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.*;

public class Main {
    static int  n;
    static int[]values;
    static int[]red;
    static int[]blue;
    static Graph g;
    static boolean[]visited;
    public static void main(String[] args) throws Exception
    {
        Scanner in = new Scanner(System.in);
        OutputWriter out = new OutputWriter(System.out);
         n  = in.nextInt();
         values = new int[n];
         red = new int[n];
         blue = new int[n];
         g = new Graph(n);
        int allRed=0;
        int allBlue=0;
       for (int i =0;i<n;i++) {
           values[i] = in.nextInt();
           if (values[i]==1)
               allBlue++;
           else if (values[i]==2)
               allRed++;
       }
       for (int i =0;i<n-1;i++) {
           int x = in.nextInt() - 1;
           int y = in.nextInt() - 1;
           g.adjList[x].add(y);
           g.adjList[y].add(x);
       }
       DFS(0);
       int ans=0;
       for (int i =0;i<n;i++)
       {
           if (red[i]==allRed&&blue[i]==0)
               ans++;
           if (blue[i]==allBlue&&red[i]==0)
               ans++;
       }
       out.printLine(ans);
       out.flush();
    }
    static void DFS(int v)
    {
       visited = new boolean[g.n];
        DFSUtil(v);
    }
    static  void DFSUtil(int v)
    {
        visited[v] = true;
        if (values[v]==1)
            blue[v]++;
        if (values[v]==2)
            red[v]++;
        int i=0;
        int size = g.adjList[v].size();

        while (i<size)
        {
            int index = g.adjList[v].get(i);
            if (!visited[index]) {
                DFSUtil(index);
                red[v]+=red[index];
                blue[v]+=blue[index];
            }
            i++;

        }
    }
    static void MergeSort(int[] a, int p, int r)
    {
        if (p < r)
        {
            int q = (r + p) / 2;
            MergeSort(a,   p, q);
            MergeSort(a,  q + 1, r);
            Merge(a,  p, q, r);
        }
    }
    static void Merge(int[] a,int p, int q, int r)
    {
        int n1 = q - p + 1;
        int n2 = r - q;
        int[] R = new int[n1 + 1];
        int[] L = new int[n2 + 1];


        for (int i = 0; i < n1; i++)
        {
            R[i] = a[p + i];


        }
        R[n1] = Integer.MAX_VALUE;
        for (int i = 0; i < n2; i++)
        {
            L[i] = a[q + i + 1];


        }
        L[n2] =Integer.MAX_VALUE;
        int n = a.length;
        int j = 0;
        int k = 0;
        for (int i = p; i <= r; i++)
        {
            if (L[j] < R[k])
            {
                a[i] = L[j];


                j++;
            }
            else
            {
                a[i] = R[k];


                k++;
            }


        }
    }
}
class Graph {


    int n;
    ArrayList<Integer>[] adjList;

    public Graph(int n) {
        this.n = n;
        adjList = new ArrayList[n];
        for (int i = 0; i < n; i++)
            adjList[i] = new ArrayList<>();
    }

}
class pair  implements Comparable
{

    int key;
    int value;
    int id;
    public pair(Object key, Object value,Object id) {

        this.key = (int)key;
        this.value=(int)value;
        this.id=(int)id;
    }

    @Override
    public int compareTo(Object o) {
        pair temp =(pair)o;
        if (key!=temp.key)
            return  key-temp.key;
        else return id-temp.id;
    }
}
class Scanner {

    StringTokenizer st;
    BufferedReader br;

    public Scanner(InputStream s) {
        br = new BufferedReader(new InputStreamReader(s));
    }

    public Scanner (FileReader f) {
        br = new BufferedReader(f);
    }

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

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

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

    public String nextLine() throws IOException {
        return br.readLine();
    }

    public double nextDouble() throws IOException {
        String x = next();
        StringBuilder sb = new StringBuilder("0");
        double res = 0, f = 1;
        boolean dec = false, neg = false;
        int start = 0;
        if (x.charAt(0) == '-') {
            neg = true;
            start++;
        }
        for (int i = start; i < x.length(); i++)
            if (x.charAt(i) == '.') {
                res = Long.parseLong(sb.toString());
                sb = new StringBuilder("0");
                dec = true;
            } else {
                sb.append(x.charAt(i));
                if (dec)
                    f *= 10;
            }
        res += Long.parseLong(sb.toString()) / f;
        return res * (neg ? -1 : 1);
    }

    public boolean ready() throws IOException {
        return br.ready();
    }

    public boolean nextEmpty() throws IOException {
        String s = nextLine();
        st = new StringTokenizer(s);
        return s.isEmpty();
    }
}
class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }

    public void print(Object... objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0)
                writer.print(' ');
            writer.print(objects[i]);
        }
    }


    public void printLine(Object... objects) {
        print(objects);
        writer.println();
    }

    public void close() {
        writer.close();
    }

    public void flush() {
        writer.flush();
    }

}