The Quest for the Sacred Groves

In the heart of ancient Romania, where dense forests meet towering mountains, lies the enchanted kingdom of Vatra Codrilor. The kingdom is protected by $n$ sacred groves, numbered from $1$ to $n$, and each grove is watched over by a guardian spirit. The groves are connected by secret paths known only to the wise elders. Formally, the secret paths form a tree.

One night, as the full moon rises, the $n$ guardians receive a divine message from the Dacian gods. The message is an ancient scroll with a list $p$. Formally, $p$ is a sequence of length $n$ in which every number from $1$ to $n$ appears exactly once. The list gives the order in which the guardians must stand in the final battle.

For each subsegment $[\ell, r]$ of the list, if the groves $p_{\ell}, p_{\ell+1}, \ldots, p_{r}$ are connected through the secret paths without involving any other groves, the guardians of these groves can meet together and draw on the power of the forest.

Count the number of subsegments $[\ell, r]$ with $1 \leq \ell \leq r \leq n$ that have this property.

The first line contains an integer $n$ ($1 \leq n \leq 2 \cdot 10^5$).

Each of the next $n - 1$ lines contains two integers $u_i$ and $v_i$ ($1 \leq u_i, v_i \leq n$), denoting an edge of the tree.

The last line contains the $n$ distinct integers $p_1, p_2, \ldots, p_n$ ($1 \leq p_i \leq n$).

Print a single integer: the number of subsegments $[\ell, r]$ with $1 \leq \ell \leq r \leq n$ such that the groves $p_{\ell}, p_{\ell+1}, \ldots, p_{r}$ form a connected subgraph.