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 <image>. 

Also, there's a number cv assigned to each vertex v. We are interested in vertices with the maximum value of <image>.

You should compute two statistics: the maximum value of <image> and the number of vertices v with the maximum <image>.

Input

The first line of the input contains one integer n (1 ≤ n ≤ 300 000) — 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 <image> over all 1 ≤ i ≤ n. 

On the second line, print the number of vertices v for which <image>.

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:

<image>

The sets of strings that can be read from individual vertices are:

<image>

Finally, the values of <image> are:

<image>

In the second sample, the values of <image> are (5, 4, 2, 1, 1, 1). The distinct strings read in T2 are <image>; note that <image> can be read down to vertices 3 or 4.
import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Calendar;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.SortedSet;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * #
 * 
 * @author pttrung
 */
public class D_Round_333_Div1 {

	public static long MOD = 1000000007;
	static long max = 0;
	static int num = 0;
	static int curIndex = 1;
	static int newNode = 0;

	public static void main(String[] args) throws FileNotFoundException {
		// PrintWriter out = new PrintWriter(new FileOutputStream(new File(
		// "output.txt")));
		PrintWriter out = new PrintWriter(System.out);
		Scanner in = new Scanner();
		int n = in.nextInt();
		long[] data = new long[n];
		ArrayList<Integer>[] map = new ArrayList[n];
		for (int i = 0; i < n; i++) {
			data[i] = in.nextLong();
			map[i] = new ArrayList();
		}
		String line = in.next();
		for (int i = 0; i < n - 1; i++) {
			int u = in.nextInt() - 1;
			int v = in.nextInt() - 1;
			map[u].add(v);
			map[v].add(u);
		}
		Node root = new Node();
		newNode++;
		boolean[] check = new boolean[n];
		check[0] = true;
		cal(0, check, root, line, data, map, new FT(n + 2));
		out.println(max);
		out.println(num);
		out.close();
	}

	static void cal(int index, boolean[] check, Node cur, String line,
			long[] data, ArrayList<Integer>[] map, FT secondNode) {
		int store = curIndex;
		cur.index = curIndex++;
		// System.out.println("CUR " + (index + 1) + " " + secondNode.get(7));
		int pre = newNode;
		long other = secondNode.get(store);
		for (int i : map[index]) {
			if (!check[i]) {
				check[i] = true;
				char c = line.charAt(i);
				if (cur.nxt.containsKey(c)) {
					Node nxt = cur.nxt.get(c);
					secondNode.update(nxt.index, 1);
					cal(i, check, nxt, line, data, map, secondNode);
				} else {
					Node nxt = new Node();
					newNode++;
					cur.nxt.put(c, nxt);
					cal(i, check, nxt, line, data, map, secondNode);
				}
			}
		}
		long v = newNode - pre + secondNode.get(store) + data[index] + 1
				- other;

		if (v > max) {
			max = v;
			num = 1;
		} else if (v == max) {
			num++;
		}
	}

	static class Node {
		HashMap<Character, Node> nxt = new HashMap();
		int index = 0;
	}

	public static int[] KMP(String val) {
		int i = 0;
		int j = -1;
		int[] result = new int[val.length() + 1];
		result[0] = -1;
		while (i < val.length()) {
			while (j >= 0 && val.charAt(j) != val.charAt(i)) {
				j = result[j];
			}
			j++;
			i++;
			result[i] = j;
		}
		return result;

	}

	public static boolean nextPer(int[] data) {
		int i = data.length - 1;
		while (i > 0 && data[i] < data[i - 1]) {
			i--;
		}
		if (i == 0) {
			return false;
		}
		int j = data.length - 1;
		while (data[j] < data[i - 1]) {
			j--;
		}
		int temp = data[i - 1];
		data[i - 1] = data[j];
		data[j] = temp;
		Arrays.sort(data, i, data.length);
		return true;
	}

	public static int digit(long n) {
		int result = 0;
		while (n > 0) {
			n /= 10;
			result++;
		}
		return result;
	}

	public static double dist(long a, long b, long x, long y) {
		double val = (b - a) * (b - a) + (x - y) * (x - y);
		val = Math.sqrt(val);
		double other = x * x + a * a;
		other = Math.sqrt(other);
		return val + other;

	}

	public static class Point implements Comparable<Point> {

		int x, y;

		public Point(int start, int end) {
			this.x = start;
			this.y = end;
		}

		@Override
		public int hashCode() {
			int hash = 5;
			hash = 47 * hash + this.x;
			hash = 47 * hash + this.y;
			return hash;
		}

		@Override
		public boolean equals(Object obj) {
			if (obj == null) {
				return false;
			}
			if (getClass() != obj.getClass()) {
				return false;
			}
			final Point other = (Point) obj;
			if (this.x != other.x) {
				return false;
			}
			if (this.y != other.y) {
				return false;
			}
			return true;
		}

		@Override
		public int compareTo(Point o) {
			return Integer.compare(x, o.x);
		}
	}

	public static class FT {

		long[] data;

		FT(int n) {
			data = new long[n];
		}

		public void update(int index, long value) {
			while (index < data.length) {
				data[index] += value;
				index += (index & (-index));
			}
		}

		public long get(int index) {
			long result = 0;
			while (index > 0) {
				result += data[index];
				index -= (index & (-index));
			}
			return result;

		}
	}

	public static long gcd(long a, long b) {
		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	public static long pow(long a, long b) {
		if (b == 0) {
			return 1;
		}
		if (b == 1) {
			return a;
		}
		long val = pow(a, b / 2);
		if (b % 2 == 0) {
			return val * val % MOD;
		} else {
			return val * (val * a % MOD) % MOD;

		}
	}

	static class Scanner {

		BufferedReader br;
		StringTokenizer st;

		public Scanner() throws FileNotFoundException {
			// System.setOut(new PrintStream(new
			// BufferedOutputStream(System.out), true));
			br = new BufferedReader(new InputStreamReader(System.in));
			// br = new BufferedReader(new InputStreamReader(new
			// FileInputStream(new File("input.txt"))));
		}

		public String next() {

			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception e) {
					throw new RuntimeException();
				}
			}
			return st.nextToken();
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public String nextLine() {
			st = null;
			try {
				return br.readLine();
			} catch (Exception e) {
				throw new RuntimeException();
			}
		}

		public boolean endLine() {
			try {
				String next = br.readLine();
				while (next != null && next.trim().isEmpty()) {
					next = br.readLine();
				}
				if (next == null) {
					return true;
				}
				st = new StringTokenizer(next);
				return st.hasMoreTokens();
			} catch (Exception e) {
				throw new RuntimeException();
			}
		}
	}
}
