Oh how the cows love to walk in their square pasture with sides of length N (1 <= N <= 750) and which is partitioned into N*N squares. They enjoy the sights, the smells, and the general ambience of the grass and trees.</p>

Bessie has decided to take the cows on the longest possible walk from the upper left corner to the center (or near the center when N is even) of the pasture, passing through each and every square along the way after starting.

She has decided to create the obvious clockwise spiral route (example below) for this evening's stroll. Write a program to create a map for her that shows the order of squares she should visit.

By way of example, for pastures of size N=3 and N=4, here are the routes Bessie should use:

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

Line 1: A single integer: N

출력 형식

Lines 1..N: N space-separated integers</p>

예제 입력

3

예제 출력

1 2 3
8 9 4
7 6 5