GNY07H - Tiling a Grid With Dominoes


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

hide comments
Anoop Chaurasiya: 2010-05-08 14:57:41

same idea as M3TILE https://www.spoj.pl/problems/M3TILE/

Akhauri Kartikeya Sinha: 2010-04-29 05:51:02

for 3 number of possibilities should be 9,how it is 11? :(


Added by:Marco Gallotta
Date:2008-03-12
Time limit:9.600s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:ACM Greater New York Regionals 2007