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 code;
import java.io.*;
import java.util.*;
import java.util.Map.Entry;
import java.text.*;
import java.math.*;
import java.util.regex.*;
import java.awt.Point;
/**
 *
 * @author prabhat // use stringbuilder,TreeSet, priorityQueue, x+y=(x&y + x|y);
 */                                                           //X+y=2*(x&y)+ x^y;
 public  class  a
   {
   public static int n,max1=1005,k,m,q,a[],a1[],mat[][],id,depth[],parent[][],len=22,tin[],tout[],count=0,size[],sum,cnt;
   public static Point[] p1,p2,p;
   public static long mod=(long)1e9+7,nCr[][],suf[][],ans=Long.MAX_VALUE,max=Long.MIN_VALUE,dp[];
   public static boolean isPrime[],visit[][],valid[][];
   public static HashSet<Integer> hash;
   public static PriorityQueue<Integer> pq[];
   public static  ArrayList<Integer> divisor[],prime,adj[],lpf,list[];
   //public static ArrayList<Character> list[];
   public static  TreeMap<Integer,Integer> tmap[];
   public static String s;
   public static pair[] pa;
   public  static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
   static PrintWriter pw;
   static int[] x={-1,0,1},y={1,0,-1};

   public static void main(String[] args) throws IOException
   {
	InputReader in = new InputReader(System.in);
	pw=new PrintWriter(System.out);
	n=in.ii();
	a=in.iia(n);
	int red=0;
	int blue=0;
	for(int i:a)if(i==1)red++; else if(i==2) blue++;
	adj=new ArrayList[n];
	for(int i=0;i<n;i++)adj[i]=new ArrayList<>();
	for(int i=0;i<n-1;i++)
	{
		int u=in.ii()-1;
		int v=in.ii()-1;
		adj[u].add(v);
		adj[v].add(u);
	}
	pa=new pair[n];
	for(int i=0;i<n;i++)pa[i]=new pair();
	dfs1(0,-1);
	int ans=0;
	for(int i=0;i<n;i++)
	{
		//pw.println(pa[i].red+" "+pa[i]);
		if(pa[i].red==red&&pa[i].blue==0)ans++;
		else if(pa[i].blue==blue&&pa[i].red==0)ans++;
	}
	pw.println(ans);
	pw.close();
   }
static void dfs1(int cur,int par)
{
	if(a[cur]==1)pa[cur].red=1;
	else if(a[cur]==2)pa[cur].blue=1;

	for(int ver:adj[cur])
	{
		if(ver==par)continue;
		dfs1(ver,cur);
		pa[cur].red+=pa[ver].red;
		pa[cur].blue+=pa[ver].blue;
	}
}
 static class pair{
	int red,blue;
	pair(){}
	pair(int a,int b)
	{
	 red=a;
	 blue=b;
	}
 }  
static int lowerBound(ArrayList<Integer> al,int tar)
{
	   int s=0;
	   int e=al.size()-1;
	   int ans=0;
	   while(s<=e)
	   {
		   int mid=(s+e)/2;
		   if(al.get(mid)<=tar){s=mid+1;ans=mid+1;}
		   else e=mid-1;
	   }
	   return ans;
}

static boolean isVowel(char c)
{
	return c=='a'||c=='e'||c=='i'||c=='o'||c=='u';
}

public  static class DSU
{
	int[] parent;
	int[] rank;
	
	int cnt;
	public DSU(int n){
		parent=new int[n];
		rank=new int[n];
		for(int i=0;i<n;i++){
			parent[i]=i;
			rank[i]=1;
		}
		cnt=n;
	}
	int find(int i){
		while(parent[i] !=i){
			parent[i]=parent[parent[i]];
			i=parent[i];
		}
		return i;
	}
	void Union(int x, int y){
		int xset = find(x);
		int yset = find(y);
		if(xset!=yset)
			cnt--;
		
		if(rank[xset]>rank[yset])
		{
			parent[yset] = xset;
		    rank[xset]+=rank[yset];
			rank[yset]=0;
			//return xset;
		}else{
			parent[xset]=yset;
			rank[yset]+=rank[xset];
			rank[xset]=0;
			//return yset;
		}
	
     return;
	}
}


 static int palin(String s)
 {
	String s1=new StringBuilder(s).reverse().toString();
	return s1.equals(s)==true?1:0;
 }
 /*static int dfs(int u, int p) {

	//discover[count1++]=arr[u];  //  it storing color or arr of vertex u
	//discover[count1++]=u;
	//tin[u] = count++;
   int d1=1000000;
   int d2=1000000;
   int cnt=0;
	//parent[u][0] = p==-1?0:p;
	//size[u]++;
	//for (int i = 1; i < len; i++)
	//	parent[u][i] = parent[parent[u][i-1]][i-1];
	for (int v :adj[u])
		if (v != p)
		{
			cnt++;
			depth[v] = depth[u] + 1;
			int y=dfs( v, u);
			if(y<d1)
			{
				d2=d1;
				d1=y;
			}
			else if(y<d2)
			{
				d2=y;
			}
	//		size[u] += size[v];
		}
	if(cnt==0)return 1;
	ans=Math.min(d1+d2,ans);
	return 1+Math.min(d1,d2);
//	if(adj[u].size()==1&&parent[u][0]!=0)last.add(u);
//	tout[u] = count-1;
}
*/

static boolean isParent(int parent, int child) {
	return tin[parent] <= tin[child] && tout[child] <= tout[parent];
}

static int lca(int a, int b) {
	if (isParent(a, b))
		return a;
	if (isParent(b, a))
		return b;
	for (int i = len - 1; i >= 0; i--)
		if (!isParent(parent[a][i], b))
			a = parent[a][i];
	return parent[a][0];
}
static boolean valid(int i,int j)
{
	return i>=0&&i<3&&j>=0&&j<3;
}
 
static int gcd(int a,int b)
{
	while(a!=0)
	{
		int temp=a;
		a=b%a;
		b=temp;
	}
	return b;
}
static void Seive()
{
	a1=new int[max1];
	isPrime=new boolean[max1];
	Arrays.fill(isPrime,true);
	prime=new ArrayList<>();
	divisor=new ArrayList[max1];
	for(int i=1;i<max1;i++)divisor[i]=new ArrayList<Integer>();
    isPrime[0]=isPrime[1]=false;
	for(int i=2;i<(max1);i++)
	{
         if(isPrime[i]){
			 divisor[i].add(i);
			 prime.add(i);
			 a1[i]=1;
			for(int j=2*i;j<max1;j+=i)
			{
				a1[j]++;
				isPrime[j]=false;
				divisor[j].add(i);
			}
		}
	}
}
public static long pow(long n,long p)
{
	 long  result = 1;
	  if(p==0)
	    return 1;

	while(p!=0)
	{
	    if(p%2==1)
	        result *= n;
	    
	    p >>=1;
	    n*=n;
	}
	return result;
}


static  class InputReader
{
   private InputStream stream;
   private byte[] buf = new byte[1024];

   private SpaceCharFilter filter;
    byte inbuffer[] = new byte[1024];
   int lenbuffer = 0, ptrbuffer = 0;
    final int M = (int) 1e9 + 7;
   int md=(int)(1e7+1);
    int[] SMP=new int[md];
   final double eps = 1e-6;
   final double pi = Math.PI;

	PrintWriter out;
   String check = "";
 InputStream   obj = check.isEmpty() ? System.in : new ByteArrayInputStream(check.getBytes());
   public InputReader(InputStream stream)
   {
       this.stream = stream;
   }

    int readByte() {
	        if (lenbuffer == -1) throw new InputMismatchException();
	        if (ptrbuffer >= lenbuffer) {
	            ptrbuffer = 0;
	            try {
	                lenbuffer = obj.read(inbuffer);
	            } catch (IOException e) {
	                throw new InputMismatchException();
	            }
	        }
	        if (lenbuffer <= 0) return -1;
	        return inbuffer[ptrbuffer++];
   }

   public  int read()
   {
       int c = read();
       while (isSpaceChar(c))
           c = read();
       int sgn = 1;
       if (c == '-')
       {
           sgn = -1;
           c = read();
       }
       int res = 0;
       do
       {
           if (c < '0' || c > '9')
               throw new InputMismatchException();
           res *= 10;
           res += c - '0';
           c = read();
       } while (!isSpaceChar(c));
       return res * sgn;
   }

   String is() {
	        int b = skip();
	        StringBuilder sb = new StringBuilder();
	        while (!(isSpaceChar(b))) // when nextLine, (isSpaceChar(b) && b!=' ')
	        {
	            sb.appendCodePoint(b);
	            b = readByte();
	        }
	        return sb.toString();
   }
   public   int ii() {
	        int num = 0, b;
	        boolean minus = false;
	        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
	        if (b == '-') {
	            minus = true;
	            b = readByte();
	        }
	        while (true) {
	            if (b >= '0' && b <= '9') {
	                num = num * 10 + (b - '0');
	            } else {
	                return minus ? -num : num;
	            }
	            b = readByte();
	        }
   }
 public   long il() {
	        long num = 0;
	        int b;
	        boolean minus = false;
	        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
	        if (b == '-') {
	            minus = true;
	            b = readByte();
	        }
	        while (true) {
	            if (b >= '0' && b <= '9') {
	                num = num * 10 + (b - '0');
	            } else {
	                return minus ? -num : num;
	            }
	            b = readByte();
	        }
   }

	    boolean isSpaceChar(int c) {
	        return (!(c >= 33 && c <= 126));
	       }

	      int skip()
	        {
	        int b;
	        while ((b = readByte()) != -1 && isSpaceChar(b)) ;
	        return b;
	        }

	    float nf() {
	        return Float.parseFloat(is());
	    }

	    double id() {
	        return Double.parseDouble(is());
	    }

	    char ic() {
	        return (char) skip();
	    }

	    int[] iia(int n) {
	        int a[] = new int[n];
	        for (int i = 0; i<n; i++) a[i] = ii();
	        return a;
	    }

	    long[] ila(int n) {
	        long a[] = new long[n];
	        for (int i = 0; i <n; i++) a[i] = il();
	        return a;
	    }

	    String[] isa(int n) {
	        String a[] = new String[n];
	        for (int i = 0; i < n; i++) a[i] = is();
	        return a;
	    }


		 long mul(long a, long b) { return a * b % M; }

		/*	long div(long a, long b)
				 {
					return mul(a, pow(b, M - 2,M));

		           }
*/


	    double[][] idm(int n, int m) {
	        double a[][] = new double[n][m];
	        for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) a[i][j] = id();
	        return a;
	        }

	    int[][] iim(int n, int m) {
	        int a[][] = new int[n][m];
	        for (int i = 0; i < n; i++) for (int j = 0; j <m; j++) a[i][j] = ii();
	        return a;
          }


   public String readLine() {
       int c = read();
       while (isSpaceChar(c))
           c = read();
       StringBuilder res = new StringBuilder();
       do {
           res.appendCodePoint(c);
           c = read();
       } while (!isEndOfLine(c));
       return res.toString();
   }

   public interface SpaceCharFilter
   {
       public boolean isSpaceChar(int ch);
   }
   public boolean isEndOfLine(int c) {
       return c == '\n' || c == '\r' || c == -1;
   }
}

}