We wish to tile a grid 4 units high and N
units long with rectangles (dominoes) 2 units by one unit (in either orientation). For example, the figure shows the five different ways that a grid 4 units high and 2 units wide may be tiled.
Write a program that takes as input the width, W
, of the grid and outputs the number of different ways to tile a 4-by-W grid.
The first line of input contains a single integer N
, (1 ≤ N
≤ 1000) which is the number of datasets that follow.
Each dataset contains a single decimal integer, the width, W
, of the grid for this problem instance.
For each problem instance, there is one line of output: The problem instance number as a decimal integer (start counting at one), a single space and the number of tilings of a 4-by-W
grid. The values of W
will be chosen so the count will fit in a 32-bit integer.