# 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.

## Constraints

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

## Format

### Input

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

Check the sample output and question video

## Example

Sample 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

### Sample Output

+ - + - X -
- + - + X +
X X + - + -
X X - + X +
- + X X X -

Question Video