CTRICK - Card Trick


The magician shuffles a small pack of cards, holds it face down and performs the following procedure:

  1. The top card is moved to the bottom of the pack. The new top card is dealt face up onto the table. It is the Ace of Spades.
  2. Two cards are moved one at a time from the top to the bottom. The next card is dealt face up onto the table. It is the Two of Spades.
  3. Three cards are moved one at a time…
  4. This goes on until the nth and last card turns out to be the n of Spades.

This impressive trick works if the magician knows how to arrange the cards beforehand (and knows how to give a false shuffle). Your program has to determine the initial order of the cards for a given number of cards, 1 ≤ n ≤ 20000.

Input

On the first line of the input is a single positive integer, telling the number of test cases to follow. Each case consists of one line containing the integer n.

Output

For each test case, output a line with the correct permutation of the values 1 to n, space separated. The first number showing the top card of the pack, etc…

Example

Input:
2
4
5

Output:
2 1 4 3
3 1 4 5 2

hide comments
zicowa: 2014-04-05 13:00:48

i solved it using seg tree in nlogn nice question

Last edit: 2014-04-05 14:09:00
innovolt: 2014-03-29 07:47:06

did it with CDLL....AC in 1 go..simple 1

Master Wad7a: 2013-06-16 14:09:36

My O(n*(n+1)/2) passes in 1.5 seconds with averagely slow input, BTW u can solve it using binary indexed trees

karan173: 2013-03-28 16:39:14

O(n^2) is giving tle, has the test data been updated?

maskit: 2012-04-10 19:00:56

m getting wa..is there any..special case........

Mitch Schwartz: 2012-01-06 12:37:58

It's possible for O(n^2) to pass in well under 1s. :P

aang*™*: 2011-09-16 05:17:21

this assumes up to 20000 of Spades. and not just 13.

darryl: 2011-05-04 05:25:46

Solve it as if the time limit is 1s

Last edit: 2011-07-27 03:29:31
Sai Kiran Reddy Jakka: 2010-07-27 15:18:28

@shaka:thanks for the information:)

Shaka Shadows: 2010-07-20 14:17:17

Time limit too easy to pass!!! Even a O(n^2) solution will get AC :)


Added by:Camilo Andrés Varela León
Date:2006-11-23
Time limit:3.279s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:Nordic Collegiate Contest 2006