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.
//package round333;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Comparator;
import java.util.InputMismatchException;
import java.util.Random;

public class D {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni();
		int[] c = na(n);
		char[] s = ns().toCharArray();
		Random gen = new Random(0);
		long mod1 = BigInteger.probablePrime(30, gen).longValue();
		long mod2 = BigInteger.probablePrime(30, gen).longValue();
		long mul1 = BigInteger.probablePrime(29, gen).longValue();
		long mul2 = BigInteger.probablePrime(29, gen).longValue();
		
		int[] from = new int[n - 1];
		int[] to = new int[n - 1];
		for (int i = 0; i < n - 1; i++) {
			from[i] = ni() - 1;
			to[i] = ni() - 1;
		}
		int[] t = new int[300005];
		for(int i = 0;i < t.length;i++){
			t[i] = gen.nextInt(1000000000);
		}
		
		int[][] g = packU(n, from, to);
		int[][] pars = parents3(g, 0);
		int[] par = pars[0], dep = pars[2];
		int[][] rights = makeRights(g, par, 0);
		int[] iord = rights[1], right = rights[2], ord = rights[0];
		
		long[] h1 = new long[n];
		long[] h2 = new long[n];
		for(int i = 0;i < n;i++){
			int cur = ord[i];
			if(cur != 0){
				h1[cur] = h1[par[cur]];
				h2[cur] = h2[par[cur]];
			}
			h1[cur] = (h1[cur] * mul1 + s[cur] * s[cur]) % mod1;
			h2[cur] = (h2[cur] * mul2 + s[cur] * s[cur]) % mod2;
		}
		for(int i = 0;i < n;i++){
			h1[i] = (h1[i] * mul1 + t[dep[i]]) % mod1;
			h2[i] = (h2[i] * mul2 + t[dep[i]]) % mod2;
		}
		
		long[] hh = new long[n];
		for(int i = 0;i < n;i++){
			hh[iord[i]] = h1[i]<<32|h2[i];
		}
		long[] shh = Arrays.copyOf(hh, n);
		Arrays.sort(shh);
		int p = 0;
		for(int i = 0;i < n;i++){
			if(i == 0 || shh[i] != shh[i-1]){
				shh[p++] = shh[i];
			}
		}
		for(int i = 0;i < n;i++){
			hh[i] = Arrays.binarySearch(shh, 0, p, hh[i]);
		}
		int[] prev = new int[p];
		Arrays.fill(prev, -1);
		int[][] rs = new int[p+n+n][];
		int q = 0;
		for(int i = 0;i < n;i++){
			int v = (int)hh[i];
			if(prev[v]+1 <= i-1){
				rs[q++] = new int[]{prev[v]+1, i-1};
			}
			prev[v] = i;
		}
		for(int i = 0;i < p;i++){
			if(prev[i]+1 <= n-1){
				rs[q++] = new int[]{prev[i]+1, n-1};
			}
		}
		for(int i = 0;i < n;i++){
			rs[q++] = new int[]{iord[i], right[iord[i]], i};
		}
		Arrays.sort(rs, 0, q, new Comparator<int[]>() {
			public int compare(int[] a, int[] b) {
				if(a[0] != b[0])return a[0] - b[0];
				if(a[1] != b[1])return -(a[1] - b[1]);
				return a.length - b.length;
			}
		});
		
		int[] ret = new int[n];
		
		int[] ft = new int[n+5];
		int all = 0;
		for(int i = 0;i < q;i++){
			int[] r = rs[i];
			if(r.length == 2){
				addFenwick(ft, r[1], 1);
				all++;
			}else{
				ret[r[2]] = p-(all-sumFenwick(ft, r[1]-1)) + c[r[2]];
			}
		}
		int max = -1;
		int maxcount = 0;
		for(int i = 0;i < n;i++){
			if(ret[i] > max){
				max = ret[i];
				maxcount = 1;
			}else if(ret[i] == max){
				maxcount++;
			}
		}
		out.println(max);
		out.println(maxcount);
	}
	
	public static int sumFenwick(int[] ft, int i) {
		int sum = 0;
		for (i++; i > 0; i -= i & -i)
			sum += ft[i];
		return sum;
	}

	public static void addFenwick(int[] ft, int i, int v) {
		if (v == 0 || i < 0)
			return;
		int n = ft.length;
		for (i++; i < n; i += i & -i)
			ft[i] += v;
	}

	public static int findGFenwick(int[] ft, int v) {
		int i = 0;
		int n = ft.length;
		for (int b = Integer.highestOneBit(n); b != 0 && i < n; b >>= 1) {
			if (i + b < n) {
				int t = i + b;
				if (v >= ft[t]) {
					i = t;
					v -= ft[t];
				}
			}
		}
		return v != 0 ? -(i + 1) : i - 1;
	}

	public static int valFenwick(int[] ft, int i) {
		return sumFenwick(ft, i) - sumFenwick(ft, i - 1);
	}

	public static int[] restoreFenwick(int[] ft) {
		int n = ft.length - 1;
		int[] ret = new int[n];
		for (int i = 0; i < n; i++)
			ret[i] = sumFenwick(ft, i);
		for (int i = n - 1; i >= 1; i--)
			ret[i] -= ret[i - 1];
		return ret;
	}

	public static int before(int[] ft, int x) {
		int u = sumFenwick(ft, x - 1);
		if (u == 0)
			return -1;
		return findGFenwick(ft, u - 1) + 1;
	}

	public static int after(int[] ft, int x) {
		int u = sumFenwick(ft, x);
		int f = findGFenwick(ft, u);
		if (f + 1 >= ft.length - 1)
			return -1;
		return f + 1;
	}

	public static int[] buildFenwick(int[] a) {
		int n = a.length;
		int[] ft = new int[n + 1];
		System.arraycopy(a, 0, ft, 1, n);
		for (int k = 2, h = 1; k <= n; k *= 2, h *= 2) {
			for (int i = k; i <= n; i += k) {
				ft[i] += ft[i - h];
			}
		}
		return ft;
	}

	public static int[] buildFenwick(int n, int v) {
		int[] ft = new int[n + 1];
		Arrays.fill(ft, 1, n + 1, v);
		for (int k = 2, h = 1; k <= n; k *= 2, h *= 2) {
			for (int i = k; i <= n; i += k) {
				ft[i] += ft[i - h];
			}
		}
		return ft;
	}
	
	public static int[] sortByPreorder(int[][] g, int root){
		int n = g.length;
		int[] stack = new int[n];
		int[] ord = new int[n];
		BitSet ved = new BitSet();
		stack[0] = root;
		int p = 1;
		int r = 0;
		ved.set(root);
		while(p > 0){
			int cur = stack[p-1];
			ord[r++] = cur;
			p--;
			for(int e : g[cur]){
				if(!ved.get(e)){
					stack[p++] = e;
					ved.set(e);
				}
			}
		}
		return ord;
	}
	
	public static int[][] makeRights(int[][] g, int[] par, int root)
	{
		int n = g.length;
		int[] ord = sortByPreorder(g, root);
		int[] iord = new int[n];
		for(int i = 0;i < n;i++)iord[ord[i]] = i;
		
		int[] right = new int[n];
		for(int i = n-1;i >= 0;i--){
			int v = i;
			for(int e : g[ord[i]]){
				if(e != par[ord[i]]){
					v = Math.max(v, right[iord[e]]);
				}
			}
			right[i] = v;
		}
		return new int[][]{ord, iord, right};
	}

	
	public static int[][] parents3(int[][] g, int root) {
		int n = g.length;
		int[] par = new int[n];
		Arrays.fill(par, -1);

		int[] depth = new int[n];
		depth[0] = 0;

		int[] q = new int[n];
		q[0] = root;
		for (int p = 0, r = 1; p < r; p++) {
			int cur = q[p];
			for (int nex : g[cur]) {
				if (par[cur] != nex) {
					q[r++] = nex;
					par[nex] = cur;
					depth[nex] = depth[cur] + 1;
				}
			}
		}
		return new int[][] { par, q, depth };
	}

	static int[][] packU(int n, int[] from, int[] to) {
		int[][] g = new int[n][];
		int[] p = new int[n];
		for (int f : from)
			p[f]++;
		for (int t : to)
			p[t]++;
		for (int i = 0; i < n; i++)
			g[i] = new int[p[i]];
		for (int i = 0; i < from.length; i++) {
			g[from[i]][--p[from[i]]] = to[i];
			g[to[i]][--p[to[i]]] = from[i];
		}
		return g;
	}
	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new D().run(); }
	
	private byte[] inbuf = new byte[1024];
	private int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}
