You've got an n × n × n cube, split into unit cubes. Your task is to number all unit cubes in this cube with positive integers from 1 to n 3 so that: each number was used as a cube's number exactly once; for each 1 ≤ i n 3 , unit cubes with numbers i and i + 1 were neighbouring (that is, shared a side); for each 1 ≤ i n there were at least two different subcubes with sizes i × i × i , made from unit cubes, which are numbered with consecutive numbers. That is, there are such two numbers x and y , that the unit cubes of the first subcube are numbered by numbers x , x + 1, ..., x + i 3 - 1, and the unit cubes of the second subcube are numbered by numbers y , y + 1, ..., y + i 3 - 1. Find and print the required numeration of unit cubes of the cube.

输入描述:

The first line contains a single integer n (1 ≤ n ≤ 50) — the size of the cube, whose unit cubes need to be numbered.

输出描述:

Print all layers of the cube as nn × n matrices. Separate them with new lines. Print the layers in the order in which they follow in the cube. See the samples for clarifications. It is guaranteed that there always is a solution that meets the conditions given in the problem statement.

备注:

In the sample the cubes with sizes 2 × 2 × 2 are numbered with integers 1, ..., 8 and 5, ..., 12.