Curious Matrix

You are given a prime $p$ and a matrix $M$ with $N$ rows (numbered $1$ through $N$) and $N$ columns (numbered $1$ through $N$). For each row $r$ and column $c$, the cell in row $r$ and column $c$ can either be empty or contain an integer $M_{r, c}$. Initially, all cells are empty. Now you should process $Q$ queries. In each query, you are given integers $x$, $y$ and $v$ and you should do the fo