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 InputReader in = new InputReader(System.in);
	static PrintWriter out = new PrintWriter(System.out);
	
	static int oo = (int)1e9;
//	static long oo = (long)1e15;
	static int mod = 1_000_000_007;
	
	static int[] di = {1, 0, 0, -1};
	static int[] dj = {0, -1, 1, 0};
	
	static int M = 1000005;
	static double EPS = 1e-5;
	
	
	public static void main(String[] args) throws IOException {

		int n = in.nextInt();
		int[] color = in.nextIntArray(n);
		int cnt1 = 0, cnt2 = 0;
		for(int i = 0; i < n; ++i) {
			if(color[i] == 1)
				cnt1++;
			else if(color[i] == 2)
				cnt2++;
		}
		ArrayList<Integer>[] adj = new ArrayList[n];
		for(int i = 0; i < n; ++i)
			adj[i] = new ArrayList<Integer>();
		for(int i = 0; i < n-1; ++i) {
			int u = in.nextInt() - 1;
			int v = in.nextInt() - 1;
			adj[u].add(v);
			adj[v].add(u);
		}
		int[] ones = new int[n];
		int[] twos = new int[n];
		dfs(adj, color, ones, twos, -1, 0);
		int ans = 0;
		for(int u = 1; u < n; ++u) {
			if(ones[u] == cnt1 && twos[u] == 0 || ones[u] == 0 && twos[u] == cnt2)
				ans++;
		}
		System.out.println(ans);
		
		out.close();
	}
	
	static void dfs(ArrayList<Integer>[] adj, int[] color, int[] ones, int[] twos, int p, int u) {
		if(color[u] == 1)
			ones[u] = 1;
		else if(color[u] == 2)
			twos[u] = 1;
		for(int v : adj[u]) {
			if(v == p)
				continue;
			dfs(adj, color, ones, twos, u, v);
			ones[u] += ones[v];
			twos[u] += twos[v];
		}
	}
	
	
	
	static int find(int[] g, int x) {
		return g[x] = g[x] == x ? x : find(g, g[x]);
	}
	
	static void union(int[] g, int[] size, int x, int y) {
		x = find(g, x); y = find(g, y);
		if(x == y)
			return;
		if(size[x] < size[y]) {
			g[x] = y;
			size[y] += size[x];
		}
		else {
			g[y] = x;
			size[x] += size[y];
		}
	}
	
	static class Segment {
		Segment left, right;
		long sum;
		long lazy;
		
		public Segment(long[] a, int l, int r) {
			super();
			if(l == r) {
				sum = a[l];
				return;
			}
			int mid = (l + r) / 2;
			left = new Segment(a, l, mid);
			right = new Segment(a, mid+1, r);
			sum = left.sum + right.sum;
		}
		
		boolean covered(int ll, int rr, int l, int r) {
			return ll <= l && rr >= r;
		}
		
		boolean noIntersection(int ll, int rr, int l, int r) {
			return ll > r || rr < l;
		}
		
		void lazyPropagation(int l, int r) {
			if(lazy != 0) {
				set(lazy, l, r); 
				if(left != null) {
					left.lazy += lazy;
					right.lazy += lazy;
				}
				lazy = 0;
			}
		}
		
		void set(long delta, int l, int r) {
			int sz = r - l + 1;
			sum += delta * sz; 
		}
		
		long query(int ll, int rr, int l, int r) {
			lazyPropagation(l, r);
			if(noIntersection(ll, rr, l, r))
				return 0;
			if(covered(ll, rr, l, r))
				return sum;
			int mid = (l + r) / 2;
			long leftSum = left.query(ll, rr, l, mid);
			long rightSum = right.query(ll, rr, mid+1, r);
			return leftSum + rightSum;
		}
		
//		int query(int k, int l, int r) {
//			Segment trace = this;
//			while(l < r) {
//				int mid = (l + r) / 2;
//				if(trace.left.size > k) {
//					trace = trace.left;
//					r = mid;
//				}
//				else {
//					k -= trace.left.size;
//					trace = trace.right;
//					l = mid + 1;
//				}
//			}
//			return trace.val;
//		}
		
		void update(int ll, int rr, long add, int l, int r) {
			lazyPropagation(l, r);
			if(noIntersection(ll, rr, l, r))
				return;
			if(covered(ll, rr, l, r)) {
				set(add, l, r);
				if(left != null) {
					left.lazy += add;
					right.lazy += add;
				}
				return;
			}
			int mid = (l + r) / 2;
			left.update(ll, rr, add, l, mid);
			right.update(ll, rr, add, mid+1, r);
			sum = left.sum + right.sum;
		}
	}
	
	static long pow(long a, long n, long mod) {
		if(n == 0)
			return 1;
		if(n % 2 == 1)
			return a * pow(a, n-1, mod) % mod;
		long x = pow(a, n / 2, mod);
		return x * x % mod;
	}
	
	
	static int[] getPi(char[] a) {
		int m = a.length;
		int j = 0;
		int[] pi = new int[m];
		for(int i = 1; i < m; ++i) {
			while(j > 0 && a[i] != a[j])
				j = pi[j-1];
			if(a[i] == a[j]) {
				pi[i] = j + 1;
				j++;
			}
		}
		return pi;
	}
	
	static long lcm(long a, long b) {
		return a * b / gcd(a, b);
	}
	
	static boolean nextPermutation(int[] a) {
		for(int i = a.length - 2; i >= 0; --i) {
			if(a[i] < a[i+1]) {
				for(int j = a.length - 1; ; --j) {
					if(a[i] < a[j]) {
						int t = a[i];
						a[i] = a[j];
						a[j] = t;
						for(i++, j = a.length - 1; i < j; ++i, --j) {
							t = a[i];
							a[i] = a[j];
							a[j] = t;
						}
						return true;
					}
				}
			}
		}
		return false;
	}
	
	static void shuffle(Object[] a) {
		Random r = new Random();
		for(int i = a.length - 1; i > 0; --i) {
			int si = r.nextInt(i);
			Object t = a[si];
			a[si] = a[i];
			a[i] = t;
		}
	}
	
	static void shuffle(int[] a) {
		Random r = new Random();
		for(int i = a.length - 1; i > 0; --i) {
			int si = r.nextInt(i);
			int t = a[si];
			a[si] = a[i];
			a[i] = t;
		}
	}
	
	static void shuffle(long[] a) {
		Random r = new Random();
		for(int i = a.length - 1; i > 0; --i) {
			int si = r.nextInt(i);
			long t = a[si];
			a[si] = a[i];
			a[i] = t;
		}
	}
	
	static int lower_bound(int[] a, int n, int k) {
		int s = 0;
		int e = n;
		int m;
		while (e - s > 0) {
			m = (s + e) / 2;
			if (a[m] < k)
				s = m + 1;
			else
				e = m;
		}
		return e;
	}
	static int lower_bound(long[] a, int n, long k) {
		int s = 0;
		int e = n;
		int m;
		while (e - s > 0) {
			m = (s + e) / 2;
			if (a[m] < k)
				s = m + 1;
			else
				e = m;
		}
		return e;
	}
	
	static int gcd(int a, int b) {
		return b == 0 ? a : gcd(b, a % b);
	}
	static long gcd(long a, long b) {
		return b == 0 ? a : gcd(b, a % b);
	}
	
	static class Pair implements Comparable<Pair> {
		int first, second;
 
		public Pair(int first, int second) {
			super();
			this.first = first;
			this.second = second;
		}
 
		@Override
		public int compareTo(Pair o) {
			return this.first != o.first ? this.first - o.first : this.second - o.second;
		}
		
//		@Override
//		public int compareTo(Pair o) {
//			return this.first != o.first ? o.first - this.first : o.second - this.second;
//		}
 
		@Override
		public int hashCode() {
			final int prime = 31;
			int result = 1;
			result = prime * result + first;
			result = prime * result + second;
			return result;
		}
 
		@Override
		public boolean equals(Object obj) {
			if (this == obj)
				return true;
			if (obj == null)
				return false;
			if (getClass() != obj.getClass())
				return false;
			Pair other = (Pair) obj;
			if (first != other.first)
				return false;
			if (second != other.second)
				return false;
			return true;
		}
	}
}
 
 
 
class InputReader {
 
	private final InputStream stream;
	private final byte[] buf = new byte[8192];
	private int curChar, snumChars;
 
	public InputReader(InputStream st) {
		this.stream = st;
	}
 
	public int read() {
		if (snumChars == -1)
			throw new InputMismatchException();
		if (curChar >= snumChars) {
			curChar = 0;
			try {
				snumChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (snumChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}
 
	public int nextInt() {
		int c = read();
		while (isSpaceChar(c)) {
			c = read();
		}
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}
 
	public long nextLong() {
		int c = read();
		while (isSpaceChar(c)) {
			c = read();
		}
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}
 
	public int[] nextIntArray(int n) {
		int a[] = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = nextInt();
		}
		return a;
	}
 
	public String readString() {
		int c = read();
		while (isSpaceChar(c)) {
			c = read();
		}
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}
 
	public String nextLine() {
		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 boolean isSpaceChar(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}
 
	private boolean isEndOfLine(int c) {
		return c == '\n' || c == '\r' || c == -1;
	}
 
}