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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Mufaddal Naya
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        E1TreesAndQueries solver = new E1TreesAndQueries();
        solver.solve(1, in, out);
        out.close();
    }

    static class E1TreesAndQueries {
        ArrayList<Integer>[] adj;
        int[][] lca;
        int[] depth;

        public void solve(int testNumber, InputReader c, OutputWriter w) {
            int n = c.readInt();
            adj = new ArrayList[n];
            for (int i = 0; i < n; i++) {
                adj[i] = new ArrayList<>();
            }
            for (int i = 0; i < n - 1; i++) {
                int u = c.readInt() - 1, v = c.readInt() - 1;
                adj[u].add(v);
                adj[v].add(u);
            }
            lca = new int[n][20];
            depth = new int[n];
            dfs_(0, 0, 0);
            int q = c.readInt();
            while (q-- > 0) {
                int x = c.readInt() - 1, y = c.readInt() - 1,
                        a = c.readInt() - 1, b = c.readInt() - 1, k = c.readInt();
                int length1 = depth[a] + depth[b] - 2 * depth[lca_(a, b)];
                int length2 =
                        depth[x] + depth[a] - 2 * depth[lca_(x, a)] + depth[b] + depth[y] - 2 * depth[lca_(y, b)] + 1;
                int length3 =
                        depth[y] + depth[a] - 2 * depth[lca_(y, a)] + depth[b] + depth[x] - 2 * depth[lca_(x, b)] + 1;
//            w.printLine(length1, length2, length3);
                if (length1 <= k && (k - length1) % 2 == 0) {
                    w.printLine("YES");
                } else if (length2 <= k && (k - length2) % 2 == 0) {
                    w.printLine("YES");
                } else if (length3 <= k && (k - length3) % 2 == 0) {
                    w.printLine("YES");
                } else {
                    w.printLine("NO");
                }
            }
        }

        private int lca_(int x, int y) {
            if (depth[x] > depth[y]) {
                return lca_(y, x);
            }
            y = binaryLift(y, depth[y] - depth[x]);
            if (x == y) {
                return y;
            }

            for (int i = 19; i >= 0; i--) {
                if (lca[x][i] != lca[y][i]) {
                    x = lca[x][i];
                    y = lca[y][i];
                }
            }
            return lca[y][0];
        }

        private int binaryLift(int y, int dist) {
            for (int i = 0; i < 20; i++) {
                if ((dist & (1 << i)) > 0) {
                    y = lca[y][i];
                }
            }
            return y;
        }

        private void dfs_(int x, int p, int dist) {
            depth[x] = dist;
            lca[x][0] = p;
            for (int i = 1; i < 20; i++) {
                lca[x][i] = lca[lca[x][i - 1]][i - 1];
            }
            for (int xx : adj[x]) {
                if (xx != p) {
                    dfs_(xx, x, dist + 1);
                }
            }
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void printLine(Object... objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}

