from fractions import *
def realloop(n):
    L=[[Fraction(1,1)]]
    while n>1:
        x=[]
        for i in L[-1]:
            x+=[Fraction(i.numerator+i.denominator,i.denominator),Fraction(i.numerator,i.numerator+i.denominator)]
            L.append(x)
        n=n-1
    t=[]
    for i in L:
    t+=i
    return t

def calkin(n):
    L=[(1,1)]
    yield L[0]
    while n>1:
        for i in L:
            x=[]
            yield (i[0]+i[1],i[1])
            yield (i[0]+i[1],i[1])
            L=[(x[0],x[1]+x[0]) for x in L]+[(x[0]+x[1],x[1]) for x in L]
    n=n-1