Grid Construction (Even)

**This is the even version of the Grid Construction Problem. Both are worth 50 points each.** You are given an **even** integer $N$. Now your task is to construct a grid $A$ containing $N$ rows and $N$ columns such that : - For every $i,j(1 \le i,j \le N)$ $1 \le A_{i,j} \le N$ have to be satisfied. - For every $x(1 \le x \le N)$, $x$ appears **exactly** $N$ times in $A$. - Let $S_1$ be the sum