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.

Input

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

Output

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.

Note

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