Stars

Description:

Input:

A single line contains an integer (1 ≤ n ≤ 100) — the number of stars to paint.

Output:

On the first line print an integer m (1 ≤ m ≤ 5·n). On the next m lines print coordinates of m distinct points with accuracy of at least 9 and at most 100 digits after decimal point. All coordinates should not exceed 5000 in their absolute value. On each of the next n lines print 5 integers — the indexes of the points that form the given star in the clockwise or counterclockwise order. On the next line print 5·n + 1 integers — the numbers of points in the order, in which Rubik paints stars. That is, if number with index i is a_i, and number with index i + 1 is a_i + 1, then points with indexes a_i and a_i + 1 will have a segment painted between them.

You can consider all m printed points indexed from 1 to m in the order, in which they occur in the output. Separate the numbers on the lines with whitespaces.

Note that the answer has an imprecise validation. Try to obtain as accurate a solution as possible. The validator performs all calculations considering that the absolute error of a participant's answer is not more than 10^- 8.

Sample Input:

1

Sample Output:

5
3.830127018922193 3.366025403784439
-3.601321235851749 10.057331467373021
0.466045194906253 19.192786043799030
10.411264148588986 18.147501411122495
12.490381056766580 8.366025403784439
1 2 3 4 5
1 3 5 2 4 1

Note:

The initial position of points in the sample is:

The order in which Rubik can paint segments is: