Magnets

hard
1. You are given n number of domino shaped bipolar magnets.
2. You have to place these magnets in M*N following the conditions.
3. Conditions are -
   a. Each box of 1*2 or 2*1 can contain a magnet or can be empty.
   b. Empty box can be represented by X's and magnets are represented by + and 
    - sign.
   c. Digits along left and top side of the board represents the number of + in 
    corresponding rows and columns.
   d. Digits along right and bottom of the board represents the number of - in 
    corresponding rows and columns.
    e. -1 denotes that the corresponding row and column can have any number of 
    +  and - signs.
    f. No two adjacent cell can have the same sign.


Note -> Check out the question video and write the recursive code as it is intended without changing signature. The judge can't force you but intends you to teach a concept.

Input Format

A number M A number N M*N characters containing only 'L', 'R', 'T' and 'B'. (For 1*2 box 'L' represents left end and 'R' represents the right end) (For 2*1 box 'T' represents top end and 'B' represents the right end) N integers representing count of '+' along the top edge. M integers representing count of '+' along the left edge. M integers representing count of '-' along the right edge. N integers representing count of '-' along the bottom edge.

Output Format

Check the sample output and question video

Constraints

2 <= M <= 10
2 <= N <= 10
Both M and N are not odd.

Notice

Try First, Check Solution later

1. You should first read the question and watch the question video.
2. Think of a solution approach, then try and submit the question on editor tab.
3. We strongly advise you to watch the solution video for prescribed approach.

Example

Input
5 6
LRLRTT
LRLRBB
TTTTLR
BBBBTT
LRLRBB
1 -1 -1 2 1 -1
2 3 -1 -1 -1
-1 -1 -1 1 -1
2 -1 -1 2 -1 3
Output
+ - + - X - 
- + - + X + 
X X + - + - 
X X - + X + 
- + X X X - 
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