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.PrintWriter;
import java.io.PrintStream;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.Collections;
import java.io.InputStream;

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

    static class TaskA {
        int[] stones;
        Edge[] first;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            stones = new int[n];
            first = new Edge[n];
            for (int i = 0; i < n; ++i) {
                stones[i] = in.nextInt();
            }
            int[] degree = new int[n];
            for (int i = 0; i < n - 1; ++i) {
                int from, to;
                from = in.nextInt() - 1;
                to = in.nextInt() - 1;
                new Edge(from, to);
                new Edge(to, from);
                ++degree[from];
                ++degree[to];
            }

            if (n == 2) {
                out.println(stones[0] == stones[1] ? "YES" : "NO");
                return;
            }

            int root = -1;
            for (int i = 0; i < n; ++i) {
                if (degree[i] > 1) {
                    root = i;
                    break;
                }
            }
            assert root != -1;
            System.err.println("root = " + root);
            out.print(dfs(root, -1) == 0 ? "YES" : "NO");
        }

        private int dfs(int x, int fa) {
            ArrayList<Integer> subtrees = new ArrayList<>();
            boolean isLeaf = true;
            long sum = 0;
            for (Edge e = first[x]; e != null; e = e.next) {
                if (e.to == fa) {
                    continue;
                }
                isLeaf = false;
                int number = dfs(e.to, x);
                if (number == -1) {
                    return -1;
                }
                subtrees.add(number);
                sum += number;
            }

            if (isLeaf) {
                return stones[x];
            }
            if (sum < stones[x]) {
                return -1;
            }

            Collections.sort(subtrees);
            long otherSum = 0;
            for (int i = 0; i < subtrees.size() - 1; ++i) {
                otherSum += subtrees.get(i);
            }

            long internalRequirement = sum - stones[x];
            long externamRequirement = stones[x] - internalRequirement;

            if (internalRequirement < 0 || externamRequirement < 0) {
                return -1;
            }


            long pairs = sum / 2;
            if (otherSum < subtrees.get(subtrees.size() - 1)) {
                pairs = otherSum;
            }
//        System.err.println("x = " + x + " pairs = " + pairs + " internal = " + internalRequirement + " external = " + externamRequirement);
            if (pairs < internalRequirement) {
                return -1;
            }

            return (int) externamRequirement;
        }

        class Edge {
            int to;
            Edge next;

            Edge(int from, int to) {
                this.to = to;
                this.next = first[from];
                first[from] = this;
            }

        }

    }

    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (Exception e) {
                    throw new UnknownError();
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}