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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.Arrays;
import java.io.IOException;
import java.io.UncheckedIOException;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 27);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            TaskF2 solver = new TaskF2();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class TaskF2 {
        MultiWayIntStack edges;
        int[][] dp;
        int[] color;
        int[] parent;
        boolean[] visited;
        Modular mod = new Modular(998244353);
        boolean valid = true;

        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();
            int k = in.readInt();
            edges = new MultiWayIntStack(n + 1, n * 2);
            dp = new int[n + 1][2];
            color = new int[n + 1];
            visited = new boolean[n + 1];
            parent = new int[n + 1];

            for (int i = 1; i <= n; i++) {
                color[i] = in.readInt();
            }

            for (int i = 1; i <= n; i++) {
                int a = in.readInt();
                int b = in.readInt();
                edges.addLast(a, b);
                edges.addLast(b, a);
            }
            LcaOnTree lcaOnTree = new LcaOnTree(edges, 1);
            int[] lca = new int[k + 1];
            dfsForParent(1, 0);
            for (int i = 1; i <= n; i++) {
                if (color[i] == 0) {
                    continue;
                }
                if (lca[color[i]] == 0) {
                    lca[color[i]] = i;
                } else {
                    lca[color[i]] = lcaOnTree.lca(lca[color[i]], i);
                }
            }
            for (int i = 1; i <= n; i++) {
                if (color[i] == 0) {
                    continue;
                }
                if (i != lca[color[i]]) {
                    paint(parent[i], lca[color[i]], color[i]);
                }
            }


            if (!valid) {
                out.println(0);
                return;
            }

            int ans = 1;
            for (int i = 1; i <= n; i++) {
                if (visited[i] || color[i] != 0) {
                    continue;
                }
                dfs(i, 0);
                ans = mod.mul(ans, dp[i][1]);
            }

            out.println(ans);
        }

        public void dfsForParent(int root, int p) {
            parent[root] = p;
            for (IntIterator iterator = edges.iterator(root); iterator.hasNext(); ) {
                int node = iterator.next();
                if (node == p) {
                    continue;
                }
                dfsForParent(node, root);
            }
        }

        public void paint(int root, int ancestor, int c) {
            if (color[root] != 0) {
                if (color[root] == c) {
                    return;
                }
                valid = false;
                return;
            }
            color[root] = c;
            if (root != ancestor) {
                paint(parent[root], ancestor, c);
            }
        }

        public void dfs(int root, int p) {
            if (visited[root]) {
                return;
            }
            visited[root] = true;
            if (color[root] != 0) {
                dp[root][0] = 0;
                dp[root][1] = 1;
                return;
            }
            dp[root][0] = 1;
            dp[root][1] = 0;
            for (IntIterator iterator = edges.iterator(root); iterator.hasNext(); ) {
                int node = iterator.next();
                if (node == p) {
                    continue;
                }
                dfs(node, root);
                int total = mod.plus(dp[node][0], dp[node][1]);
                dp[root][1] = mod.plus(mod.mul(dp[root][1], total), mod.mul(dp[root][0], dp[node][1]));
                dp[root][0] = mod.mul(dp[root][0], total);
            }
        }

    }

    static class MultiWayIntStack {
        private int[] values;
        private int[] next;
        private int[] heads;
        private int alloc;
        private int stackNum;

        public IntIterator iterator(final int queue) {
            return new IntIterator() {
                int ele = heads[queue];


                public boolean hasNext() {
                    return ele != 0;
                }


                public int next() {
                    int ans = values[ele];
                    ele = next[ele];
                    return ans;
                }
            };
        }

        private void doubleCapacity() {
            int newSize = Math.max(next.length + 10, next.length * 2);
            next = Arrays.copyOf(next, newSize);
            values = Arrays.copyOf(values, newSize);
        }

        public void alloc() {
            alloc++;
            if (alloc >= next.length) {
                doubleCapacity();
            }
            next[alloc] = 0;
        }

        public int stackNumber() {
            return stackNum;
        }

        public MultiWayIntStack(int qNum, int totalCapacity) {
            values = new int[totalCapacity + 1];
            next = new int[totalCapacity + 1];
            heads = new int[qNum];
            stackNum = qNum;
        }

        public void addLast(int qId, int x) {
            alloc();
            values[alloc] = x;
            next[alloc] = heads[qId];
            heads[qId] = alloc;
        }

        public String toString() {
            StringBuilder builder = new StringBuilder();
            for (int i = 0; i < stackNum; i++) {
                builder.append(i).append(": ");
                for (IntIterator iterator = iterator(i); iterator.hasNext(); ) {
                    builder.append(iterator.next()).append(",");
                }
                if (builder.charAt(builder.length() - 1) == ',') {
                    builder.setLength(builder.length() - 1);
                }
                builder.append('\n');
            }
            return builder.toString();
        }

    }

    static class Modular {
        int m;

        public Modular(int m) {
            this.m = m;
        }

        public Modular(long m) {
            this.m = (int) m;
            if (this.m != m) {
                throw new IllegalArgumentException();
            }
        }

        public Modular(double m) {
            this.m = (int) m;
            if (this.m != m) {
                throw new IllegalArgumentException();
            }
        }

        public int valueOf(int x) {
            x %= m;
            if (x < 0) {
                x += m;
            }
            return x;
        }

        public int valueOf(long x) {
            x %= m;
            if (x < 0) {
                x += m;
            }
            return (int) x;
        }

        public int mul(int x, int y) {
            return valueOf((long) x * y);
        }

        public int plus(int x, int y) {
            return valueOf(x + y);
        }

        public String toString() {
            return "mod " + m;
        }

    }

    static class LcaOnTree {
        int[] parent;
        int[] preOrder;
        int[] I;
        int[] head;
        int[] A;
        int time;

        void dfs1(MultiWayIntStack tree, int u, int p) {
            parent[u] = p;
            I[u] = preOrder[u] = time++;
            for (IntIterator iterator = tree.iterator(u); iterator.hasNext(); ) {
                int v = iterator.next();
                if (v == p) continue;
                dfs1(tree, v, u);
                if (Integer.lowestOneBit(I[u]) < Integer.lowestOneBit(I[v])) {
                    I[u] = I[v];
                }
            }
            head[I[u]] = u;
        }

        void dfs2(MultiWayIntStack tree, int u, int p, int up) {
            A[u] = up | Integer.lowestOneBit(I[u]);
            for (IntIterator iterator = tree.iterator(u); iterator.hasNext(); ) {
                int v = iterator.next();
                if (v == p) continue;
                dfs2(tree, v, u, A[u]);
            }
        }

        public LcaOnTree(MultiWayIntStack tree, int root) {
            int n = tree.stackNumber();
            preOrder = new int[n];
            I = new int[n];
            head = new int[n];
            A = new int[n];
            parent = new int[n];

            dfs1(tree, root, -1);
            dfs2(tree, root, -1, 0);
        }

        private int enterIntoStrip(int x, int hz) {
            if (Integer.lowestOneBit(I[x]) == hz)
                return x;
            int hw = Integer.highestOneBit(A[x] & (hz - 1));
            return parent[head[I[x] & -hw | hw]];
        }

        public int lca(int x, int y) {
            int hb = I[x] == I[y] ? Integer.lowestOneBit(I[x]) : Integer.highestOneBit(I[x] ^ I[y]);
            int hz = Integer.lowestOneBit(A[x] & A[y] & -hb);
            int ex = enterIntoStrip(x, hz);
            int ey = enterIntoStrip(y, hz);
            return preOrder[ex] < preOrder[ey] ? ex : ey;
        }

    }

    static interface IntIterator {
        boolean hasNext();

        int next();

    }

    static class FastOutput implements AutoCloseable, Closeable {
        private StringBuilder cache = new StringBuilder(10 << 20);
        private final Writer os;

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput println(int c) {
            cache.append(c).append('\n');
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }
}