Infix Maze

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

1
3
3
1 5 4 
+ - * 
+ 6 8 

Sample Output

1
3
3
1 5 4 
+ - * 
+ 6 8 
Yes
15 - 68 
15 68 -