Magic Square and Sudoku

Jisu became friends with Joshua Müller, a passionate math puzzle fan, while studying in Germany. Joshua especially likes magic squares (Zauberquadrat) and Sudoku. According to Joshua, people think Sudoku is fun to solve at any time, but magic squares are rarely solved because their easy solving method is well known.

A magic square is defined as follows.

The board of a magic square is an $N \times N$ grid. Each cell must contain exactly one integer from $1$ to $N^2$. The sum of the numbers in each of the $N$ rows, each of the $N$ columns, and the 2 diagonals must all be equal.

A Sudoku is defined as follows.

The board of a Sudoku is an $N^2 \times N^2$ grid, divided into $N^2$ smaller boards of size $N \times N$. Each cell can contain an integer from $1$ to $N^2$. In each of the $N^2$ rows, $N^2$ columns, and $N^2$ smaller boards, each integer from $1$ to $N^2$ must appear exactly once.

Joshua wants to combine magic squares with Sudoku. He tries to build an $N^2 \times N^2$ Sudoku in which each of the $N^2$ smaller boards is a magic square. Joshua found quickly that such a puzzle is impossible when $N = 3$. Soon after, he easily built a $16 \times 16$ ($N = 4$) puzzle that meets his conditions.

Joshua asks Jisu to build a $16 \times 16$ puzzle that meets his conditions. Jisu is busy with an internship at a lab, so you will build the $16 \times 16$ puzzle instead.

This problem has no input.

Print the constructed puzzle over 16 lines. If there are several answers, print any one of them.