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 n3 so that: Find and print the required numeration of unit cubes of the cube. The first line contains a single integer n (1 ≤ n ≤ 50) -- the size of the cube, whose unit cubes need to be numbered. Print all layers of the cube as n n × 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. In the sample the cubes with sizes 2 × 2 × 2 are numbered with integers 1, ..., 8 and 5, ..., 12.