21013번 - Occult Square 스페셜 저지다국어

A magic square is a square array of non-negative integers where the sums of the numbers on each row, each column, and both main diagonals are the same. An N × N occult square is a magic square with N rows and N columns with additional constraints:

• The integers in the square are between 0 and N, inclusive.
• For all 1 ≤ i ≤ N, the number i appears at most i times in the square.
• There are at least two distinct positive integers in the square.

For example, the following is a 5 × 5 occult square, where the sums of the numbers on each row, each column, and both main diagonals are 7:

0 0 0 3 4
2 4 0 0 1
0 0 3 4 0
5 0 0 0 2
0 3 4 0 0

For a given prime number P, you are asked to construct a P × P occult square, or determine whether no such occult square exists.

Input contains a prime number: P (2 ≤ P ≤ 1000) representing the number of rows and columns in the occult square.

If there is no P × P occult square, simply output -1 in a line. Otherwise, output P lines, each contains P integers representing an occult square. The j^th integer on the i^th line is the integer on the i^th row and the j^th column in the occult square. You may output any P × P occult square.