#!/usr/bin/env python
# mu.py
# an automated MIU solver by aLT 08

from random import randint


def intro():
    print "\nThe  game of the MU MU!!"
    print "Your starting string will be <MI>"
    print "You must try and derive the axiom <MU> by applying four procedural rules\n"
    print "RULE 1: If the string ends in <I> you may append a <U>"
    print "RULE 2: If you have <Mx> you may make it <Mxx> - X equals any string"
    print "RULE 3: If <III> occurrs you may substitute <U> in it's place"
    print "RULE 4: If <UU> occurs you may drop it"
    print "Good luck. Have you sunk it?\n"
    start = raw_input("Begin?")


def double(str):
    str = str + str[1 : len(str)+1]
    countI(str)
    print str    
    return str


def countI(str):
    tally = 0
    for z in str:
        if z == "I":
            tally += 1
    print tally
    

def countU(str):
    tally = 0
    for z in str:
        if z == "U":
            tally += 1
    print tally


def addU(str):
    str = str + "U"
    print str    
    return str


def swapI(str, amt):
    tally = 0
    mark = 0
    count = 0
    for z in str:
        mark += 1
        if count >= amt:
            break
        elif z == "I":
            tally += 1
            if tally == 3:
                str = str[0:mark-3] + "U" + str[mark:len(str)]
                tally = 0
                mark = mark - 2
                count += 1
        else:
            tally = 0
    print str    
    countU(str)    
    return str
    

def dropU(str):
    tally = 0
    mark = 0
    for z in str:
        mark += 1
        if z == "U":
            tally += 1
            if tally == 2:
                str = str[0:mark-2] + str[mark:len(str)]
                tally = 0
                mark = mark - 2
        else:
            tally = 0
    print str    
    return str


def main():
    #intro()
    muStr = "MI"
    muStr = double(muStr)
    muStr = double(muStr)
    muStr = double(muStr)
    muStr = double(muStr)
    muStr = swapI(muStr, 2)
    muStr = dropU(muStr)
    muStr = double(muStr)
    muStr = double(muStr)
    muStr = double(muStr)
    muStr = double(muStr)
    muStr = swapI(muStr, 34)
    muStr = addU(muStr)
    muStr = swapI(muStr, 19)
    muStr = dropU(muStr)
    print muStr

    

if __name__ == '__main__':
    main()