5000: Acyclic Organic Compounds
内存限制：256 MB
时间限制：2 S
标准输入输出
题目类型：传统
评测方式：文本比较
上传者：
提交：1
通过：1
题目描述
D. Acyclic Organic Compounds
time limit per test
3 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output
You are given a tree T with n vertices (numbered 1 through n) and a letter in each vertex. The tree is rooted at vertex 1.
Let's look at the subtree Tv of some vertex v. It is possible to read a string along each simple path starting at v and ending at some vertex in Tv (possibly v itself). Let's denote the number of distinct strings which can be read this way as
.
Also, there's a number cv assigned to each vertex v. We are interested in vertices with the maximum value of
.
You should compute two statistics: the maximum value of and the number of vertices v with the maximum .
Let's look at the subtree Tv of some vertex v. It is possible to read a string along each simple path starting at v and ending at some vertex in Tv (possibly v itself). Let's denote the number of distinct strings which can be read this way as
. Also, there's a number cv assigned to each vertex v. We are interested in vertices with the maximum value of
. You should compute two statistics: the maximum value of
and the number of vertices v with the maximum .
Input
The first line of the input contains one integer n (1≤n≤300000)− the number of vertices of the tree. The second line contains n space-separated integers ci (0≤ci≤109).
The third line contains a string s consisting of n lowercase English letters− the i-th character of this string is the letter in vertex i.
The following n-1 lines describe the tree T. Each of them contains two space-separated integers u and v (1≤u,v≤n) indicating an edge between vertices u and v.
It's guaranteed that the input will describe a tree.
Output
Print two lines. On the first line, print
over all 1≤i≤n. On the second line, print the number of vertices v for which
.
Examples
Input
10 1 2 7 20 20 30 40 50 50 50 cacabbcddd 1 2 6 8 7 2 6 2 5 4 5 9 3 10 2 5 2 3
Output
51 3
Input
6 0 2 4 1 1 1 raaaba 1 2 2 3 2 4 2 5 3 6
Output
6 2
Note
In the first sample, the tree looks like this: 
The sets of strings that can be read from individual vertices are: 
Finally, the values of 
are: 
In the second sample, the values of 
are (5,4,2,1,1,1). The distinct strings read in T2 are 
; note that 
can be read down to vertices 3 or 4. 输入样例 复制
输出样例 复制