Magic of David Copperfield 

The well-known magician David Copperfield loves to show the following trick: a square with N rows and N columns of different pictures appears on a TV screen. Let us number all the pictures in the following order:

1	2	$\dots$	N
$\vdots$	$\vdots$	$\ddots$	$\vdots$
N*(N-1)+1	N*(N-1)+2	$\dots$	N*N

Each member of the audience is asked to put a finger on the upper left picture (i.e., picture number one) and The Magic begins: the magician tells the audience to move the finger k₁ times through the pictures (each move is a shift of the finger to the adjacent picture up, down, left or right provided that there is a picture to move to), then with a slight movement of his hand he removes some of the pictures with an exclamation ``You are not there!", and ... it is true - your finger is not pointing to any of the pictures removed. Then again, he tells the audience to make k<sub>2</sub> moves, and so on. At the end he removes all the pictures but one and smiling triumphantly declares, ``I've caught you" (applause).

Just now, David is trying to repeat this trick. Unfortunately, he had a hard day before, and you know how hard to conjure with a headache. You have to write a program that will help David to make his trick.

Input 

The input file contains a single integer number N ( $2 \le N \le 100$).

Output 

Your program should write the following lines with numbers to the output file:

$k_1 \ x_{1,1} \ x_{1,2} \ \dots \ x_{1,m1}$

$k_2 \ x_{2,1} \ x_{2,2} \ \dots \ x_{2,m2}$

$\dots$

$k_e \ x_{e,1} \ x_{e,2} \ \dots \ x_{e,me}$

where k_i is a number of moves the audience should make on the i-th turn ( $2N \le k \le 10000$). All k_i should be different (i.e. k_i <> k_j when i <> j). $x_{i,1}, x_{i,2}, \dots, x_{i,mi}$ are the numbers of the pictures David should remove after the audience will make k_i moves (the number of the pictures removed is arbitrary, but each picture should be listed only once, and at least one picture should be removed on each turn).

A description of the every next turn should begin with a new line. All numbers on each line should be separated by one or more spaces. After e iterations, all pictures except one should be removed.

Sample input 

3

Sample Output 

8     4 6
13    9
10    7 1
7     8
11    3 5