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:
//package Graph_theory;
import java.util.*;
import java.io.*;
public class TreeCutting
{
	static ArrayList<Integer> adj[] = new ArrayList[(int) 3e5 + 1];
	static boolean vis[]=new boolean[adj.length];
	static int colour[]=new int[adj.length];
	static int cnt[]=new int[3];
	static final int mod=(int)1e9+7;
	static final int inf=(int)1e9;
	static final long INF=(long)1e18;
	static long ans=0;
	public static void main(String[] args) throws IOException
	{
		FastScanner fs=new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
	    int nodes=fs.nextInt();
	    for(int i=1;i<=nodes;i++)adj[i]=new ArrayList<>();
	    for(int i=1;i<=nodes;i++){colour[i]=fs.nextInt();cnt[colour[i]]++;}
	    for(int i=1;i<=nodes-1;i++)
	    {
	    	int u=fs.nextInt();int v=fs.nextInt();
	    	adj[u].add(v);adj[v].add(u);
	    }
	    dfs(1);
//	    for(int i=1;i<=nodes;i++)
//	    {
//	    	if(cnt_col[i].red==cnt[1] && cnt_col[i].blue==0)ans++;
//	    	else if(cnt_col[i].blue==cnt[2] && cnt_col[i].red==0)ans++;
//	    }
	    out.println(ans);
	    out.close();
	}
	static class Triple
	{
		int white,red,blue;
		Triple(int white,int red,int blue)
		{
			this.blue=blue;
			this.white=white;
			this.red=red;
		}
	}
	public static Triple dfs(int node)
	{
		vis[node]=true;
		Triple tri=new Triple(0,0,0);
		for(int child:adj[node])
		{
			if(!vis[child])
			{
				Triple prev=dfs(child);
				tri.red+=prev.red;tri.white+=prev.white;tri.blue+=prev.blue;
			}
		}
		if(colour[node]==0)tri.white++;
		else if(colour[node]==1)tri.red++;
		else tri.blue++;
		if(tri.red==cnt[1] && tri.blue==0)ans++;
		else if(tri.blue==cnt[2] && tri.red==0)ans++;
		return tri;
	}
	//returns the index of the smallest element in the array that is greater than or equal to
	//the given element.
	public static int lower_bound(int arr[],int key)
	{
		int index=inf,num=0;
		int left=0,right=arr.length-1;
		while(left<=right)
		{
			int mid=left+(right-left)/2;
			if(arr[mid]>=key) {index=mid;num=arr[mid];right=mid-1;}
			else 
				left=mid+1;
		}
		return index==inf ? arr.length:index;
	}
	//returns the index of the smallest element in the array that is less than or equal to
    //the given element.
	public static int upper_bound(int arr[],int key)
	{
		int index=inf,num=0;
		int left=0,right=arr.length-1;
		while(left<=right)
		{
			int mid=left+(right-left)/2;
			if(arr[mid]<=key) {index=mid;num=arr[mid];left=mid+1;}
			else 
				right=mid-1;
		}
		return index==inf ? arr.length:index;
	}
}
class FastScanner 
{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");
		public String next() 
		{
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
			
		}
		public String nextLine() throws IOException
		{
		    return br.readLine();
		}
		int[] sort(int arr[])
		{
			ArrayList<Integer> list = new ArrayList<Integer>();
			for(int i:arr)list.add(i);
			Collections.sort(list);
			for(int i=0;i<arr.length;i++)
			{
				arr[i]=list.get(i);
			}
			return arr;
		}
		char[] charsort(char arr[])
	        {
	    	ArrayList<Character> list = new ArrayList<>();
	    	for(char c:arr)list.add(c);
	    	Collections.sort(list);
	    	for(int i=0;i<list.size();i++)
	    	{
	    		arr[i]=list.get(i);
	    	}
	    	return arr;
	        }
		long[] longsort(long arr[])
		{
			ArrayList<Long> list = new ArrayList<Long>();
			for(long i:arr)list.add(i);
			Collections.sort(list);
			for(int i=0;i<arr.length;i++)
			{
				arr[i]=list.get(i);
			}
			return arr;
		}
		public int nextInt() 
		{
			return Integer.parseInt(next());
		}
		public int[] readArray(int n)
		{
			int[] arr=new int[n];
			for (int i=0; i<n; i++) arr[i]=nextInt();
			return arr;
		}	
		public long nextLong()
		{
			return Long.parseLong(next());
		}
		public long[] longreadArray(int n) 
		{
			long[] a=new long[n];
			for (int i=0; i<n; i++) a[i]=nextLong();
			return a;
		}
}