Balanced 0-1 Tree

You have a tree of $N$ vertices rooted at vertex $1$, where $N$ is **even**. The $i$-th vertex has a binary value $A_i$ written on it (i.e, each $A_i$ is either $0$ or $1$). A tree is said to be **balanced** if and only if the number of zeros written on its vertices equals the number of ones written on its vertices. You can select some **disjoint** subtrees and flip the values on them (i.e, make