Problem $2$: Mistakes Were Made

Extend your scrabble program from Problem $1$ to handle one change. The list may include words that

cannot be legally placed. All words that cannot be placed should be identified and not added to the board.

Input

The input format is the same as in Problem $1.$

Processing

Same as problem $1,$ except that words that cannot be legally placed should be identified and not placed

on the board. A word cannot be legally placed if one or more of the following conditions hold.

if the word extends past the edge of the board

If the word does not cross one or more other words, except in the case of the first word to be

placed.

If there is a letter mismatch at a crossing$-$point of two words. I.e$.,$ the letter at the crossing point

of the word to be placed is not the same as the letter of crossing point of the already placed word.

If the word can be legally placed, it is added to the board. Otherwise, the program should identify the

illegal word. The program then prints out the board, just like in Problem $1.$

Output

As the words are being placed, identify each illegal word by outputting the following:

Invalid word placement: $(x,Y)D,S$

where $x,Y,D,$ and $S,$ are as described in the Input section of Problem $1.$ Lastly, output the game board as

in Problem $1.$

Examples