Build the String

Let us have some virtual machine. The machine has a memory stack that can infinitely widen and can contain strings of any finite non-zero length.

The machine supports four operations:

• copy --- copy a string at the stack's end and place it in the stack's end;
• swap --- swap the last string in the stack and the one before the last;
• roll --- cyclically shift three last strings in the stack away from the stack's end;
• fuse --- extract two strings from the stack's end and then place their concatenation at the stack's end.

More formally it looks like that: ([...] stands for some sequence of strings at the beginning of the stack, perhaps of zero length):

• copy: [...] x $\to$ [...] x x;
• swap: [...] x y $\to$ [...] y x;
• roll: [...] x y z $\to$ [...] y z x;
• fuse: [...] x y $\to$ [...] xy.

Program for a given virtual machine is represented by a command sequence; the machine performs the commands one after another. If the stack doesn't have enough strings to perform the program's current command, then an event CRASH occurs and the machine stops functioning. The machine also stops if the program runs out of commands (in this case the CRASH event never occurs).

Initially the virtual machine's stack contains two strings and has the form of "a b". You have to write a program for the given machine; the program's progress should result in an $s$ string located at the stack's end (at the end of the program's progress the stack can have more than one string left). The program should contain no more than $3 \times |s|$ commands ($|s|$ --- is the $s$ string's length). Of course, the program's progress shouldn't lead to the CRASH event.

The first line contains the $s$ string. It only consists of lowercase Latin letters "a" and "b" and has the length from $1$ to $10^5$ characters.

Print on the first output line number $k$ the number of commands in the program ($0 \le k \le 3 \times |s|$). Print on the next $k$ lines $k$ commands, one command per line. The acceptable commands are "copy", "swap", "roll" and "fuse". As the result of the program's progress the last element in the stack should be string $s$ (the stack can have more than one string left). The program shouldn't lead to the CRASH event. If there are several acceptable decisions, print any of them. See the samples for clarifications.

During the sample program's progress the virtual machine's stack changes in the following manner:

a b $\to$ b a $\to$ b a a $\to$ a a b $\to$ a ab $\to$ a ab ab $\to$ a abab $\to$ a abab abab $\to$ abab abab a $\to$ abab ababa