Problem: You are given an undirected tree of n vertices. 

Some vertices are colored blue, some are colored red and some are uncolored. It is guaranteed that the tree contains at least one red vertex and at least one blue vertex.

You choose an edge and remove it from the tree. Tree falls apart into two connected components. Let's call an edge nice if neither of the resulting components contain vertices of both red and blue colors.

How many nice edges are there in the given tree?

Input

The first line contains a single integer n (2 ≤ n ≤ 3 ⋅ 10^5) — the number of vertices in the tree.

The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 2) — the colors of the vertices. a_i = 1 means that vertex i is colored red, a_i = 2 means that vertex i is colored blue and a_i = 0 means that vertex i is uncolored.

The i-th of the next n - 1 lines contains two integers v_i and u_i (1 ≤ v_i, u_i ≤ n, v_i ≠ u_i) — the edges of the tree. It is guaranteed that the given edges form a tree. It is guaranteed that the tree contains at least one red vertex and at least one blue vertex.

Output

Print a single integer — the number of nice edges in the given tree.

Examples

Input


5
2 0 0 1 2
1 2
2 3
2 4
2 5


Output


1


Input


5
1 0 0 0 2
1 2
2 3
3 4
4 5


Output


4


Input


3
1 1 2
2 3
1 3


Output


0

Note

Here is the tree from the first example:

<image>

The only nice edge is edge (2, 4). Removing it makes the tree fall apart into components \{4\} and \{1, 2, 3, 5\}. The first component only includes a red vertex and the second component includes blue vertices and uncolored vertices.

Here is the tree from the second example:

<image>

Every edge is nice in it.

Here is the tree from the third example:

<image>

Edge (1, 3) splits the into components \{1\} and \{3, 2\}, the latter one includes both red and blue vertex, thus the edge isn't nice. Edge (2, 3) splits the into components \{1, 3\} and \{2\}, the former one includes both red and blue vertex, thus the edge also isn't nice. So the answer is 0.

Solution (in JAVA):

Solution:

import java.io.*;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.*;

public class Solu {

    static StringBuffer str = new StringBuffer();
    static InputReader in = new InputReader(System.in);
    static int mm = 1000000007;
    static int n;
    static ArrayList<Integer> tree[];
    static int r,b;
    static int a[];
    static Entity ch[];
    static boolean vis[];
    static void dfs(int x){
        vis[x]=true;
        ch[x]=new Entity(a[x]==1?1:0,a[x]==2?1:0);
        for(Integer it:tree[x]){
            if(vis[it]==false){
                dfs(it);
                ch[x].a=ch[x].a+ch[it].a;
                ch[x].c=ch[x].c+ch[it].c;
            }            
        }        
    }
    public static void main(String[] args) {
        int t, i, j, tt, m, k;
        t = 1;
        for (tt = 0; tt < t; tt++) {
            n=in.nextInt();
            a=new int[n];
            r=0;
            b=0;
            for(i=0;i<n;i++){
                a[i]=in.nextInt();
                if(a[i]==1)
                    r++;
                if(a[i]==2)
                    b++;
            }
            tree=new ArrayList[n];
            for(i=0;i<n;i++){
                tree[i]=new ArrayList();
            }
            for(i=0;i<n-1;i++){
                int x=in.nextInt()-1;
                int y=in.nextInt()-1;
                tree[x].add(y);
                tree[y].add(x);
            }
            ch=new Entity[n];
            vis=new boolean[n];
            dfs(0);
            int cc=0;
            for(i=1;i<n;i++){
                int r1=r-ch[i].a;
                int b1=b-ch[i].c;
                if((r1>0 && b1>0) || (ch[i].a >0 && ch[i].c>0) )
                    continue;
                cc++;
            }
            System.out.println(cc);
        }
        pn();
    }
    static final Comparator<Entity> com = new Comparator<Entity>() {
        public int compare(Entity x, Entity y) {
            int xx = Integer.compare(x.a, y.a);
            if (xx == 0) {
                return Long.compare(y.c, x.c);
            } else {
                return xx;
            }
        }
    };

    static class Pair {

        int a, b, c;

        Pair(int x, int y, int z) {
            a = x;
            b = y;
            c = z;
        }
    }

    static class Entity {

        int a;
        int c;

        Entity(int p, int q) {
            a = p;
            c = q;
        }
    }

    static long gcd(long a, long b) {
        return (b == 0) ? a : gcd(b, a % b);
    }

    static int gcdi(int a, int b) {
        return (b == 0) ? a : gcdi(b, a % b);
    }

    static long power(long x, int y, int m) {
        if (y == 0) {
            return 1;
        }
        long p = power(x, y / 2, m) % m;
        p = (p * p) % m;
        return (y % 2 == 0) ? p : (x * p) % m;
    }

    public static void ap(String st) {
        str.append(st);
    }

    public static void pn() {
        System.out.println(str);
    }

    static class InputReader {

        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new UnknownError();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new UnknownError();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int peek() {
            if (numChars == -1) {
                return -1;
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    return -1;
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar];
        }

        public void skip(int x) {
            while (x-- > 0) {
                read();
            }
        }

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

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

        public String nextString() {
            return next();
        }

        public String next() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuffer res = new StringBuffer();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));

            return res.toString();
        }

        public String nextLine() {
            StringBuffer buf = new StringBuffer();
            int c = read();
            while (c != '\n' && c != -1) {
                if (c != '\r') {
                    buf.appendCodePoint(c);
                }
                c = read();
            }
            return buf.toString();
        }

        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E') {
                    return res * Math.pow(10, nextInt());
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E') {
                        return res * Math.pow(10, nextInt());
                    }
                    if (c < '0' || c > '9') {
                        throw new InputMismatchException();
                    }
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public boolean hasNext() {
            int value;
            while (isSpaceChar(value = peek()) && value != -1) {
                read();
            }
            return value != -1;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    }
}