Gildong was hiking a mountain, walking by millions of trees. Inspired by them, he suddenly came up with an interesting idea for trees in data structures: What if we add another edge in a tree?

Then he found that such tree-like graphs are called 1-trees. Since Gildong was bored of solving too many tree problems, he wanted to see if similar techniques in trees can be used in 1-trees as well. Instead of solving it by himself, he's going to test you by providing queries on 1-trees.

First, he'll provide you a tree (not 1-tree) with n vertices, then he will ask you q queries. Each query contains 5 integers: x, y, a, b, and k. This means you're asked to determine if there exists a path from vertex a to b that contains exactly k edges after adding a bidirectional edge between vertices x and y. A path can contain the same vertices and same edges multiple times. All queries are independent of each other; i.e. the added edge in a query is removed in the next query.

Input

The first line contains an integer n (3 ≤ n ≤ 10^5), the number of vertices of the tree.

Next n-1 lines contain two integers u and v (1 ≤ u,v ≤ n, u ≠ v) each, which means there is an edge between vertex u and v. All edges are bidirectional and distinct.

Next line contains an integer q (1 ≤ q ≤ 10^5), the number of queries Gildong wants to ask.

Next q lines contain five integers x, y, a, b, and k each (1 ≤ x,y,a,b ≤ n, x ≠ y, 1 ≤ k ≤ 10^9) – the integers explained in the description. It is guaranteed that the edge between x and y does not exist in the original tree.

Output

For each query, print "YES" if there exists a path that contains exactly k edges from vertex a to b after adding an edge between vertices x and y. Otherwise, print "NO".

You can print each letter in any case (upper or lower).

Example

Input


5
1 2
2 3
3 4
4 5
5
1 3 1 2 2
1 4 1 3 2
1 4 1 3 3
4 2 3 3 9
5 2 3 3 9


Output


YES
YES
NO
YES
NO

Note

The image below describes the tree (circles and solid lines) and the added edges for each query (dotted lines).

<image>

Possible paths for the queries with "YES" answers are: 

  * 1-st query: 1 – 3 – 2 
  * 2-nd query: 1 – 2 – 3 
  * 4-th query: 3 – 4 – 2 – 3 – 4 – 2 – 3 – 4 – 2 – 3 
import java.io.*;
import java.util.*;

public class E implements Runnable {
	boolean judge = false;
	FastReader scn;
	PrintWriter out;
	String INPUT = "";

	void solve() {
		int n = scn.nextInt();
		int[] from = new int[n - 1], to = new int[n - 1];
		for (int i = 0; i < n - 1; i++) {
			from[i] = scn.nextInt() - 1;
			to[i] = scn.nextInt() - 1;
		}
		int[][] g = packU(n, from, to);

		int[][] parents3 = parents3(g, 0);
		int[] par = parents3[0], depth = parents3[2];

		int[][] sparse = logstepParents(par);

		int q = scn.nextInt();
		while (q-- > 0) {
			int x = scn.nextInt() - 1, y = scn.nextInt() - 1;
			int a = scn.nextInt() - 1, b = scn.nextInt() - 1;
			int k = scn.nextInt();
			
			int lcaAB = lca2(a, b, sparse, depth);
			int disAB = depth[a] + depth[b] - 2 * depth[lcaAB];
			
			if(k >= disAB && k % 2 == disAB % 2) {
				out.println("YES");
				continue;
			}
			
			int lcaXY = lca2(x, y, sparse, depth);
			int disXY = depth[x] + depth[y] - 2 * depth[lcaXY];
			
			int lcaAX = lca2(a, x, sparse, depth);
			int lcaAY = lca2(a, y, sparse, depth);
			
			int lcaBX = lca2(b, x, sparse, depth);
			int lcaBY = lca2(b, y, sparse, depth);
			
			int dAX = depth[a] + depth[x] - 2 * depth[lcaAX];
			int dAY = depth[a] + depth[y] - 2 * depth[lcaAY];
			int dBX = depth[b] + depth[x] - 2 * depth[lcaBX];
			int dBY = depth[b] + depth[y] - 2 * depth[lcaBY];
			
			int dAB = Math.min(dAX + dBY, dAY + dBX) + 1;
			
			if(k >= dAB && k % 2 == dAB % 2) {
				out.println("YES");
				continue;
			} else {
				out.println("NO");
			}
		}
	}

	int lca2(int a, int b, int[][] sparse, int[] depth) {
		if (depth[a] < depth[b]) {
			b = ancestor(b, depth[b] - depth[a], sparse);
		} else if (depth[a] > depth[b]) {
			a = ancestor(a, depth[a] - depth[b], sparse);
		}
		if (a == b) {
			return a;
		}
		int sa = a, sb = b;
		for (int low = 0, high = depth[a], t = Integer.highestOneBit(high), k = Integer
				.numberOfTrailingZeros(t); t > 0; t >>>= 1, k--) {
			if ((low ^ high) >= t) {
				if (sparse[k][sa] != sparse[k][sb]) {
					low |= t;
					sa = sparse[k][sa];
					sb = sparse[k][sb];
				} else {
					high = low | t - 1;
				}
			}
		}
		return sparse[0][sa];
	}

	int ancestor(int u, int dep, int[][] sparse) {
		for (int i = 0; dep > 0 && u != -1; dep >>>= 1, i++) {
			if ((dep & 1) == 1)
				u = sparse[i][u];
		}
		return u;
	}

	int[][] logstepParents(int[] parent) {
		int n = parent.length;
		int m = Integer.numberOfTrailingZeros(Integer.highestOneBit(n - 1)) + 1;
		int[][] sparse = new int[m][n];
		sparse[0] = parent;
		for (int j = 1; j < m; j++) {
			for (int i = 0; i < n; i++) {
				sparse[j][i] = sparse[j - 1][i] == -1 ? -1 : sparse[j - 1][sparse[j - 1][i]];
			}
		}
		return sparse;
	}

	int[][] parents3(int[][] g, int root) {
		int n = g.length;
		int[] par = new int[n];
		Arrays.fill(par, -1);

		int[] depth = new int[n];
		depth[0] = 0;

		int[] q = new int[n];
		q[0] = root;
		for (int p = 0, r = 1; p < r; p++) {
			int cur = q[p];
			for (int nex : g[cur]) {
				if (par[cur] != nex) {
					q[r++] = nex;
					par[nex] = cur;
					depth[nex] = depth[cur] + 1;
				}
			}
		}
		return new int[][] { par, q, depth };
	}

	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;
	}

	public void run() {
		long time = System.currentTimeMillis();
		boolean oj = System.getProperty("ONLINE_JUDGE") != null || judge;
		out = new PrintWriter(System.out);
		scn = new FastReader(oj);
		solve();
		out.flush();
		if (!oj) {
			System.out.println(Arrays.deepToString(new Object[] { System.currentTimeMillis() - time + " ms" }));
		}
	}

	public static void main(String[] args) {
		new Thread(null, new E(), "Main", 1 << 26).start();
	}

	class FastReader {
		InputStream is;

		public FastReader(boolean onlineJudge) {
			is = onlineJudge ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		}

		byte[] inbuf = new byte[1024];
		public int lenbuf = 0, ptrbuf = 0;

		int readByte() {
			if (lenbuf == -1)
				throw new InputMismatchException();
			if (ptrbuf >= lenbuf) {
				ptrbuf = 0;
				try {
					lenbuf = is.read(inbuf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return -1;
			}
			return inbuf[ptrbuf++];
		}

		boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}

		int skip() {
			int b;
			while ((b = readByte()) != -1 && isSpaceChar(b))
				;
			return b;
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		char nextChar() {
			return (char) skip();
		}

		String next() {
			int b = skip();
			StringBuilder sb = new StringBuilder();
			while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}

		String nextLine() {
			int b = skip();
			StringBuilder sb = new StringBuilder();
			while ((!isSpaceChar(b) || b == ' ')) { // when nextLine, (isSpaceChar(b) && b != ' ')
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}

		char[] next(int n) {
			char[] buf = new char[n];
			int b = skip(), p = 0;
			while (p < n && !(isSpaceChar(b))) {
				buf[p++] = (char) b;
				b = readByte();
			}
			return n == p ? buf : Arrays.copyOf(buf, p);
		}

		int nextInt() {
			int num = 0, b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}

			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}

		long nextLong() {
			long num = 0;
			int b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}

			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}

		char[][] nextMatrix(int n, int m) {
			char[][] map = new char[n][];
			for (int i = 0; i < n; i++)
				map[i] = next(m);
			return map;
		}

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

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

		int[][] next2DInt(int n, int m) {
			int[][] arr = new int[n][];
			for (int i = 0; i < n; i++) {
				arr[i] = nextIntArray(m);
			}
			return arr;
		}

		long[][] next2DLong(int n, int m) {
			long[][] arr = new long[n][];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLongArray(m);
			}
			return arr;
		}

		int[] shuffle(int[] arr) {
			Random r = new Random();
			for (int i = 1, j; i < arr.length; i++) {
				j = r.nextInt(i);
				int c = arr[i];
				arr[i] = arr[j];
				arr[j] = c;
			}
			return arr;
		}

		long[] shuffle(long[] arr) {
			Random r = new Random();
			for (int i = 1, j; i < arr.length; i++) {
				j = r.nextInt(i);
				long c = arr[i];
				arr[i] = arr[j];
				arr[j] = c;
			}
			return arr;
		}

		int[] uniq(int[] arr) {
			arr = scn.shuffle(arr);
			Arrays.sort(arr);
			int[] rv = new int[arr.length];
			int pos = 0;
			rv[pos++] = arr[0];
			for (int i = 1; i < arr.length; i++) {
				if (arr[i] != arr[i - 1]) {
					rv[pos++] = arr[i];
				}
			}
			return Arrays.copyOf(rv, pos);
		}

		long[] uniq(long[] arr) {
			arr = scn.shuffle(arr);
			Arrays.sort(arr);
			long[] rv = new long[arr.length];
			int pos = 0;
			rv[pos++] = arr[0];
			for (int i = 1; i < arr.length; i++) {
				if (arr[i] != arr[i - 1]) {
					rv[pos++] = arr[i];
				}
			}
			return Arrays.copyOf(rv, pos);
		}

		int[] reverse(int[] arr) {
			int l = 0, r = arr.length - 1;
			while (l < r) {
				arr[l] = arr[l] ^ arr[r];
				arr[r] = arr[l] ^ arr[r];
				arr[l] = arr[l] ^ arr[r];
				l++;
				r--;
			}
			return arr;
		}

		long[] reverse(long[] arr) {
			int l = 0, r = arr.length - 1;
			while (l < r) {
				arr[l] = arr[l] ^ arr[r];
				arr[r] = arr[l] ^ arr[r];
				arr[l] = arr[l] ^ arr[r];
				l++;
				r--;
			}
			return arr;
		}

		int[] compress(int[] arr) {
			int n = arr.length;
			int[] rv = Arrays.copyOf(arr, n);
			rv = uniq(rv);
			for (int i = 0; i < n; i++) {
				arr[i] = Arrays.binarySearch(rv, arr[i]);
			}
			return arr;
		}

		long[] compress(long[] arr) {
			int n = arr.length;
			long[] rv = Arrays.copyOf(arr, n);
			rv = uniq(rv);
			for (int i = 0; i < n; i++) {
				arr[i] = Arrays.binarySearch(rv, arr[i]);
			}
			return arr;
		}
	}
}