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.math.BigInteger;
import java.security.SecureRandom;
import java.text.DecimalFormat;
import java.util.*;
import java.io.*;
import java.util.concurrent.CompletableFuture;


public class Main {

    private static int n;
    private static int [] A;
    private static ArrayList<Integer> [] G;
    private static int [] R,B;

    private static int dfs(int u,int p,int totR,int totB) {
        if (A[u] == 1) R[u]++;
        else if (A[u] == 2) B[u]++;

        int ret = 0;
        for (int v : G[u])
            if (v != p) {
                ret += dfs(v,u,totR,totB);
                // v -> no blue
                // u -> no red
                boolean y = false;
                if (B[v] == 0 && totR - R[v] == 0)
                    y = true;
                // v-> no red
                // u-> no blue
                if (R[v] == 0 && totB - B[v] == 0)
                    y = true;
                ret += y ? 1 : 0;
                R[u] += R[v];
                B[u] += B[v];
            }
        return ret;
    }

    public static void main(String[] args) throws Exception {
        IO io ;
        try {
            io = new IO("in.in", null);
        } catch (IOException e) {
            io = new IO(null, null);
        }
        n = io.getNextInt();
        A = new int[n+1];
        R = new int[n+1];
        B = new int[n+1];
        G = new ArrayList[n+1];
        int red = 0,blue = 0;
        for (int i = 1;i <= n;i++) {
            A[i] = io.getNextInt();
            G[i] = new ArrayList<>();
            red += (A[i] == 1) ? 1 : 0;
            blue += (A[i] == 2) ? 1 : 0;
        }
        for (int e = 0;e < n-1;e++) {
            int a = io.getNextInt();
            int b = io.getNextInt();
            G[a].add(b);
            G[b].add(a);
        }

        io.println(dfs(1,0,red,blue));
        io.close();
    }
    private static final int onebillion7 = 1000000007;
}





class pair{
    int val,type;
    public pair(int v,int t) {
        val = v;
        type = t;
    }
    @Override
    public String toString(){
        return "(" + val + ", " + type + ")";
    }
}

class Buffer{
    ArrayList<Character> AS;
    public Buffer(){
        AS = new ArrayList<>();
    }
    public void append(String s){
        for (char c : s.toCharArray())
            AS.add(c);
    }
    public void appendLine(String s) {
        append(s);
        AS.add('\n');
    }
    public void clear(){
        AS.clear();
    }
    public String toString(){
        StringBuilder sb = new StringBuilder();
        for (char c : AS)
            sb.append(c);
        return sb.toString();
    }
}

class IO{
    private BufferedReader br;
    private StringTokenizer st;
    private PrintWriter writer;
    private String inputFile,outputFile;

    public boolean hasMore() throws IOException{
        if(st != null && st.hasMoreTokens()) return true;
        if(br != null && br.ready()) return true;
        return false;
    }

    public String getNext() throws FileNotFoundException, IOException{
        while(st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

    public String getNextLine() throws FileNotFoundException, IOException{
        return br.readLine().trim();
    }

    public int getNextInt() throws FileNotFoundException, IOException{
        return Integer.parseInt(getNext());
    }
    public long getNextLong() throws FileNotFoundException, IOException{
        return Long.parseLong(getNext());
    }

    public void print(double x,int num_digits) throws  IOException{
        writer.printf("%." + num_digits + "f" ,x);
    }
    public void println(double x,int num_digits) throws  IOException{
        writer.printf("%." + num_digits + "f\n" ,x);
    }
    public void print(Object o) throws  IOException{
        writer.print(o.toString());
    }

    public void println(Object o) throws  IOException{
        writer.println(o.toString());
    }
    public IO(String x,String y) throws FileNotFoundException, IOException{
        inputFile = x;
        outputFile = y;
        if(x != null) br = new BufferedReader(new FileReader(inputFile));
        else br = new BufferedReader(new InputStreamReader(System.in));
        if(y != null) writer = new PrintWriter(new BufferedWriter(new FileWriter(outputFile)));
        else writer = new PrintWriter(new OutputStreamWriter(System.out));
    }

    protected void close() throws IOException{
        br.close();
        writer.close();
    }
    public void outputArr(Object [] A) throws IOException{
        int L = A.length;
        for (int i = 0;i < L;i++) {
            if(i > 0) writer.print(" ");
            writer.print(A[i]);
        }
        writer.print("\n");
    }
}



//class PollardRho {
//    private final static BigInteger ZERO = new BigInteger("0");
//    private final static BigInteger ONE  = new BigInteger("1");
//    private final static BigInteger TWO  = new BigInteger("2");
//    private final static SecureRandom random = new SecureRandom();
//    private static ArrayList<Long> primes = new ArrayList<>();
//
//    private static BigInteger rho(BigInteger N) {
//        BigInteger divisor;
//        BigInteger c  = new BigInteger(N.bitLength(), random);
//        BigInteger x  = new BigInteger(N.bitLength(), random);
//        BigInteger xx = x;
//
//        // check divisibility by 2
//        if (N.base(TWO).compareTo(ZERO) == 0) return TWO;
//
//        do {
//            x  =  x.multiply(x).base(N).add(c).base(N);
//            xx = xx.multiply(xx).base(N).add(c).base(N);
//            xx = xx.multiply(xx).base(N).add(c).base(N);
//            divisor = x.subtract(xx).gcd(N);
//        } while((divisor.compareTo(ONE)) == 0);
//
//        return divisor;
//    }
//
//    private static void factor(BigInteger N) {
//        if (N.compareTo(ONE) == 0) return;
//        if (N.isProbablePrime(20)) {
//            primes.add(N.longValue());
//            return;
//        }
//        BigInteger divisor = rho(N);
//        factor(divisor);
//        factor(N.divide(divisor));
//    }
//
//
//    public static ArrayList<Long> factor(Long n) {
//        primes.clear();
//        factor(BigInteger.valueOf(n));
//        return primes;
//    }
//}