# 1206.py

# ly ... lista degli y.
def iniettiva (f,dom):
  ly=[]
  for x in dom:
    y=f(x)
    if y in ly: return 0
    ly.append(y)
  return 1

def suriettiva (f,dom,cod):
  return int(set(cod)<=set([f(x) for x in dom]))

def biiettiva (f,dom,cod):
  return iniettiva(f,dom) and suriettiva(f,dom,cod)

dom=xrange(10)

def f (x): return (x*x+2)%6

for x in dom: print x,
print
for x in dom: print f(x),
print
# 0 1 2 3 4 5 6 7 8 9
# 2 3 0 5 0 3 2 3 0 5

print iniettiva(f,dom), suriettiva(f,dom,xrange(6))
# 0 0

print suriettiva(f,dom,[0,2,3,5]) # 1
print iniettiva(f,[0,1,2,3]) # 1

#######################################

# sx ... sequenza degli x.
def associativa (f,sx):
  for a in sx:
    for b in sx:
      for c in sx:
        if f(f(a,b),c)!=f(a,f(b,c)): return 0
  return 1

def f (x,y): return (x+y)%4
def g (x,y): return (x+y*x)%4

print associativa(f,xrange(4)) # 1
print associativa(g,xrange(4)) # 0