2D-Nim#1009
The 2D-Nim board game is played on a rectangular grid, where pieces are placed on grid points. On each move, a player may remove any positive number of contiguous pieces in any row or column. For example, consider the left board in the following figure:
The player can remove (A), (B), (A, B), (A, B, C), or (B, F), and so on. However, it is not allowed to remove (A, C), (D, E), (H, I), or (B, G).
For the purpose of creating 2D-Nim-playing software, it is necessary to determine whether a given board configuration has already been analyzed. According to the game rules, the two positions shown above are considered equivalent. That is, if there is a winning strategy for the left board, the same strategy applies to the right board as well. The contiguous groups of pieces may appear in any location or orientation. The key point is that both boards contain the same clusters of pieces (a cluster is a group of adjacent pieces connected by a series of single-cell moves horizontally or vertically). For example, the cluster (A, B, C, F, G) appears on both boards, although it may be reflected, rotated, or shifted.
Your task is to determine whether two given board configurations are equivalent as described above.
The first line contains a single integer (1 \leq t \leq 10) — the number of test cases.
The first line of each test case contains three integers , , and (1 \leq W, H \leq 100). Here, is the width and is the height of the grid, measured in grid points. is the number of pieces on the board.
The second line contains pairs of integers (x_i, y_i) describing the coordinates of the pieces on the first board (0 \leq x_i < W, 0 \leq y_i < H).
The third line contains the coordinates of the pieces on the second board in the same format.
For each test case, output either YES or NO depending on whether the two given positions are equivalent.
Example 1