Problem:
Score : 700 points

Problem Statement

There is a tree with N vertices, numbered 1 through N.
The i-th of the N-1 edges connects vertices a_i and b_i.

Currently, there are A_i stones placed on vertex i.
Determine whether it is possible to remove all the stones from the vertices by repeatedly performing the following operation:

Select a pair of different leaves. Then, remove exactly one stone from every vertex on the path between those two vertices.
Here, a leaf is a vertex of the tree whose degree is 1, and the selected leaves themselves are also considered as vertices on the path connecting them.

Note that the operation cannot be performed if there is a vertex with no stone on the path.

Constraints

2 ≦ N ≦ 10^5

1 ≦ a_i,b_i ≦ N

0 ≦ A_i ≦ 10^9

The given graph is a tree.

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 … A_N
a_1 b_1
:
a_{N-1} b_{N-1}

Output

If it is possible to remove all the stones from the vertices, print YES. Otherwise, print NO.

Sample Input 1

5
1 2 1 1 2
2 4
5 2
3 2
1 3

Sample Output 1

YES

All the stones can be removed, as follows:

Select vertices 4 and 5. Then, there is one stone remaining on each vertex except 4.

Select vertices 1 and 5. Then, there is no stone on any vertex.

Sample Input 2

3
1 2 1
1 2
2 3

Sample Output 2

NO

Sample Input 3

6
3 2 2 2 2 2
1 2
2 3
1 4
1 5
4 6

Sample Output 3

YES

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.util.List;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author prakharjain
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        agc010c solver = new agc010c();
        solver.solve(1, in, out);
        out.close();
    }

    static class agc010c {
        List[] g;
        int[] a;
        boolean isp = true;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();

            a = new int[n];

            for (int i = 0; i < n; i++) {
                a[i] = in.nextInt();
            }

            g = new List[n];

            for (int i = 0; i < n; i++) {
                g[i] = new ArrayList();
            }

            for (int i = 0; i < n - 1; i++) {
                int u = in.nextInt() - 1;
                int v = in.nextInt() - 1;

                g[u].add(v);
                g[v].add(u);
            }

            long val = dfs(0, -1);

            if ((g[0].size() == 1 || val == 0) && isp) {
                out.print("YES");
            } else {
                out.print("NO");
            }
        }

        long dfs(int u, int p) {

            long sum = 0;
            int tot = 0;
            List<Long> rl = new ArrayList<>();

            for (int v : (List<Integer>) g[u]) {
                if (v != p) {
                    tot++;
                    long val = dfs(v, u);
                    sum += val;
                    rl.add(val);
                }
            }

            rl.sort((x, y) -> (int) Math.signum(x - y));

            long minsum = 0;

            if (tot == 0) {
                return a[u];
            }

            if (tot == 1) {
                if (sum != a[u]) {
                    isp = false;
                    return -1;
                } else {
                    return sum;
                }
            }

            for (int i = 0; i < rl.size() - 1; i++) {
                minsum += rl.get(i);
            }

            if (sum < a[u]) {
                isp = false;
                return -1;
            }

            if (sum == a[u]) {
                return sum;
            }

            if (sum > a[u]) {
                long rem = sum - a[u];
                if (rem <= a[u] && 2 * rem <= sum && minsum >= rem) {
                    return a[u] - rem;
                } else {
                    isp = false;
                    return -1;
                }
            }

            return -1;
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void close() {
            writer.close();
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 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 {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}