2016 Gauss 8 Problem 23

Zeus starts at the origin (0,0) and can make repeated moves of one unit either up, down, left or right, but cannot make a move in the same direction twice in a row. For example, he cannot move from (0,0) to (1,0) to (2,0). What is the smallest number of moves that he can make to get to the point (1056, 1007)?

\textbf{(A)}\ 2112\quad \textbf{(B)}\ 2161\quad \textbf{(C)}\ 2063\quad \textbf{(D)}\ 2111\quad \textbf{(E)}\ 2113

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.