Matrix Pathfinding with Directional Movement

You are given an n x m matrix, where each cell contains one of the characters \(P\), \(Q\), or \(R\). Each character represents a type of allowed movement from that cell:

• P: You can only move right or down.
• Q: You can only move left or up.
• R: You can move in all four directions (right, down, left, up).

Your task is to determine whether there is a valid path from the top-left corner (cell \((0,0)\)) to the bottom-right corner (cell \((n-1, m-1)\)) following the movement rules given by the characters in each cell.

If such a path exists, output YES. Otherwise, output NO.

Note: All movement must remain within the boundaries of the matrix.

inputFormat

The input is read from stdin and has the following format:

n m
row1
row2
...
rown

Where n and m are integers representing the number of rows and columns of the matrix. Each of the following n lines contains a string of exactly m characters (each character is either P, Q, or R), representing one row of the matrix.

outputFormat

Output a single line to stdout containing either YES if a valid path exists from the top-left to the bottom-right corner, or NO if not.

## sample

3 3
PQQ
RQR
RRR

YES