Азербайджан - подготовка. Март 16
In how many ways can you tile a 2 × n rectangle with triominoes? A triomino is a geometric shape made from three squares joined along complete edges. There are only two possible triominoes:
For example, you can tile a 2 × 3 rectangle only in 3 different ways. As the answer can be quite big, you just need to find the number of ways modulo 106.
The first line contains the number of test cases t (1 ≤ t ≤ 100). Each of the following t lines contains the value of n (0 < n < 109).
For each test case print in a separate line a number of ways you can tile a 2 × n rectangle. Print the answer modulo 106.
3 3 4 6
3 0 11