HOW MANY GENERATIONS WERE THERE FROM THE BABYLONIAN EXILE UNTIL CHRIST?

Matthew 1:12-16  And after they were brought to Babylon, Jechonias begat Salathiel; and Salathiel begat Zorobabel; And Zorobabel begat Abiud; and Abiud begat Eliakim; and Eliakim begat Azor; And Azor begat Sadoc; and Sadoc begat Achim; and Achim begat Eliud; And Eliud begat Eleazar; and Eleazar begat Matthan; and Matthan begat Jacob; And Jacob begat Joseph the husband of Mary, of whom was born Jesus, who is called Christ. (KJV) Matthew 1:17  So all the generations from Abraham to David are fourteen generations; and from David until the carrying away into Babylon are fourteen generations; and from the carrying away into Babylon unto Christ are fourteen generations. (KJV)

Note: the assumption of contradiction is that the 1:12-16 passage shows only thirteen generations, while 1:17 says there were fourteen. However, there are two ways that people count generations 1. With a man to his son to his grandson being 2 generations (the gap between being considered a generation) 2. With a man to his son to his grandson being 3 generations (with each person being considered a separate generation) To be fair, though, Matthew does count the 14 generations from Abraham to David, and the 14 generations from David until Babylon the first way (one less than the number of names), while counting the 14 generations from Babylon to Christ the second way (equal to the number of names).  Slightly inconsistent, yes, but there are no errors, so this is not a contradiction.