In this problem we consider
n ×
n tables
filled with integers from 1 to
n^{2} in such a way that the following conditions are satisfied.
 Each number occurs exactly once in the table.
 For each i from 2 to n^{2} the cells of the
table that contain i and i − 1 must have a shared side.
Let’s define a primality of a column as the number of its cells
containing prime numbers, and a primality of a table as the
maximum primality of all its columns.
Find the table with the maximum primality among all
tables that satisfy the stated conditions.
Input
The only line contains an integer n (1 ≤ n ≤ 256).
Output
Output the required table. If there are several tables with the maximum
primality, you may output any of them.
Sample
input  output 

4
 2 1 12 11
3 16 13 10
4 15 14 9
5 6 7 8

Notes
The primality of the table in the sample output is equal to 3 (this is the primality of its first column).
Problem Author: Mikhail Rubinchik, special thanks to Alexander Ipatov
Problem Source: Open Ural FU Championship 2013