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GNY07H - Tiling a Grid With Dominoes

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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.

Input

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.

Output

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.

Example

Input:
3
2
3
7

Output:
1 5
2 11
3 781

Added by:Marco Gallotta
Date:2008-03-12
Time limit:9.600s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel Pentium G860 3GHz)
Languages:All except: ERL JS NODEJS PERL 6 VB.net
Resource:ACM Greater New York Regionals 2007

hide comments
detel: 2015-07-20 23:53:47

There's no need of image!!
0 <= W <= 22

xxbloodysantaxx: 2015-07-09 21:59:36

No Image found ! Link broken

Rishabh Joshi: 2015-03-15 06:58:15

Very nice problem!! Learnt a lot! (hint: how can you start the series? Write all combinations of dominos by which you can start(and continue), and the answer will start to present itself)!

Govind Lahoti: 2015-02-13 08:45:32

Awesome problem. Enjoyed solving it :)

mayank: 2014-12-18 11:21:07

Tried after M3TILE. Almost similar. Could not get it straight though! :P

fanatique: 2014-07-01 19:25:33

good one :)

Ravi Shankar Mondal: 2014-06-24 21:34:24

100th green light :)

Noob: 2014-05-26 17:18:19

Good one!

Himanshu: 2014-01-30 06:33:30

Shouldn't input 3 give 5 + 2*5 - 1 = 14 as each tiling (except last) for input 2 can be widened by adding a column to the left or to the right.

Ankit Kumar: 2013-12-30 07:51:38

my 50th on SPOJ :)