<title>Problem 11859</title>

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11859 - infix maze   

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Status  |  Limits

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Limits

          <tr>
            <th>Case 1</th>
            <td>1 sec</td>
            <td>32 MB</td>
          </tr>
          
          <tr>
            <th>Case 2</th>
            <td>1 sec</td>
            <td>32 MB</td>
          </tr>
          
          <tr>
            <th>Case 3</th>
            <td>1 sec</td>
            <td>32 MB</td>
          </tr>
          
          <tr>
            <th>Case 4</th>
            <td>1 sec</td>
            <td>32 MB</td>
          </tr>
          
          <tr>
            <th>Case 5</th>
            <td>1 sec</td>
            <td>32 MB</td>
          </tr>
          
          <tr>
            <th>Case 6</th>
            <td>1 sec</td>
            <td>32 MB</td>
          </tr>
          
          <tr>
            <th>Case 7</th>
            <td>1 sec</td>
            <td>32 MB</td>
          </tr>
          
          <tr>
            <th>Case 8</th>
            <td>1 sec</td>
            <td>32 MB</td>
          </tr>
          
          <tr>
            <th>Case 9</th>
            <td>1 sec</td>
            <td>32 MB</td>
          </tr>
          
          <tr>
            <th>Case 10</th>
            <td>1 sec</td>
            <td>32 MB</td>
          </tr>
          
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Description

Determine whether a matrix contains at least a legal infix expression which need to be from the top-left corner to the bottom-right corner. If yes, convert it based on the postfix notation.

There are some rules to be followed. 

• Each cell can be reached by four directions(up, down, right, left).
• Matrices are consisted of 1~9, +,-,*,/, (, )
• Each cell can be visited at most one time.
• The priority directions are: down>right>left>up.
• No negative number. EX: - 5 + 3 is illegal.

 

Input

First line is total number of matrices.

Second and third line are matrix width nad height.

Width and height <100.

Following lines are matrix.

Output

Repeat all inputs.
For matrix, there is a white space after every elements.

If there is a legal infix expression from the top-left corner to the bottom-right corner,  output
Yes
infix expression ( there is a white space after every elements.)
postfix expression ( there is a white space after every elements.)

If No, output
No

Sample Input  Download

<textarea id='11859_sampleIn' class='panel-body sampleIO' readonly>1 3 3 1 5 4 + - * + 6 8 </textarea>

Sample Output  Download

<textarea id='11859_sampleOut' class='panel-body sampleIO' readonly>1 3 3 1 5 4 + - * + 6 8 Yes 15 - 68 15 68 - </textarea>

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