Problem:
Score : 800 points

Problem Statement

We have a tree with N vertices. The vertices are numbered 1, 2, ..., N. The i-th (1 ≦ i ≦ N - 1) edge connects the two vertices A_i and B_i.

Takahashi wrote integers into K of the vertices. Specifically, for each 1 ≦ j ≦ K, he wrote the integer P_j into vertex V_j. The remaining vertices are left empty. After that, he got tired and fell asleep.

Then, Aoki appeared. He is trying to surprise Takahashi by writing integers into all empty vertices so that the following condition is satisfied:

Condition: For any two vertices directly connected by an edge, the integers written into these vertices differ by exactly 1.

Determine if it is possible to write integers into all empty vertices so that the condition is satisfied. If the answer is positive, find one specific way to satisfy the condition.

Constraints

1 ≦ N ≦ 10^5

1 ≦ K ≦ N

1 ≦ A_i, B_i ≦ N (1 ≦ i ≦ N - 1)

1 ≦ V_j ≦ N (1 ≦ j ≦ K) (21:18, a mistake in this constraint was corrected)

0 ≦ P_j ≦ 10^5 (1 ≦ j ≦ K)

The given graph is a tree.

All v_j are distinct.

Input

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

N
A_1 B_1
A_2 B_2
:
A_{N-1} B_{N-1}
K
V_1 P_1
V_2 P_2
:
V_K P_K

Output

If it is possible to write integers into all empty vertices so that the condition is satisfied, print Yes. Otherwise, print No.

If it is possible to satisfy the condition, print N lines in addition. The v-th (1 ≦ v ≦ N) of these N lines should contain the integer that should be written into vertex v. If there are multiple ways to satisfy the condition, any of those is accepted.

Sample Input 1

5
1 2
3 1
4 3
3 5
2
2 6
5 7

Sample Output 1

Yes
5
6
6
5
7

The figure below shows the tree when Takahashi fell asleep. For each vertex, the integer written beside it represents the index of the vertex, and the integer written into the vertex is the integer written by Takahashi.

Aoki can, for example, satisfy the condition by writing integers into the remaining vertices as follows:

This corresponds to Sample Output 1. Note that other outputs that satisfy the condition will also be accepted, such as:

Yes
7
6
8
7
7

Sample Input 2

5
1 2
3 1
4 3
3 5
3
2 6
4 3
5 7

Sample Output 2

No

Sample Input 3

4
1 2
2 3
3 4
1
1 0

Sample Output 3

Yes
0
-1
-2
-3

The integers written by Aoki may be negative or exceed 10^6.

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.IO;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using System.Collections.Generic;
using System.Diagnostics;
using System.Numerics;
using Enu = System.Linq.Enumerable;

public class Program
{
    static readonly int Unknown = int.MinValue;

    public void Solve()
    {
        int N = Reader.Int();
        var G = EdgeRead(N);
        int K = Reader.Int();
        var Val = Enu.Repeat(Unknown, N).ToArray();
        var heap = new Heap<long>();

        for (int i = 0; i < K; i++)
        {
            int at = Reader.Int() - 1, val = Reader.Int();
            Val[at] = val;
            heap.Push(((long)val << 32) + at);
        }
        while (heap.Count > 0)
        {
            long mask = heap.Pop();
            int val = (int)(mask >> 32);
            int at = (int)mask;
            foreach (int next in G[at])
                if (Val[next] == Unknown)
                {
                    heap.Push(((long)val + 1 << 32) + next);
                    Val[next] = val + 1;
                }
                else if (Math.Abs(Val[next] - val) != 1)
                {
                    Console.WriteLine("No"); return;
                }
        }

        Console.WriteLine("Yes\n" + string.Join("\n", Val));
    }

    int[][] EdgeRead(int V, int E = -1, int origin = 1)
    {
        if (E == -1) E = V - 1;
        var es = new List<int>[V];
        for (int i = 0; i < V; i++) es[i] = new List<int>();
        for (int i = 0; i < E; i++)
        {
            int a = Reader.Int() - origin, b = Reader.Int() - origin;
            es[a].Add(b);
            es[b].Add(a);
        }
        return es.Select(a => a.ToArray()).ToArray();
    }

    class Heap<T>
    {
        private const int InitialSize = 1024;
        private readonly int sign;
        private readonly Comparer<T> comp = Comparer<T>.Default;
        private T[] A = new T[InitialSize];
        public int Count { get; private set; }
        public Heap(bool greater = false) { sign = greater ? 1 : -1; }
        public T Peek() { return A[0]; }
        public bool Empty() { return Count == 0; }
        public void Push(T val)
        {
            if (Count == A.Length)
            {
                T[] next = new T[A.Length * 2];
                Array.Copy(A, next, A.Length);
                A = next;
            }
            A[Count++] = val;
            int i = Count - 1;
            while (i > 0)
            {
                int parent = (i - 1) / 2;
                if (Math.Sign(comp.Compare(val, A[parent])) == sign)
                {
                    A[i] = A[parent];
                    i = parent;
                }
                else break;
            }
            A[i] = val;
        }
        public T Pop()
        {
            T res = A[0];
            T val = A[--Count];
            if (Count == 0) return res;
            int i = 0;
            while (i * 2 + 1 < Count)
            {
                int L = i * 2 + 1;
                int R = i * 2 + 2;
                if (R < Count && Math.Sign(comp.Compare(A[R], A[L])) == sign) L = R;
                if (Math.Sign(comp.Compare(A[L], val)) == sign) { A[i] = A[L]; i = L; }
                else break;
            }
            A[i] = val;
            return res;
        }
    }
}


class Entry { static void Main() { new Program().Solve(); } }
class Reader
{
    static TextReader reader = Console.In;
    static readonly char[] separator = { ' ' };
    static readonly StringSplitOptions op = StringSplitOptions.RemoveEmptyEntries;
    static string[] A = new string[0];
    static int i;
    static void Init() { A = new string[0]; }
    public static void Set(TextReader r) { reader = r; Init(); }
    public static void Set(string file) { reader = new StreamReader(file); Init(); }
    public static bool HasNext() { return CheckNext(); }
    public static string String() { return Next(); }
    public static int Int() { return int.Parse(Next()); }
    public static long Long() { return long.Parse(Next()); }
    public static double Double() { return double.Parse(Next()); }
    public static int[] IntLine() { return Array.ConvertAll(Split(Line()), int.Parse); }
    public static int[] IntArray(int N) { return Range(N, Int); }
    public static int[][] IntTable(int H) { return Range(H, IntLine); }
    public static string[] StringArray(int N) { return Range(N, Next); }
    public static string[][] StringTable(int N) { return Range(N, () => Split(Line())); }
    public static string Line() { return reader.ReadLine().Trim(); }
    public static T[] Range<T>(int N, Func<T> f) { var r = new T[N]; for (int i = 0; i < N; r[i++] = f()) ; return r; }
    static string[] Split(string s) { return s.Split(separator, op); }
    static string Next() { CheckNext(); return A[i++]; }
    static bool CheckNext()
    {
        if (i < A.Length) return true;
        string line = reader.ReadLine();
        if (line == null) return false;
        if (line == "") return CheckNext();
        A = Split(line);
        i = 0;
        return true;
    }
}