White-Black Balanced Subtrees

1000ms

262144K

Description:

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.

$\text{[math]}$ 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.

Input:

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 $$$a_2, \dots, a_n$$$ ($$$1 \le a_i < i$$$) — 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 $$$2 \cdot 10^5$$$.

Output:

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

Sample Input:

3
7
1 1 2 3 3 5
WBBWWBW
2
1
BW
8
1 2 3 4 5 6 7
BWBWBWBW

Sample Output:

2
1
4

Note:

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.

Informação

Provedor Codeforces

Código CF1676G