LRUD Game

We have a rectangular grid of squares with H horizontal rows and W vertical columns. Let (i,j) denote the square at the i-th row from the top and the j-th column from the left. On this grid, there is a piece, which is initially placed at square (s_r,s_c).

Takahashi and Aoki will play a game, where each player has a string of length N. Takahashi's string is S, and Aoki's string is T. S and T both consist of four kinds of letters: L, R, U and D.

The game consists of N steps. The i-th step proceeds as follows:

• First, Takahashi performs a move. He either moves the piece in the direction of S_i, or does not move the piece.
• Second, Aoki performs a move. He either moves the piece in the direction of T_i, or does not move the piece.

Here, to move the piece in the direction of L, R, U and D, is to move the piece from square (r,c) to square (r,c-1), (r,c+1), (r-1,c) and (r+1,c), respectively. If the destination square does not exist, the piece is removed from the grid, and the game ends, even if less than N steps are done.

Takahashi wants to remove the piece from the grid in one of the N steps. Aoki, on the other hand, wants to finish the N steps with the piece remaining on the grid. Determine if the piece will remain on the grid at the end of the game when both players play optimally.

Constraints

• 2 \leq H,W \leq 2 \times 10^5
• 2 \leq N \leq 2 \times 10^5
• 1 \leq s_r \leq H
• 1 \leq s_c \leq W
• |S|=|T|=N
• S and T consists of the four kinds of letters L, R, U and D.

Input

Input is given from Standard Input in the following format:

H W N s_r s_c S T

Output

If the piece will remain on the grid at the end of the game, print YES; otherwise, print NO.

Examples

Input

2 3 3 2 2 RRL LUD

Output

YES

Input

4 3 5 2 2 UDRRR LLDUD

Output

NO

Input

5 6 11 2 1 RLDRRUDDLRL URRDRLLDLRD

Output

NO

inputFormat

Input

Input is given from Standard Input in the following format:

H W N s_r s_c S T

outputFormat

Output

If the piece will remain on the grid at the end of the game, print YES; otherwise, print NO.

Examples

Input

2 3 3 2 2 RRL LUD

Output

YES

Input

4 3 5 2 2 UDRRR LLDUD

Output

NO

Input

5 6 11 2 1 RLDRRUDDLRL URRDRLLDLRD

Output

NO

样例

2 3 3
2 2
RRL
LUD

YES