# Arup Guha
# 4/13/2023
# Code to verify answer for COT 3100H Quiz 2 Problem 5

# Run Brute Force here
def main():
    ctr = go(5,5,1,"")
    print("count =",ctr)

# a = # of A's left, b = # of B's left, c = # of c's left.
def go(a,b,c,s):

    # Store # of solutions here.
    ctr = 0

    # Got one, process it and return.
    if a == 0 and b == 0 and c == 0:
        print(s)
        ctr+=1
        return ctr

    # We can always do three cases here.
    if len(s) == 0:
        ctr += go(a-1,b,c,s+"a")
        ctr += go(a,b-1,c,s+"b")
        ctr += go(a,b,c-1,s+"c")
        return ctr

    # Here we have to look at the previous character and frequencies
    # to decide what could go next.
    else:

        if a > 0 and s[-1] != 'a':
            ctr += go(a-1,b,c,s+"a")
        if b > 0 and s[-1] != 'b':
            ctr += go(a,b-1,c,s+"b")
        if c > 0 and s[-1] != 'c':
            ctr += go(a,b,c-1,s+"c")
        return ctr
    
main()