Let T(n) be the number of tours over a 4 n playing board such that:
- The tour starts in the top left corner.
- The tour consists of moves that are up, down, left, or right one square.
- The tour visits each square exactly once.
- The tour ends in the bottom left corner.
The diagram shows one tour over a 4 10 board:
T(10) is 2329. What is T(1012) modulo 108?