Problem: 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.

Examples

Input

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


Output

Yes
5
6
6
5
7


Input

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


Output

No


Input

4
1 2
2 3
3 4
1
1 0


Output

Yes
0
-1
-2
-3

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

public class Main {

    static BufferedReader in;
    static PrintWriter out;
    static StringTokenizer tok;

    void solve() throws IOException {
        int n = ni();
        int[] a = new int[n];
        int[] b = new int[n];
        for (int i = 0; i < n - 1; i++) {
            a[i] = ni() - 1;
            b[i] = ni() - 1;
        }
        int k = ni();
        int[] v = new int[k];
        int[] p = new int[k];
        for (int i = 0; i < k; i++) {
            v[i] = ni() - 1;
            p[i] = ni();
        }

        ArrayList<ArrayList<Edge>> G = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            G.add(new ArrayList<>());
        }

        for (int i = 0; i < n - 1; i++) {
            G.get(a[i]).add(new Edge(b[i], 1));
            G.get(b[i]).add(new Edge(a[i], 1));
        }

        G.add(new ArrayList<>());
        for (int i = 0; i < k; i++) {
            G.get(n).add(new Edge(v[i], p[i]));
        }

        Dijkstra d = new Dijkstra(G);
        int[] dist = d.getDist(n);

        boolean flg = true;
        for (int i = 0; i < n - 1; i++) {
            if (Math.abs(dist[a[i]] - dist[b[i]]) != 1) {
                flg = false;
                break;
            }
        }
        if (flg) {
            for (int i = 0; i < k; i++) {
                if (dist[v[i]] != p[i]) {
                    flg = false;
                    break;
                }
            }
        }

        if (flg) {
            out.println("Yes");
            for (int i = 0; i < n; i++) {
                out.println(dist[i]);
            }
        } else {
            out.println("No");
        }
    }

    class Dijkstra {
        int n;
        ArrayList<ArrayList<Edge>> G;

        int INF = Integer.MAX_VALUE / 3;

        public Dijkstra(ArrayList<ArrayList<Edge>> G) {
            n = G.size();
            this.G = G;
        }

        int[] getDist(int s) {
            PriorityQueue<Pair> Q = new PriorityQueue<>();
            Q.add(new Pair(s, 0));
            int[] dist = new int[n];
            Arrays.fill(dist, INF);
            boolean[] used = new boolean[n];
            while (!Q.isEmpty()) {
                Pair p = Q.poll();
                if (used[p.x]) continue;
                used[p.x] = true;
                dist[p.x] = p.y;

                for (Edge e : G.get(p.x)) {
                    Q.add(new Pair(e.to, p.y + e.cost));
                }
            }
            return dist;
        }

        public class Pair implements Comparable<Pair> {
            int x, y;

            public Pair(int x, int y) {
                this.x = x;
                this.y = y;
            }

            public int compareTo(Pair p) {
                return y - p.y;
            }
        }
    }

    class Edge implements Comparable<Edge> {
        int to;
        int cost;

        public Edge(int to, int cost) {
            this.to = to;
            this.cost = cost;
        }

        public int compareTo(Edge edge) {
            return cost - edge.cost;
        }
    }

    String ns() throws IOException {
        while (!tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine(), " ");
        }
        return tok.nextToken();
    }

    int ni() throws IOException {
        return Integer.parseInt(ns());
    }

    long nl() throws IOException {
        return Long.parseLong(ns());
    }

    double nd() throws IOException {
        return Double.parseDouble(ns());
    }

    String[] nsa(int n) throws IOException {
        String[] res = new String[n];
        for (int i = 0; i < n; i++) {
            res[i] = ns();
        }
        return res;
    }

    int[] nia(int n) throws IOException {
        int[] res = new int[n];
        for (int i = 0; i < n; i++) {
            res[i] = ni();
        }
        return res;
    }

    long[] nla(int n) throws IOException {
        long[] res = new long[n];
        for (int i = 0; i < n; i++) {
            res[i] = nl();
        }
        return res;
    }

    public static void main(String[] args) throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        tok = new StringTokenizer("");
        Main main = new Main();
        main.solve();
        out.close();
    }
}