CF1676G.White-Black Balanced Subtrees

You are given a rooted tree consisting of $n$ vertices numbered from $1$ to $n$. The root is vertex $1$. There is also a string $s$ denoting the color of each vertex: if $s_i = \texttt{B}$, then vertex $i$ is black, and if $s_i = \texttt{W}$, then vertex $i$ is white.

A subtree of the tree is called balanced if the number of white vertices equals the number of black vertices. Count the number of balanced subtrees.

A tree is a connected undirected graph without cycles. A rooted tree is a tree with a selected vertex, which is called the root. In this problem, all trees have root $1$.

The tree is specified by an array of parents $a_2, \dots, a_n$ containing $n-1$ numbers: $a_i$ is the parent of the vertex with the number $i$ for all $i = 2, \dots, n$. The parent of a vertex $u$ is a vertex that is the next vertex on a simple path from $u$ to the root.

The subtree of a vertex $u$ is the set of all vertices that pass through $u$ on a simple path to the root. For example, in the picture below, $7$ is in the subtree of $3$ because the simple path $7 \to 5 \to 3 \to 1$ passes through $3$. Note that a vertex is included in its subtree, and the subtree of the root is the entire tree.

The picture shows the tree for $n=7$, $a=[1,1,2,3,3,5]$, and $s=\texttt{WBBWWBW}$. The subtree at the vertex $3$ is balanced.

你被给定一棵包含 $n$ 个顶点（编号从 $1$ 到 $n$）的有根树，根节点为顶点 $1$。同时给定一个字符串 $s$，表示每个顶点的颜色：若 $s_i = \texttt{B}$，则顶点 $i$ 为黑色；若 $s_i = \texttt{W}$，则顶点 $i$ 为白色。

若一棵子树中白色顶点的数量等于黑色顶点的数量，则称该子树为平衡的。请计算平衡子树的总数。

树是一个无环的连通无向图。有根树是一棵选定某个顶点作为根的树。本题中，所有树的根均为 $1$。

该树由一个父节点数组 $a_2, \dots, a_n$（共 $n-1$ 个数）给出：对所有 $i = 2, \dots, n$，$a_i$ 表示编号为 $i$ 的顶点的父节点。顶点 $u$ 的父节点是指从 $u$ 到根节点的简单路径上的下一个顶点。

顶点 $u$ 的子树是指所有在通往根节点的简单路径上经过 $u$ 的顶点构成的集合。例如，在下图中，$7$ 属于顶点 $3$ 的子树，因为简单路径 $7 \to 5 \to 3 \to 1$ 经过了 $3$。注意：每个顶点都属于其自身的子树，且根节点的子树即为整棵树。

图中展示了 $n=7$、$a=[1,1,2,3,3,5]$、$s=\texttt{WBBWWBW}$ 对应的树。顶点 $3$ 处的子树是平衡的。

The first line of input contains an integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

The first line of each test case contains an integer $n$ ($2 \le n \le 4000$) — the number of vertices in the tree.

The second line of each test case contains $n-1$ integers $a_2, \dots, a_n$ ($1 \le a_i \lt i$) — the parents of the vertices $2, \dots, n$.

The third line of each test case contains a string $s$ of length $n$ consisting of the characters $\texttt{B}$ and $\texttt{W}$ — the coloring of the tree.

It is guaranteed that the sum of the values $n$ over all test cases does not exceed $2 \cdot 10^5$.

输入的第一行包含一个整数 $t$（$1 \le t \le 10^4$）——测试用例的数量。

每个测试用例的第一行包含一个整数 $n$（$2 \le n \le 4000$）——树中顶点的数量。

每个测试用例的第二行包含 $n-1$ 个整数 $a_2, \dots, a_n$（$1 \le a_i \lt i$）——顶点 $2, \dots, n$ 的父节点。

每个测试用例的第三行包含一个长度为 $n$ 的字符串 $s$，由字符 $\texttt{B}$ 和 $\texttt{W}$ 组成——树的着色方案。

保证所有测试用例的 $n$ 值之和不超过 $2 \cdot 10^5$。

For each test case, output a single integer — the number of balanced subtrees.

对于每个测试用例，输出一个整数——平衡子树的数量。

The first test case is pictured in the statement. Only the subtrees at vertices $2$ and $3$ are balanced.

In the second test case, only the subtree at vertex $1$ is balanced.

In the third test case, only the subtrees at vertices $1$, $3$, $5$, and $7$ are balanced.

第一个测试用例如题面图示所示。仅有顶点 $2$ 和 $3$ 处的子树是平衡的。

第二个测试用例中，仅有顶点 $1$ 处的子树是平衡的。

第三个测试用例中，仅有顶点 $1$、$3$、$5$ 和 $7$ 处的子树是平衡的。