Ancient Archive Puzzle

You are given a 2×2 grid where each cell either contains a positive integer or is empty. In the grid, the positive integers present are exactly the first k positive integers (if any), and the remaining cells are empty. You are allowed to perform a series of moves to transform the grid.

In each move, you may choose a cell that contains a positive integer and an adjacent cell (sharing an edge) that is empty, and then move the integer into the empty cell.

You are provided with an initial configuration and a target configuration. Determine whether it is possible to transform the initial configuration into the target configuration by a finite sequence of valid moves.

Note:

• The grid size is fixed at 2×2.
• An integer 0 represents an empty cell.
• The grid may contain no positive integers or may have no empty cell.

All formulas are represented in LaTeX format. For example, the grid size is given as $2\times2$, and the set of positive integers is $\{1,2,\dots, k\}$.

inputFormat

The input consists of two 2×2 grids. The first grid is the initial configuration, and the second grid is the target configuration. Each grid is described by 2 lines, and each line contains 2 integers separated by spaces. A value of 0 indicates an empty cell while any positive integer represents a tile.

For example:

1 0
0 2
0 1
0 2

outputFormat

Output YES if it is possible to transform the initial configuration into the target configuration through a sequence of valid moves. Otherwise, output NO.

sample

0 0
0 0
0 0
0 0

YES