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.math.*;
import java.util.*;

import static java.util.Arrays.*;

public class Main {
	private static final int mod = (int)1e9+7;

	final Random random = new Random(0);
	final IOFast io = new IOFast();

	/// MAIN CODE
	public void run() throws IOException {
//		int TEST_CASE = Integer.parseInt(new String(io.nextLine()).trim());
		int TEST_CASE = 1;
		while(TEST_CASE-- != 0) {
			int n = io.nextInt();
			g = new SimpleAdjListGraph(n, 2*n);
			for (int i = 0; i < n - 1; i++) {
				int a = io.nextInt() - 1;
				int b = io.nextInt() - 1;
				g.addEdge(a, b);
				g.addEdge(b, a);
			}
			int r = -1;
			val = new int[n];
			Arrays.fill(val, -INF);
			int K = io.nextInt();
			for (int i = 0; i < K; i++) {
				int v = io.nextInt() - 1;
				val[v] = io.nextInt();
				r = v;
			}
			int[][] dp = g.bfs(r);
//			for (int i = 0; i < n; i++) if (val[i] != -1) {
//				if (Math.abs(val[i] - val[r]) > dp[0][i]) {
//					io.out.println("No");
//					return;
//				}
//				if (Math.abs(val[i] - val[r]) % 2 != dp[0][i] % 2) {
//					io.out.println("No");
//					return;
//				}
//			}
			range = new int[n][];
			prev = dp[1];
			dfs2(r);
			if(!dfs(r)) {
				io.out.println("No");
				return;
			}
			io.out.println("Yes");
			for(int v : val) io.out.println(v);
		}
	}
	
	final int INF = 1<<29;
	
	int[] val;
	int[][] range;
	SimpleAdjListGraph g;
	int[] prev;
	boolean dfs(int v) {
		if(val[v] == -INF) {
			range[v][0] = Math.max(range[v][0], val[prev[v]] - 1);
			range[v][1] = Math.min(range[v][1], val[prev[v]] + 1);
			boolean ok = false;
			for (int i = -1; i <= 1; i += 2) {
				val[v] = val[prev[v]] + i;
				if (val[v] >= range[v][0] && val[v] <= range[v][1]) {
					ok = true;
					break;
				}
			}
			if (!ok) {
//				dump(v + 1, val[v], range);
				return false;
			}
		}
		if (!(val[v] >= range[v][0] && val[v] <= range[v][1])) {
			return false;
		}
		for(int e = g.head[v]; e != -1; e = g.next[e]) {
			int t = g.to[e];
			if (t == prev[v]) continue;
			if (!dfs(t)) {
				return false;
			}
			if (Math.abs(val[v] - val[t]) != 1) {
				return false;
			}
		}
		return true;
	}
	int[] dfs2(int v) {
		if (val[v] != -INF) range[v] = new int[]{val[v], val[v]};
		else range[v] = new int[]{-INF, INF};
		for(int e = g.head[v]; e != -1; e = g.next[e]) {
			int t = g.to[e];
			if (t == prev[v]) continue;
			int[] rr = dfs2(t);
			range[v][0] = Math.max(range[v][0], rr[0] - 1);
			range[v][1] = Math.min(range[v][1], rr[1] + 1);
		}
		return range[v];
	}

	static
	class SimpleAdjListGraph {
		int m, V, E;
		int[] head, next, to;
	
		public SimpleAdjListGraph(int V, int E) {
			head = new int[V];
			next = new int[E];
			to = new int[E];
			this.V = V;
			this.E = E;
			clear();
		}
	
		public void clear() {
			m = 0;
			Arrays.fill(head, -1);
		}
	
		public void addEdge(int s, int t) {
			next[m] = head[s];
			head[s] = m;
			to[m++] = t;
		}
		

		public int[][] bfs(final int src) {
			final int[] dist = new int[head.length];
			final int[] prev = new int[head.length];
			final int[] q = new int[2 * head.length + 10];
			int s = 0, t = 0;
			
			Arrays.fill(dist, -1);
			Arrays.fill(prev, -1);
			dist[src] = 0;
			q[t++] = src;
			while(s != t) {
				final int v = q[s++];
				for(int e = head[v]; e != -1; e = next[e]) {
					final int u = to[e];
					if(dist[u] == -1) {
						dist[u] = dist[v] + 1;
						prev[u] = v;
						q[t++] = u;
					}
				}
			}
			return new int[][] { dist, prev };
		}
	}


	/// TEMPLATE
	static int gcd(int n, int r) { return r == 0 ? n : gcd(r, n%r); }
	static long gcd(long n, long r) { return r == 0 ? n : gcd(r, n%r); }
	
	static <T> void swap(T[] x, int i, int j) { T t = x[i]; x[i] = x[j]; x[j] = t; }
	static void swap(int[] x, int i, int j) { int t = x[i]; x[i] = x[j]; x[j] = t; }

	void printArrayLn(int[] xs) { for(int i = 0; i < xs.length; i++) io.out.print(xs[i] + (i==xs.length-1?"\n":" ")); }
	void printArrayLn(long[] xs) { for(int i = 0; i < xs.length; i++) io.out.print(xs[i] + (i==xs.length-1?"\n":" ")); }
	
	static void dump(Object... o) { System.err.println(Arrays.deepToString(o)); } 
	
	void main() throws IOException {
		//		IOFast.setFileIO("rle-size.in", "rle-size.out");
		try { run(); }
		catch (EndOfFileRuntimeException e) { }
		io.out.flush();
	}
	public static void main(String[] args) throws IOException { new Main().main(); }
	
	static class EndOfFileRuntimeException extends RuntimeException {
		private static final long serialVersionUID = -8565341110209207657L; }

	static
	public class IOFast {
		private BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		private PrintWriter out = new PrintWriter(System.out);

		void setFileIn(String ins) throws IOException { in.close(); in = new BufferedReader(new FileReader(ins)); }
		void setFileOut(String outs) throws IOException { out.flush(); out.close(); out = new PrintWriter(new FileWriter(outs)); }
		void setFileIO(String ins, String outs) throws IOException { setFileIn(ins); setFileOut(outs); }

		private static int pos, readLen;
		private static final char[] buffer = new char[1024 * 8];
		private static char[] str = new char[500*8*2];
		private static boolean[] isDigit = new boolean[256];
		private static boolean[] isSpace = new boolean[256];
		private static boolean[] isLineSep = new boolean[256];

		static { for(int i = 0; i < 10; i++) { isDigit['0' + i] = true; } isDigit['-'] = true; isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true; isLineSep['\r'] = isLineSep['\n'] = true; }
		public int read() throws IOException { if(pos >= readLen) { pos = 0; readLen = in.read(buffer); if(readLen <= 0) { throw new EndOfFileRuntimeException(); } } return buffer[pos++]; }
		public int nextInt() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); int i = 0; int ret = 0; if(str[0] == '-') { i = 1; } for(; i < len; i++) ret = ret * 10 + str[i] - '0'; if(str[0] == '-') { ret = -ret; } return ret; }
		public long nextLong() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); int i = 0; long ret = 0; if(str[0] == '-') { i = 1; } for(; i < len; i++) ret = ret * 10 + str[i] - '0'; if(str[0] == '-') { ret = -ret; } return ret; }
		public char nextChar() throws IOException { while(true) { final int c = read(); if(!isSpace[c]) { return (char)c; } } }
		int reads(int len, boolean[] accept) throws IOException { try { while(true) { final int c = read(); if(accept[c]) { break; } if(str.length == len) { char[] rep = new char[str.length * 3 / 2]; System.arraycopy(str, 0, rep, 0, str.length); str = rep; } str[len++] = (char)c; } } catch(EndOfFileRuntimeException e) { ; } return len; }
		int reads(char[] cs, int len, boolean[] accept) throws IOException { try { while(true) { final int c = read(); if(accept[c]) { break; } cs[len++] = (char)c; } } catch(EndOfFileRuntimeException e) { ; } return len; }
		public char[] nextLine() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isLineSep); try { if(str[len-1] == '\r') { len--; read(); } } catch(EndOfFileRuntimeException e) { ; } return Arrays.copyOf(str, len); }
		public String nextString() throws IOException { return new String(next()); }
		public char[] next() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); return Arrays.copyOf(str, len); }
//		public int next(char[] cs) throws IOException { int len = 0; cs[len++] = nextChar(); len = reads(cs, len, isSpace); return len; }
		public double nextDouble() throws IOException { return Double.parseDouble(nextString()); }
		public long[] nextLongArray(final int n) throws IOException { final long[] res = new long[n]; for(int i = 0; i < n; i++) { res[i] = nextLong(); } return res; }
		public int[] nextIntArray(final int n) throws IOException { final int[] res = new int[n]; for(int i = 0; i < n; i++) { res[i] = nextInt(); } return res; }
		public int[][] nextIntArray2D(final int n, final int k) throws IOException { final int[][] res = new int[n][]; for(int i = 0; i < n; i++) { res[i] = nextIntArray(k); } return res; }
		public int[][] nextIntArray2DWithIndex(final int n, final int k) throws IOException { final int[][] res = new int[n][k+1]; for(int i = 0; i < n; i++) { for(int j = 0; j < k; j++) { res[i][j] = nextInt(); } res[i][k] = i; } return res; }
		public double[] nextDoubleArray(final int n) throws IOException { final double[] res = new double[n]; for(int i = 0; i < n; i++) { res[i] = nextDouble(); } return res; }
	}
}