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 F1118 {
    static HashMap<Integer,ArrayList<Integer>> map;
    static boolean vis[];static int a[][],col[],c=0;
    public static void main(String args[])throws IOException
        {
            Reader sc=new Reader();
            int n=sc.nextInt();
            map=new HashMap<>();
            vis=new boolean[n+1];
            a=new int[n+1][3];
            col=new int[n+1];
            for(int i=1;i<=n;i++)
            {
                col[i]=sc.nextInt();
                map.put(i,new ArrayList<>());
            }
            for(int i=1;i<n;i++)
            {
                int x=sc.nextInt();
                int y=sc.nextInt();
                map.get(x).add(y);
                map.get(y).add(x);
            }
            dfs(1);
            vis=new boolean[n+1];
            dfs2(1);
            //System.out.println(a[1][0]+" "+a[1][1]+" "+a[1][2]);
            System.out.println(c);
            
        }
    static void dfs2(int ind)
    {
        vis[ind]=true;
        for(int i:map.get(ind))
        {
            if(!vis[i])
            {
                int x0=a[1][0]-a[i][0],x1=a[1][1]-a[i][1],x2=a[1][2]-a[i][2];
                //System.out.println(ind+" "+i);
                //System.out.println(x0+" "+x1+" "+x2);
                //System.out.println(a[i][0]+" "+a[i][1]+" "+a[i][2]);
                if((x1==0 || x2==0) && (a[i][1]==0 || a[i][2]==0))
                    c++;
                dfs2(i);
            }
        }
    }
    static void dfs(int ind)
    {
        vis[ind]=true;
        for(int i:map.get(ind))
        {
            if(!vis[i])
            {
                dfs(i);
                a[ind][0]+=a[i][0];
                a[ind][1]+=a[i][1];
                a[ind][2]+=a[i][2];
            }
            
        }
        a[ind][col[ind]]++;
    }

}

class Reader {
		final private int BUFFER_SIZE = 1 << 16;
		private DataInputStream din;
		private byte [] buffer;
		private int bufferPointer, bytesRead;
		
		public Reader () {
			din = new DataInputStream (System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}
		
		public Reader (String file_name) throws IOException {
			din = new DataInputStream (new FileInputStream (file_name));
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}
		
		public String readLine () throws IOException {
			byte [] buf = new byte[1024];
			int cnt = 0, c;
			while ((c = read ()) != -1) {
				if (c == '\n')
					break;
				buf[cnt++] = (byte) c;
			}
			return new String (buf, 0, cnt);
		}
		
		public int nextInt () throws IOException {
			int ret = 0;
			byte c = read ();
			while (c <= ' ')
				c = read ();
			boolean neg = (c == '-');
			if (neg)
				c = read ();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read ()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}
		
		public long nextLong () throws IOException {
			long ret = 0;
			byte c = read ();
			while (c <= ' ')
				c = read ();
			boolean neg = (c == '-');
			if (neg)
				c = read ();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read ()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}
		
		public double nextDouble () throws IOException {
			double ret = 0, div = 1;
			byte c = read ();
			while (c <= ' ')
				c = read ();
			boolean neg = (c == '-');
			if (neg)
				c = read ();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read ()) >= '0' && c <= '9');
			if (c == '.')
				while ((c = read ()) >= '0' && c <= '9')
					ret += (c - '0') / (div *= 10);
			if (neg)
				return -ret;
			return ret;
		}
		
		private void fillBuffer () throws IOException {
			bytesRead = din.read (buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1)
				buffer[0] = -1;
		}
		
		private byte read () throws IOException {
			if (bufferPointer == bytesRead)
				fillBuffer ();
			return buffer[bufferPointer++];
		}
		
		public void close () throws IOException {
			if (din == null)
				return;
			din.close ();
		}
	}