from math import *


def v(n):
    c=0
    while n%2==0:
        c=c+1
        n=n//2
    return c

def s(n):
    if n<2:
        return n
    else:
        return s(n//2)+n%2



def prod(m,n):
    return [v(m*n),v(m),v(n),v(m*n)-(v(m)+v(n))]

def verif():
    for n in range(2,10001):
        if v(n)-s(n-1)+s(n)-1!=0:
            return 'faux'
    return 'vrai'