Odd Matrix

You are given an integer $N$. Your task is to construct a matrix of size $N\times N$ satisfying all the following conditions: - All elements are between $1$ and $N^2$; - All elements are pairwise **distinct**; - The sum of elements in every row is **odd**; - The sum of elements in every column is **odd**. It can be shown that under the given constraints, at least one such matrix exists for every