof contiguous pieces in any row or column. The player who removes the lastpiece wins. For example, consider the left grid in the following figure.

The player on move may remove (A), (B), (A,B), (A, B, C), or (B,F), etc., but may not remove (A, C),(D, E), (H, I) or (B, G). For purposes of writing 2D-Nim-playingsoftware, a certain programmer wants to be able to tell whether or not acertain position has ever been analyzed previously. Because of the rules of 2D-Nim,it should be clear that the two boards above are essentially equivalent. Thatis, if there is a winning strategy for the left board, the same one must applyto the right board. The fact that the contiguous groups of pieces appear indifferent places and orientations is clearly irrelevant. All that matters isthat the same clusters of pieces (a cluster being a set of contiguous piecesthat can be reached from each other by a sequence of one-square vertical orhorizontal moves) appear in each. For example, the cluster of pieces (A, B,C, F, G) appears on both boards, but it has been reflected (swapping leftand right), rotated, and moved. Your task is to determine whether two givenboard states are equivalent in this sense or not.

Input

The first line of the input file contains a single integert (1<=t<=12), the number of test cases,  followed by the input data for each testcase. The first line of each test case consists of three integers W, H,and n (1 <=W, H<=100). W is the width, and H is the height of the gridin terms of the number of grid points. n(n<=3000) is the number of pieces on each board. Thesecond line of each test case contains a sequence of npairs of integers x_i,y_i, givingthe coordinates of the pieces on the first board (0 =< x_i < W and 0 =< y_i<H). The third line of the test case describes the coordinates of the pieceson the second board in the same format.

Output

Your program should produce a single line for each testcase containing a word YES or NO indicating whether the twoboards are equivalent or not.

SampleInput                                      Output for Sample Input

2

8 5 11

0 0 1 0 2 0 5 0 7 0 1 1 2 1 5 1 3 3 5 2 4 4

0 4 0 3 0 2 1 1 1 4 1 3 3 3 5 2 6 2 7 2 7 4

8 5 11

0 0 1 0 2 0 5 0 7 0 1 1 2 1 5 1 3 3 6 1 4 4

0 4 0 3 0 2 1 1 1 4 1 3 3 3 5 2 6 2 7 2 7 4

YES

NO

Problem Source: IranianContest

Special Thanks: Jimmy Mårdell, EPS.