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: Wrong Answer)

// package agc.agc010;

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.List;

public class Main {
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);


        int n = in.nextInt();
        a = new long[n];
        for (int i = 0; i < n ; i++) {
            a[i] = in.nextLong();
        }
        graph = buildGraph(in, n, n-1);

        out.println(isOK(n) ? "YES" : "NO");
        out.flush();
    }

    static boolean isOK(int n) {
        isOK = true;
        if (n == 2) {
            return a[0] == a[1];
        }
        for (int i = 0; i < n ; i++) {
            if (graph[i].length >= 2) {
                isOK &= dfs(i, -1) == 0;
                break;
            }
        }
        return isOK;
    }

    static long[] a;
    static int[][] graph;
    static boolean isOK;

    static long dfs(int now, int par) {
        boolean has = false;
        long upsum = 0;
        long max = 0;
        for (int to : graph[now]) {
            if (to == par) {
                continue;
            }
            has = true;
            long l = dfs(to, now);
            max = Math.max(max, l);
            upsum += l;
        }
        if (!has) {
            return a[now];
        }


        isOK &= a[now] <= upsum;
        long pair = upsum - a[now];
        long maxpair = max * 2 <= upsum ? upsum / 2 : (upsum - max);
        isOK &= pair <= maxpair;

        long up = a[now] * 2 - upsum;

        // debug(now, a[now], upsum, up);

        return up;
    }
    
    static int[][] buildGraph(InputReader in, int n, int m) {
        int[][] edges = new int[m][];
        int[][] graph = new int[n][];
        int[] deg = new int[n];
        for (int i = 0 ; i < m ; i++) {
            int a = in.nextInt()-1;
            int b = in.nextInt()-1;
            deg[a]++;
            deg[b]++;
            edges[i] = new int[]{a, b};
        }
        for (int i = 0 ; i < n ; i++) {
            graph[i] = new int[deg[i]];
        }
        for (int i = 0 ; i < m ; i++) {
            int a = edges[i][0];
            int b = edges[i][1];
            graph[a][--deg[a]] = b;
            graph[b][--deg[b]] = a;
        }
        return graph;
    }


    public static void debug(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }

    public static class InputReader {
        private static final int BUFFER_LENGTH = 1 << 12;
        private InputStream stream;
        private byte[] buf = new byte[BUFFER_LENGTH];
        private int curChar;
        private int numChars;

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

        private int next() {
            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 char nextChar() {
            return (char) skipWhileSpace();
        }

        public String nextToken() {
            int c = skipWhileSpace();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char) c);
                c = next();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public int nextInt() {
            return (int) nextLong();
        }

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

        public double nextDouble() {
            return Double.valueOf(nextToken());
        }

        int skipWhileSpace() {
            int c = next();
            while (isSpaceChar(c)) {
                c = next();
            }
            return c;
        }

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