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.*;
import java.util.*;
import java.util.function.Function;

public class Main {

    static int N;
    static int[] A, B;
    static int K;
    static int[] V, P;

    public static void main(String[] args) {
        FastScanner sc = new FastScanner(System.in);
        N = sc.nextInt();
        A = new int[N-1];
        B = new int[N-1];
        for (int i = 0; i < N-1; i++) {
            A[i] = sc.nextInt()-1;
            B[i] = sc.nextInt()-1;
        }
        K = sc.nextInt();
        V = new int[K];
        P = new int[K];
        for (int i = 0; i < K; i++) {
            V[i] = sc.nextInt()-1;
            P[i] = sc.nextInt();
        }

        int[] ans = solve();
        if( ans != null ) {
            System.out.println("Yes");
            writeLines(ans);
        } else {
            System.out.println("No");
        }
    }

    static int[] solve() {
        int[][] G = adjB(N, A, B);
        if( !checkParity(G) ) {
            return null;
        }

        int[][] cond = new int[N][];
        for (int i = 0; i < K; i++) {
            cond[V[i]] = new int[]{P[i], P[i]};
        }

        for (Node node : orderFromLeaf(N, G, 0)) {
            int min = Integer.MIN_VALUE;
            int max = Integer.MAX_VALUE;

            for (int b : G[node.a]) {
                if( b == node.parent ) continue;

                if( cond[b] != null ) {
                    min = Math.max(min, cond[b][0]-1);
                    max = Math.min(max, cond[b][1]+1);
                }
            }
            if( max < min ) return null;

            if( cond[node.a] != null ) {
                // check
                if( min != Integer.MIN_VALUE ) {
                    int p = cond[node.a][0];
                    if( p < min || max < p ) return null;
                }

            } else {
                // set
                if( min != Integer.MIN_VALUE ) {
                    cond[node.a] = new int[]{min, max};
                }
            }
        }

        int[] ans = new int[N];
        for (Node node : orderFromRoot(N, G, 0)) {
            if( cond[node.a] == null ) {
                ans[node.a] = ans[node.parent] + 1; // 何でもよい

            } else {
                int min = cond[node.a][0];
                int max = cond[node.a][1];
                if( node.a == 0 ) {
                    ans[node.a] = min;

                } else {
                    int parent = ans[node.parent];
                    if( min <= parent - 1 && parent -1 <= max ) {
                        ans[node.a] = parent - 1;
                    } else {
                        ans[node.a] = parent + 1;
                    }
                }
            }
        }

        return ans;
    }

    static boolean checkParity(int[][] G) {
        int[] parity = new int[N];
        for (int i = 0; i < K; i++) {
            parity[V[i]] = P[i] % 2 == 0 ? 2 : 1;
        }
        for (Node node : orderFromLeaf(N, G, 0)) {
            int p = 0;
            for (int b : G[node.a]) {
                if( b == node.parent ) continue;
                if( parity[b] == 0 ) continue;

                int req = parity[b] == 1 ? 2 : 1;
                if( p == 0 ) {
                    p = req;

                } else {
                    if( p != req ) {
                        return false;
                    }
                }
            }
            // debug(node.a, p);
            if( p != 0 ) {
                if( parity[node.a] == 0 ) {
                    parity[node.a] = p;
                } else {
                    if( parity[node.a] != p ) return false;
                }
            }
        }
        return true;
    }

    static Node[] orderFromRoot(int N, int[][] G, int root) {
        ArrayDeque<Node> q = new ArrayDeque<>();
        Node[] ret = new Node[N];
        int idx = 0;
        q.add(new Node(-1, root));
        while(!q.isEmpty()) {
            Node n = q.poll();
            ret[idx++] = n;
            for (int next : G[n.a]) {
                if( next == n.parent ) continue;

                q.add(new Node(n.a, next));
            }
        }
        return ret;
    }

    static Node[] orderFromLeaf(int N, int[][] G, int root) {
        ArrayDeque<Node> q = new ArrayDeque<>();
        Node[] ret = new Node[N];
        int idx = N-1;
        q.add(new Node(-1, root));
        while(!q.isEmpty()) {
            Node n = q.poll();
            ret[idx--] = n;
            for (int next : G[n.a]) {
                if( next == n.parent ) continue;

                q.add(new Node(n.a, next));
            }
        }
        return ret;
    }

    static class Node {
        int parent, a;

        public Node(int parent, int a) {
            this.parent = parent;
            this.a = a;
        }
    }

    static int[][] adjB(int n, int[] from, int[] to) {
        int[][] adj = new int[n][];
        int[] cnt = new int[n];
        for (int f : from) {
            cnt[f]++;
        }
        for (int t : to) {
            cnt[t]++;
        }
        for (int i = 0; i < n; i++) {
            adj[i] = new int[cnt[i]];
        }
        for (int i = 0; i < from.length; i++) {
            adj[from[i]][--cnt[from[i]]] = to[i];
            adj[to[i]][--cnt[to[i]]] = from[i];
        }
        return adj;
    }

    @SuppressWarnings("unused")
    static class FastScanner {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken("\n");
        }

        long nextLong() {
            return Long.parseLong(next());
        }

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

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        int[] nextIntArray(int n, int delta) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt() + delta;
            return a;
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }
    }

    static <A> void writeLines(A[] as, Function<A, String> f) {
        PrintWriter pw = new PrintWriter(System.out);
        for (A a : as) {
            pw.println(f.apply(a));
        }
        pw.flush();
    }

    static void writeLines(int[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int a : as) pw.println(a);
        pw.flush();
    }

    static void writeLines(long[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (long a : as) pw.println(a);
        pw.flush();
    }

    static int max(int... as) {
        int max = Integer.MIN_VALUE;
        for (int a : as) max = Math.max(a, max);
        return max;
    }

    static int min(int... as) {
        int min = Integer.MAX_VALUE;
        for (int a : as) min = Math.min(a, min);
        return min;
    }

    static void debug(Object... args) {
        StringJoiner j = new StringJoiner(" ");
        for (Object arg : args) {
            if (arg instanceof int[]) j.add(Arrays.toString((int[]) arg));
            else if (arg instanceof long[]) j.add(Arrays.toString((long[]) arg));
            else if (arg instanceof double[]) j.add(Arrays.toString((double[]) arg));
            else if (arg instanceof Object[]) j.add(Arrays.toString((Object[]) arg));
            else if ( arg != null ) j.add(arg.toString());
            else j.add("null");
        }
        System.err.println(j.toString());
    }
}