PostScript Emulation

PostScript® is a page-description language widely used by laser printers. Its basic unit of measurement is the point, and there are exactly 72 points per inch. The default coordinate system is the usual Cartesian one, with the origin (where both the x and y coordinates are zero) at the lower-left corner of the page.

In this problem you must recognize a small subset of PostScript, consisting of the commands below. Every command is written in lower-case letters. Wherever the word number appears, the input contains a floating-point value with an optional sign and decimal point. When a command takes two numbers, the first is the x coordinate and the second is the y coordinate. Each command appears alone on its own line, its components separated by single spaces, followed immediately by an end-of-line character. A line containing a single asterisk in column one terminates the input.

• number rotate — number is an angle in degrees. Rotates the coordinate system number degrees counterclockwise about the current origin. Lines already drawn are unaffected. Example: 90 rotate turns the axes 90° counterclockwise, so the positive y axis then points left and the positive x axis points up.
• number number translate — Moves the origin of the coordinate system to the given position, measured relative to the current origin. Example: on an 8.5" × 11" page in portrait orientation, 612 792 translate moves the origin to the upper-right corner, after which only points with negative x and y lie on the physical page.
• number number scale — Multiplies the x and y sizes of objects by the given factors. Example: after 3 2 scale, a line from (0, 0) to (72, 72) is drawn as if from the lower-left corner to a point three inches right and two inches up (assuming the original coordinate system held just before the command).
• number number moveto — Moves the current point to the given absolute coordinates. Example: in the original coordinate system, 72 144 moveto places the current point one inch right of the left edge and two inches above the bottom edge.
• number number rmoveto — Like moveto, but the coordinates are relative to the current position. Example: following the previous example, 144 -36 rmoveto shifts the current point two inches further right and half an inch down, to (216, 108). Numbers may be negative.
• number number lineto — Draws a line from the current position to the given absolute coordinates; the current position becomes that point. Example: from (216, 108), 216 144 lineto draws a half-inch vertical line ending at (216, 144).
• number number rlineto — Like lineto, but the coordinates are relative to the current position; the far end of the line becomes the new current position. Example: from (216, 144), 0 144 rlineto draws a two-inch vertical line ending at (216, 288).

Read one such PostScript program and output a program that produces the same drawing without using rotate, translate, or scale. Every moveto, rmoveto, lineto, and rlineto command in the input must appear in the output (usually with different numbers), while the rotate, translate, and scale commands must not appear at all. Assume the original coordinate system is in effect when execution begins.

Output format. Print one command per line. For each coordinate value, print it as an integer when it equals a whole number after rounding to two decimal places; otherwise print it rounded to exactly two digits after the decimal point. Print a value of zero as 0 (never -0). Separate the two numbers and the command name with single spaces.