## IPSC 2006

## Problem I – Ideal Matches

At a party, **N** couples play the following game: In the beginning, each boy takes his girl's
right hand into his left hand. Now, everybody closes their eyes and they all start
to move around randomly. At a given signal, everybody reaches out with his/her
free hand and catches somebody else's hand. Then everybody opens their eyes.

The game is considered a *success* if all players form one large cycle
and a *failure* otherwise.

After the players became tired of the game and started to chat, Tony exclaimed:
"Once I was at a party where we played the game **2N-2** times, and each time
it was a success. And moreover, nobody did hold somebody else's hand more than once.
(Of course, except for his partner's hand.)"

Everybody knows that Tony is a notorious jester, so nobody took his exclamation
too seriously. "Nah, it's not even possible!" said one of his friends.

Help Tony prove that his story really could have happened.

### Problem specification

You are given the number of couples **N**. The boys are numbered from **0**
to **N-1**, the girls from **N** to **2N-1**. The girlfriend of the boy
**i** is the girl **i+N**.

We may specify the result of a given game by specifying **N** pairs of numbers
– one for each pair of people (other than a couple) that are holding hands.

Find one possible set of **2N-2** game results such that each game is
a *success* and, except for the couples, nobody did hold somebody else's hand
more than once.

### Input specification

The first line of the input file contains an integer **T**
specifying the number of test cases.
Each test case is preceded by a blank line.

Each test case consists of a single line containing a single integer **N**.

### Output specification

For each test case output **2N-2** lines. The **i**-th of these lines should contain
**2N** space-separated integers **a**_{0}, ..., a_{2N-1}, where for each **j**
the people **a**_{2j} and **a**_{2j+1} were holding hands in the **i**-th
game.

If there is more than one solution, you may output any one of them.
If there is no solution, instead of the **2N-2** lines as specified above
output a single line with the word "`IMPOSSIBLE`

".

### Example

**Input:**
1
2

**Output:**
0 1 2 3
0 3 2 1

In the example, the couples are 0-2 and 1-3. In the first game, 0-1 and 2-3 were holding hands,
thereby forming a circle 0-1-3-2. In the second game, we saw the circle 0-3-1-2.

**Credits:**

**Problemsetter(s):** misof

**Contest-related materials:** misof

**Acknowledgements:** Riso