def createTree(choices,levels):
    #This is a special kind of tree. Let's say you have 4 choices
    #The first choice has 4 branches stemming from it
    #The second has 3 branches stemming from it
    #The third has 2
    #The fourth has only 1
    #This pattern repeats for every level
    choiceArray = ['r','g','b','y'];#Hardcode choices to 4 for now
    i = 0;
    nodeList = []
    tmpNodeList = []
    for choice in choiceArray:
        Node = {'index':i,'parent':0,'name':choice}
        i+= 1;
        nodeList.append(Node);
    while(len(nodeList) > 0):
        node = nodeList.pop(0)
        #Translate index to how many branches
        branches = len(choiceArray) - node['index']

        for i in range(0,branches):
            newNode = {'index':i+node['index'],'parent':node,'name':choiceArray[i+node['index']]}
            tmpNodeList.append(newNode)
        if(len(nodeList) == 0):
            for node in tmpNodeList:
                nodeList.append(node)
            tmpNodeList = [];
            levels -= 1;
            if(levels <= 1):
                #Done!
                print(len(nodeList))
                break

for i in range(2,11):
    print("Num: " + str(i))
    createTree(['r','g','b','y'],i)