Let $G$ be an $n \times n$ grid graph, with each undirected edge having a certain weight. Specifically, the vertices of $G$ can be labeled as $(i,j)$ where $1 \le i,j \le n$. There is an edge between $(i,j)$ and $(k,\ell)$ if and only if $|i-k|+|j-\ell|=1$. Suppose we want to compute the value of a minimum cut that separates $(1,1)$ and $(n,n)$. The value of a cut is defined as the sum of weights to all edges crossing the cut.

Four students proposed different ideas for solving this task. Let us examine their approaches and select all correct statements below.