I. Silver table
time limit per test
1 second
memory limit per test
64 megabytes
input
standard input
output
standard output

Few people know that long long ago they used to apply silver tables besides well-known silver bullets to fight with evil spirits (witches, vampires, werewolves, etc.). The use principle of these tables is simple: if You want to protect yourself from the N - creatures, You need to carve on your door a table. The size of a table should be 2N × 2N, filled with integers from the set S = {1, 2, ..., 2N + 1 - 1}.

But, of course, not every table is considered silver. In order to definitely protect You from N units of evil, the table must have a special property: for every integer i from 1 to 2N the set formed by the i-th row, and the set formed by the i-th column, in the union must give the set S.

Nowadays there is fewer and fewer confidence that vampires and witches don't exist. Therefore, the ability to create a silver table for arbitrary N is in your best interest :)

Input

Single line contains a positive integer N (1 ≤ N ≤ 10) — the number of creatures, from which the silver table of size 2N  ×  2N will protect you.

Output

Output 2N lines with 2N numbers. Each number should belong to the set S and the resulting table should be silver.

Examples
Input
1
Output
1 3 
2 1