Bypass matrix with "snake"

For a given number n fill the square matrix of size n * n with integers from 1 to n^2 as follows:

• The number 1 is in the upper left corner;

• Then numbers go like a "snake", i.e. in ascending order from left to right in the odd lines and from right to left in the even;

Input

One integer n (1 ≤ n ≤ 100).

Output

Print the filled matrix in the form of n rows by n integers each.

Examples