“Paper cutting is the art of cutting paper designs. ”
“Chinese Paper Cutting or Jianzhi is the first type of papercutting design, since paper was
invented by Cai Lun in the Eastern Han Dynasty in China. The art form later spread to other
parts of the world with different regions adopting their own cultural styles. Because the cut
outs are also used to decorate doors and windows, they are sometimes referred to "chuāng
huā", meaning Window Flower.”

--WikiPedia

Alice is a fan of interesting Chinese paper cutting (ICPC). When she first saw it in her
grandmother’s house, she immediately fell in love with this art. And from then on, she began
to collect various paper cutting designs and tried to create her own works as well. At first, she
couldn’t manipulate her scissors and often cut inappropriate parts. Sometimes, she even hurt
herself. She had many beautiful designs in her mind, but she was unable to realize them. She
was so disappointed for that. However, she didn’t give up. She persisted in practicing,
learning from books and experts. At last, she found a key feature of paper cutting. That is
symmetry.

Symmetry is very important for paper cutting. It not only beautifies the whole work but also
makes the cutting process easy. Therefore, cutting each part of a work independently is not a
good choice. Instead, it will be better to fold and cut alternately.
Now Alice is experienced and works out a paper cutting process which is safe and easy. So
she invents a machine that can perform paper cutting following her instructions.
This machine has a wide foldable board and a coordinate system on the board. Before the
machine runs, she puts a piece of rectangular paper on the board. Two edges of the paper
accord with X-axis and y-axis respectively. X-axis is from left to right and y-axis is from top
down.

Then she starts up the machine and performs a paper cutting process by repeating two types
of instructions:

• 
  fold A B:
  
  To execute this instruction, the part of the board containing
  the point A will be folded onto the other part. So the point
  A will coincide with B after folding. Then, the folded part will
  come back to the original position.
  As showed in figure 1, Sa is folded onto Sb to make A and B coincide,
  meanwhile, the paper is folded along the line l . Then, Sa is
  put back to the original position. But the folded area of the
  paper is left on Sb.
  In some cases, the paper may be completely within Sa. If so,
  the whole paper will be reversed and left on Sb. In contrast,
  the paper will be unchanged if it is completely within Sb.
  The folding is limited to be vertical or horizontal.


• 
  cut
  The machine is equipped with a small sharp knife. First, it will
  use the knife to cut the paper along the line segment . If
  there are multiple layers under , it will penetrate all of
  them. After that, it will continue to cut along the segment
  and then , etc. can be outside the paper. The machine will
  cut nothing if it finds the knife is outside the paper.
  Sometimes it may happen to cut along the joining line of two
  layers. The knife is so sharp that it will cut off them all the
  same.
  
  If the paper is divided to several pieces after cutting, the
  machine will automatically get rid of all pieces but the one
  with the largest area (after unfolding). If there is a tie, it
  will keep the one containing the most top-left point in the
  original paper, i.e. the most left point in the most top
  horizontal line.

Finally, she unfolds the paper and sees a fantastic design.
For some complex designs, she is not sure whether her instructions will exactly make what
she wants. She doesn’t want to waste paper. So she needs you to write a program that can
simulate her instructions and tell her the final design. Given her instructions, your job is to
print the final design.