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 Solution {
	
	public static final int max = Integer.MAX_VALUE;
	
    public static void main (String[] args) throws IOException{
    	FastReader f=new FastReader();
    	int v = f.nextInt();
    	ArrayList<Integer>[] edges = new ArrayList[v];
    	int[] verts = new int[v];
    	int tblue = 0;
    	int tred = 0;
    	for (int i=0;i<v;i++) {
    		verts[i] = f.nextInt();
    		if (verts[i]==1) tred++;
    		if (verts[i]==2) tblue++;
    	}
    	int[] bluec = new int[v];
    	int[] redc = new int[v];
    	
    	for (int i=0;i<v-1;i++) {
    		int a = f.nextInt()-1;
    		int b = f.nextInt()-1;
    		if (edges[a]==null) edges[a] = new ArrayList<Integer>();
    		if (edges[b]==null) edges[b] = new ArrayList<Integer>();
    		edges[a].add(b);
    		edges[b].add(a);

    	}
    	boolean[] visited = new boolean[v];
    	dfs(edges,0,redc,verts,1,visited);
    	visited = new boolean[v];
    	dfs(edges,0,bluec,verts,2,visited);
    	
    	int ans = 0;
    	
    	
    	for (int i=0;i<v;i++) {
    		for (int j=0;j<edges[i].size();j++) {
    			int k = edges[i].get(j);
    			int cb = bluec[k];
    			int cr = redc[k];
    			int pb = tblue - cb;
    			int pr = tred - cr;
    			
    			if ((cb==0 && pr==0)||(cr==0 && pb==0))
    				ans++;
    		}
    	}
    	visited = new boolean[v];
    	System.out.println(dfs2(edges,0,visited,tblue,tred,bluec,redc));
    	
    }
    
    public static int dfs2(ArrayList<Integer>[] edges,int curr,boolean[] visited,int tblue,int tred,int[] bluec,int[] redc) {
    	if (visited[curr]) return 0;
    	visited[curr] = true;
    	int ans=0;
    	for (int i=0;i<edges[curr].size();i++) {
    		int k = edges[curr].get(i);
    		if (visited[k]) continue;
			int cb = bluec[k];
			int cr = redc[k];
			int pb = tblue - cb;
			int pr = tred - cr;
			
			if ((cb==0 && pr==0)||(cr==0 && pb==0))
				ans++;
			ans+=dfs2(edges,k,visited,tblue,tred,bluec,redc);
    		
    	}
    	return ans;
    }
    
    public static int dfs(ArrayList<Integer>[] edges,int curr,int[] colarray,int[] verts,int c,boolean[] visited) {
    	if (visited[curr]) return 0;
    	visited[curr] = true;
    	int cols = 0;
    	if (verts[curr]==c)
    		cols++;
    	for (int i=0;i<edges[curr].size();i++) {
    		if (visited[edges[curr].get(i)]) continue;
			cols+=dfs(edges,edges[curr].get(i),colarray,verts,c,visited);
		}
    	colarray[curr] = cols;
    	return cols;
    }
    
	public static int binlog( int bits ){
        int log = 0;
        if( ( bits & 0xffff0000 ) != 0 ) { bits >>>= 16; log = 16; }
        if( bits >= 256 ) { bits >>>= 8; log += 8; }
        if( bits >= 16  ) { bits >>>= 4; log += 4; }
        if( bits >= 4   ) { bits >>>= 2; log += 2; }
        return log + ( bits >>> 1 );
    }

    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
  
}