Power Plant

The JOI power plant has $N$ bases numbered from 1 to $N$. The bases are connected by $N-1$ wires. The $i$-th wire ($1 \le i \le N-1$) connects the base $A_i$ and the base $B_i$, in both directions. You can travel from any base to any other base by passing through some wires.

Each base has at most one power generator, and each generator has a switch. At the beginning, the switch of every generator is OFF. You are the director of the plant. You may choose some generators and turn their switches ON. Choosing none is allowed. The generators have the following properties.

• Suppose bases $x$, $y$, and $z$ have generators, and you can travel from $x$ to $y$ and then from $y$ to $z$ without passing through the same wire twice. If the switches of the generators at $x$ and $z$ are ON, then the generator at $y$ is broken.
• A generator is activated if its switch is ON and it is not broken.

You get 1 yen for each activated generator. You pay 1 yen for each broken generator. Your profit is the total reward minus the total repair expense.

Write a program that, given the bases, the wires, and the generator information, computes the maximum profit.

The first line contains $N$. Each of the next $N-1$ lines contains $A_i$ and $B_i$. The last line contains a string $S$ of length $N$.

N
A_1 B_1
...
A_{N-1} B_{N-1}
S

The $i$-th character of $S$ describes base $i$. It is 0 if the base has no generator and 1 if it has one.

Write one line to the standard output containing the maximum profit when you choose some generators and turn their switches ON.

• $1 \le N \le 200\,000$.
• $S$ is a string of length $2N$ consisting of B and W. The character B appears $N$ times in $S$, and the character W appears $N$ times in $S$.