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:

/**
 * Date: 19 Feb, 2019
 * Link:
 *
 * @author Prasad-Chaudhari
 * @linkedIn: https://www.linkedin.com/in/prasad-chaudhari-841655a6/
 * @git: https://github.com/Prasad-Chaudhari
 */
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.Arrays;
import java.util.Stack;

public class newProgram8 {

    public static void main(String[] args) throws IOException {
        // TODO code application logic here
        FastIO in = new FastIO();
        int n = in.ni();
        int a[] = in.gia(n);
        int adja[][] = in.gg(n, n - 1);
        int red[] = new int[n + 1];
        int blue[] = new int[n + 1];
        Stack<Integer> st = new Stack<Integer>();
        boolean b[] = new boolean[n + 1];
        b[1] = true;
        st.push(1);
        int parent[] = new int[n + 1];
        while (!st.isEmpty()) {
            int root = st.peek();
            boolean p = true;
            for (int i : adja[root]) {
                p &= b[i];
            }
            if (p) {
                if (a[root - 1] == 1) {
                    red[root]++;
                } else if (a[root - 1] == 2) {
                    blue[root]++;
                }
                for (int i : adja[root]) {
                    if (i != parent[root]) {
                        red[root] += red[i];
                        blue[root] += blue[i];
                    }
                }
                st.pop();
            } else {
                for (int i : adja[root]) {
                    if (!b[i]) {
                        b[i] = true;
                        st.push(i);
                        parent[i] = root;
                    }
                }
            }
        }
        Arrays.fill(b, false);
        st.push(1);
        int count = 0;
        b[1] = true;
//        for (int i = 1; i <= n; i++) {
//            System.out.println(i + " " + red[i] + " " + blue[i]);
//        }
        int count_red = red[1];
        int count_blue = blue[1];
        while (!st.isEmpty()) {
            int root = st.pop();
            for (int i : adja[root]) {
                if (!b[i]) {
                    b[i] = true;
                    st.push(i);
                    count_red -= red[i];
                    count_blue -= blue[i];
                    if (!(count_red != 0 && count_blue != 0) && !(red[i] != 0 && blue[i] != 0)) {
                        count++;
//                        System.out.println(root + " " + i);
                    }
                    count_red += red[i];
                    count_blue += blue[i];
                }
            }
        }
        System.out.println(count);
    }

    static class FastIO {

        private final BufferedReader br;
        private final BufferedWriter bw;
        private String s[];
        private int index;
        private StringBuilder sb;

        public FastIO() throws IOException {
            br = new BufferedReader(new InputStreamReader(System.in));
            bw = new BufferedWriter(new OutputStreamWriter(System.out, "UTF-8"));
            s = br.readLine().split(" ");
            sb = new StringBuilder();
            index = 0;
        }

        public int ni() throws IOException {
            return Integer.parseInt(nextToken());
        }

        public double nd() throws IOException {
            return Double.parseDouble(nextToken());
        }

        public long nl() throws IOException {
            return Long.parseLong(nextToken());
        }

        public String next() throws IOException {
            return nextToken();
        }

        public String nli() throws IOException {
            try {
                return br.readLine();
            } catch (IOException ex) {

            }
            return null;
        }

        public int[] gia(int n) throws IOException {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }

        public int[] gia(int n, int start, int end) throws IOException {
            validate(n, start, end);
            int a[] = new int[n];
            for (int i = start; i < end; i++) {
                a[i] = ni();
            }
            return a;
        }

        public double[] gda(int n) throws IOException {
            double a[] = new double[n];
            for (int i = 0; i < n; i++) {
                a[i] = nd();
            }
            return a;
        }

        public double[] gda(int n, int start, int end) throws IOException {
            validate(n, start, end);
            double a[] = new double[n];
            for (int i = start; i < end; i++) {
                a[i] = nd();
            }
            return a;
        }

        public long[] gla(int n) throws IOException {
            long a[] = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nl();
            }
            return a;
        }

        public long[] gla(int n, int start, int end) throws IOException {
            validate(n, start, end);
            long a[] = new long[n];
            for (int i = start; i < end; i++) {
                a[i] = nl();
            }
            return a;
        }

        public int[][][] gwtree(int n) throws IOException {
            int m = n - 1;
            int adja[][] = new int[n + 1][];
            int weight[][] = new int[n + 1][];
            int from[] = new int[m];
            int to[] = new int[m];
            int count[] = new int[n + 1];
            int cost[] = new int[n + 1];
            for (int i = 0; i < m; i++) {
                from[i] = i + 1;
                to[i] = ni();
                cost[i] = ni();
                count[from[i]]++;
                count[to[i]]++;
            }
            for (int i = 0; i <= n; i++) {
                adja[i] = new int[count[i]];
                weight[i] = new int[count[i]];
            }
            for (int i = 0; i < m; i++) {
                adja[from[i]][count[from[i]] - 1] = to[i];
                adja[to[i]][count[to[i]] - 1] = from[i];
                weight[from[i]][count[from[i]] - 1] = cost[i];
                weight[to[i]][count[to[i]] - 1] = cost[i];
                count[from[i]]--;
                count[to[i]]--;
            }
            return new int[][][]{adja, weight};
        }

        public int[][][] gwg(int n, int m) throws IOException {
            int adja[][] = new int[n + 1][];
            int weight[][] = new int[n + 1][];
            int from[] = new int[m];
            int to[] = new int[m];
            int count[] = new int[n + 1];
            int cost[] = new int[n + 1];
            for (int i = 0; i < m; i++) {
                from[i] = ni();
                to[i] = ni();
                cost[i] = ni();
                count[from[i]]++;
                count[to[i]]++;
            }
            for (int i = 0; i <= n; i++) {
                adja[i] = new int[count[i]];
                weight[i] = new int[count[i]];
            }
            for (int i = 0; i < m; i++) {
                adja[from[i]][count[from[i]] - 1] = to[i];
                adja[to[i]][count[to[i]] - 1] = from[i];
                weight[from[i]][count[from[i]] - 1] = cost[i];
                weight[to[i]][count[to[i]] - 1] = cost[i];
                count[from[i]]--;
                count[to[i]]--;
            }
            return new int[][][]{adja, weight};
        }

        public int[][] gtree(int n) throws IOException {
            int adja[][] = new int[n + 1][];
            int from[] = new int[n - 1];
            int to[] = new int[n - 1];
            int count[] = new int[n + 1];
            for (int i = 0; i < n - 1; i++) {
                from[i] = i + 1;
                to[i] = ni();
                count[from[i]]++;
                count[to[i]]++;
            }
            for (int i = 0; i <= n; i++) {
                adja[i] = new int[count[i]];
            }
            for (int i = 0; i < n - 1; i++) {
                adja[from[i]][--count[from[i]]] = to[i];
                adja[to[i]][--count[to[i]]] = from[i];
            }
            return adja;
        }

        public int[][] gg(int n, int m) throws IOException {
            int adja[][] = new int[n + 1][];
            int from[] = new int[m];
            int to[] = new int[m];
            int count[] = new int[n + 1];
            for (int i = 0; i < m; i++) {
                from[i] = ni();
                to[i] = ni();
                count[from[i]]++;
                count[to[i]]++;
            }
            for (int i = 0; i <= n; i++) {
                adja[i] = new int[count[i]];
            }
            for (int i = 0; i < m; i++) {
                adja[from[i]][--count[from[i]]] = to[i];
                adja[to[i]][--count[to[i]]] = from[i];
            }
            return adja;
        }

        public void print(String s) throws IOException {
            bw.write(s);
        }

        public void println(String s) throws IOException {
            bw.write(s);
            bw.newLine();
        }

        private String nextToken() throws IndexOutOfBoundsException, IOException {
            if (index == s.length) {
                s = br.readLine().split(" ");
                index = 0;
            }
            return s[index++];
        }

        private void validate(int n, int start, int end) {
            if (start < 0 || end >= n) {
                throw new IllegalArgumentException();
            }
        }
    }

    static class Data implements Comparable<Data> {

        int a, b;

        public Data(int a, int b) {
            this.a = a;
            this.b = b;
        }

        @Override
        public int compareTo(Data o) {
            if (a == o.a) {
                return Integer.compare(b, o.b);
            }
            return Integer.compare(a, o.a);
        }

        public static void sort(int a[]) {
            Data d[] = new Data[a.length];
            for (int i = 0; i < a.length; i++) {
                d[i] = new Data(a[i], 0);
            }
            Arrays.sort(d);
            for (int i = 0; i < a.length; i++) {
                a[i] = d[i].a;
            }
        }
    }
}