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)

import java.io.IOException;
import java.io.InputStream;
import java.util.NoSuchElementException;


public class Main {
  private static int N;
  private static int[][] g;
  private static long[] A;

  private static long[] last;

  public static void main(String[] args) {
    FastScanner sc = new FastScanner();
    N = sc.nextInt();
    A = sc.nextLongList(N);
    
    int[] from = new int[N - 1];
    int[] to = new int[N - 1];
    for (int i = 0; i < N - 1; i ++) {
      from[i] = sc.nextInt() - 1;
      to[i] = sc.nextInt() - 1;
    }
    g = packU(N, from, to);
  
    last = new long[N];

    int s = -1;
    for (int i = 0; i < N; i ++) {
      if (g[i].length > 1) {
        s = i;
        break;
      }
    }
    if (s >= 0) {
      boolean ret = dfs(s, -1);
      if (ret && last[s] == 0) { 
        System.out.println("YES");
      } else {
        System.out.println("NO");
      }
    } else {
      System.out.println(A[0] == A[1] ? "YES" : "NO");
    }
  }

  private static boolean dfs(int now, int pre) {
    if (pre >= 0 && g[now].length == 1) {
      last[now] = A[now];
      return true;
    }

    long a = 0;
    long max = 0;
    for (int v : g[now]) {
      if (v != pre) {
        boolean ret = dfs(v, now);
        if (!ret) {
          return false;
        }
        a += last[v];
        max = Math.max(max, a);
      }
    }

    if (pre >= 0 && g[now].length == 2) {
      last[now] = A[now];
      return a == A[now];
    } else {
      if (a <= A[now] * 2 && A[now] <= a) {
        last[now] = A[now] * 2 - a;
        
        if (A[now] > max) {
          return false;
        }
        return true;
      } else {
        return false;
      }
    }
  }
  
  public static int[][] packU(int n, int[] from, int[] to)
  {
      int[][] g = new int[n][];
      int[] p = new int[n];
      for(int f : from)p[f]++;
      for(int t : to)p[t]++;
      for(int i = 0;i < n;i++)g[i] = new int[p[i]];
      for(int i = 0;i < from.length;i++){
          g[from[i]][--p[from[i]]] = to[i];
          g[to[i]][--p[to[i]]] = from[i];
      }
      return g;
  }
}


class FastScanner {
	public static String debug = null;

	private final InputStream in = System.in;
	private int ptr = 0;
	private int buflen = 0;
	private byte[] buffer = new byte[1024];
	private boolean eos = false;

	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		} else {
			ptr = 0;
			try {
				if (debug != null) {
					buflen = debug.length();
					buffer = debug.getBytes();
					debug = "";
					eos = true;
				} else {
					buflen = in.read(buffer);
				}
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen < 0) {
				eos = true;
				return false;
			} else if (buflen == 0) {
				return false;
			}
		}
		return true;
	}

	private int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}

	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <= 126;
	}

	private void skipUnprintable() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr]))
			ptr++;
	}

	public boolean isEOS() {
		return this.eos;
	}

	public boolean hasNext() {
		skipUnprintable();
		return hasNextByte();
	}

	public String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	public long nextLong() {
		if (!hasNext())
			throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while (true) {
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			} else if (b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			} else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}

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

	public long[] nextLongList(int n) {
		return nextLongTable(1, n)[0];
	}

	public int[] nextIntList(int n) {
		return nextIntTable(1, n)[0];
	}

	public long[][] nextLongTable(int n, int m) {
		long[][] ret = new long[n][m];
		for (int i = 0; i < n; i ++) {
			for (int j = 0; j < m; j ++) {
				ret[i][j] = nextLong();
			}
		}
		return ret;
	}

	public int[][] nextIntTable(int n, int m) {
		int[][] ret = new int[n][m];
		for (int i = 0; i < n; i ++) {
			for (int j = 0; j < m; j ++) {
				ret[i][j] = nextInt();
			}
		}
		return ret;
	}
}