On Diffie-Hellman key exchange

The book I am reading, explains the algorithm as follows: - 2 people think of 2 public "n and g" numbers both are aware of. - 2 people think of 2 private "x and "y" numbers they keep secret. Exchange happens as illustrated I put together the following python code to see how this works and .... it does not. Please help me understand what am i missing: ``` #!/usr/bin/python n=22 # publicly known g=42 # publicly known x=13 # only Alice knows this y=53 # only Bob knows this aliceSends = (g**x)%n bobComputes = aliceSends**y bobSends = (g**y)%n aliceComputes = bobSends**x print "Alice sends ", aliceSends print "Bob computes ", bobComputes print "Bob sends ", bobSends print "Alice computes ", aliceComputes print "In theory both should have ", (g**(x*y))%n --- Alice sends 14 Bob computes 5556302616191343498765890791686005349041729624255239232159744 Bob sends 14 Alice computes 793714773254144 In theory both should have 16 ```