2G. Zero Distance

You are given a directed graph with $n$ vertices and $m$ directed edges.
Each directed edge $(u \to v)$ has an integer weight $w$.

If you traverse an edge in its given direction $(u \to v)$, the cost is $w$.
If you traverse it in the opposite direction $(v \to u)$, the cost is $-w$.

For any walk, its cost is the sum of costs of its steps.

Define $dist(a,b)$ as the minimum possible cost among all walks from $a$ to $b$.

We say the graph is good if it has no negative closed walk, meaning there is no walk that starts and ends at the same vertex with total cost $< 0$.
Equivalently, the graph is good iff for every vertex $v$, we have $dist(v,v)=0$.

In one operation, you may choose one directed edge and do one of the following:

• increase its weight by $1$
• decrease its weight by $1$

Find the minimum number of operations needed to make the graph good.

Constraints:

• $1 \le n \le 20$
• $0 \le m \le 400$
• $0 \le w \le 100$
• $v \neq u$