CF902B.Coloring a Tree

You are given a rooted tree with n vertices. The vertices are numbered from 1 to n, the root is the vertex number 1.

Each vertex has a color, let's denote the color of vertex v by c__v. Initially c__v = 0.

You have to color the tree into the given colors using the smallest possible number of steps. On each step you can choose a vertex v and a color x, and then color all vectices in the subtree of v (including v itself) in color x. In other words, for every vertex u, such that the path from root to u passes through v, set c__u = x.

It is guaranteed that you have to color each vertex in a color different from 0.

You can learn what a rooted tree is using the link: https://en.wikipedia.org/wiki/Tree_(graph_theory).

你被给定一棵包含 $n$ 个顶点的有根树。顶点编号为 $1$ 到 $n$，其中根节点为顶点 $1$。

每个顶点都有一个颜色，记顶点 $v$ 的颜色为 $c_v$。初始时 $c_v = 0$。

你需要通过最少的操作次数，将整棵树染成目标颜色。每次操作中，你可以选择一个顶点 $v$ 和一种颜色 $x$，并将 $v$ 的子树（包括 $v$ 自身）中所有顶点染成颜色 $x$。换言之，对每个顶点 $u$，若从根到 $u$ 的路径经过 $v$，则令 $c_u = x$。

题目保证：最终每个顶点的颜色均不为 $0$。

你可通过如下链接了解有根树的定义：https://en.wikipedia.org/wiki/Tree_(graph_theory)。

The first line contains a single integer n (2 ≤ n ≤ 104) — the number of vertices in the tree.

The second line contains n - 1 integers _p_2, _p_3, ..., p__n (1 ≤ p__i < i), where p__i means that there is an edge between vertices i and p__i.

The third line contains n integers _c_1, _c_2, ..., c__n (1 ≤ c__i ≤ n), where c__i is the color you should color the i-th vertex into.

It is guaranteed that the given graph is a tree.

第一行包含一个整数 $n$（$2 \leq n \leq 10^4$）——树中顶点的数量。

第二行包含 $n-1$ 个整数 $p_2,\ p_3,\ \dots,\ p_n$（$1 \leq p_i < i$），其中 $p_i$ 表示顶点 $i$ 与顶点 $p_i$ 之间存在一条边。

第三行包含 $n$ 个整数 $c_1,\ c_2,\ \dots,\ c_n$（$1 \leq c_i \leq n$），其中 $c_i$ 表示第 $i$ 个顶点应被染成的颜色。

保证所给图是一棵树。

Print a single integer — the minimum number of steps you have to perform to color the tree into given colors.

输出一个整数——将树染成给定颜色所需的最少操作步数。

The tree from the first sample is shown on the picture (numbers are vetices' indices):

On first step we color all vertices in the subtree of vertex 1 into color 2 (numbers are colors):

On seond step we color all vertices in the subtree of vertex 5 into color 1:

On third step we color all vertices in the subtree of vertex 2 into color 1:

The tree from the second sample is shown on the picture (numbers are vetices' indices):

On first step we color all vertices in the subtree of vertex 1 into color 3 (numbers are colors):

On second step we color all vertices in the subtree of vertex 3 into color 1:

On third step we color all vertices in the subtree of vertex 6 into color 2:

On fourth step we color all vertices in the subtree of vertex 4 into color 1:

On fith step we color all vertices in the subtree of vertex 7 into color 3:

第一个样例中的树如图所示（数字为顶点的编号）：

第一步：我们将顶点 1 的子树中所有顶点染成颜色 2（数字表示颜色）：

第二步：我们将顶点 5 的子树中所有顶点染成颜色 1：

第三步：我们将顶点 2 的子树中所有顶点染成颜色 1：

第二个样例中的树如图所示（数字为顶点的编号）：

第一步：我们将顶点 1 的子树中所有顶点染成颜色 3（数字表示颜色）：

第二步：我们将顶点 3 的子树中所有顶点染成颜色 1：

第三步：我们将顶点 6 的子树中所有顶点染成颜色 2：

第四步：我们将顶点 4 的子树中所有顶点染成颜色 1：

第五步：我们将顶点 7 的子树中所有顶点染成颜色 3：