Problem: Donghyun's new social network service (SNS) contains n users numbered 1, 2, …, n. Internally, their network is a tree graph, so there are n-1 direct connections between each user. Each user can reach every other users by using some sequence of direct connections. From now on, we will denote this primary network as T_1.

To prevent a possible server breakdown, Donghyun created a backup network T_2, which also connects the same n users via a tree graph. If a system breaks down, exactly one edge e ∈ T_1 becomes unusable. In this case, Donghyun will protect the edge e by picking another edge f ∈ T_2, and add it to the existing network. This new edge should make the network be connected again. 

Donghyun wants to assign a replacement edge f ∈ T_2 for as many edges e ∈ T_1 as possible. However, since the backup network T_2 is fragile, f ∈ T_2 can be assigned as the replacement edge for at most one edge in T_1. With this restriction, Donghyun wants to protect as many edges in T_1 as possible.

Formally, let E(T) be an edge set of the tree T. We consider a bipartite graph with two parts E(T_1) and E(T_2). For e ∈ E(T_1), f ∈ E(T_2), there is an edge connecting \\{e, f\} if and only if graph T_1 - \\{e\} + \\{f\} is a tree. You should find a maximum matching in this bipartite graph.

Input

The first line contains an integer n (2 ≤ n ≤ 250 000), the number of users. 

In the next n-1 lines, two integers a_i, b_i (1 ≤ a_i, b_i ≤ n) are given. Those two numbers denote the indices of the vertices connected by the corresponding edge in T_1.

In the next n-1 lines, two integers c_i, d_i (1 ≤ c_i, d_i ≤ n) are given. Those two numbers denote the indices of the vertices connected by the corresponding edge in T_2. 

It is guaranteed that both edge sets form a tree of size n.

Output

In the first line, print the number m (0 ≤ m < n), the maximum number of edges that can be protected.

In the next m lines, print four integers a_i, b_i, c_i, d_i. Those four numbers denote that the edge (a_i, b_i) in T_1 is will be replaced with an edge (c_i, d_i) in T_2.

All printed edges should belong to their respective network, and they should link to distinct edges in their respective network. If one removes an edge (a_i, b_i) from T_1 and adds edge (c_i, d_i) from T_2, the network should remain connected. The order of printing the edges or the order of vertices in each edge does not matter.

If there are several solutions, you can print any.

Examples

Input


4
1 2
2 3
4 3
1 3
2 4
1 4


Output


3
3 2 4 2
2 1 1 3
4 3 1 4


Input


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


Output


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


Input


9
7 9
2 8
2 1
7 5
4 7
2 4
9 6
3 9
1 8
4 8
2 9
9 5
7 6
1 3
4 6
5 3


Output


8
4 2 9 2
9 7 6 7
5 7 5 9
6 9 4 6
8 2 8 4
3 9 3 5
2 1 1 8
7 4 1 3

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.Arrays;
import java.io.IOException;
import java.util.ArrayList;
import java.io.UncheckedIOException;
import java.util.List;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 27);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            FNewYearAndSocialNetwork solver = new FNewYearAndSocialNetwork();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class FNewYearAndSocialNetwork {
        Node[] t1;
        Node[] t2;
        LcaOnTree lcaOnTree;
        FastOutput out;

        public void solve(int testNumber, FastInput in, FastOutput out) {
            this.out = out;

            int n = in.readInt();
            t1 = new Node[n + 1];
            t2 = new Node[n + 1];
            MultiWayIntegerStack edges = new MultiWayIntegerStack(n + 1, (n + 1) * 2);
            edges.addLast(0, 1);

            for (int i = 1; i <= n; i++) {
                t1[i] = new Node();
                t1[i].id = i;

                t2[i] = new Node();
                t2[i].id = i;
            }

            for (int i = 1; i < n; i++) {
                Node a = t1[in.readInt()];
                Node b = t1[in.readInt()];
                addEdge(a, b);
                edges.addLast(a.id, b.id);
                edges.addLast(b.id, a.id);
            }
            lcaOnTree = new LcaOnTree(edges, 0);

            for (int i = 1; i < n; i++) {
                Node a = t2[in.readInt()];
                Node b = t2[in.readInt()];
                addEdge(a, b);
            }

            out.println(n - 1);
            dfsT1(t1[1], null, 0);
            dfsT2(t2[1], null);
        }

        public void dfsT1(Node root, Edge from, int depth) {
            root.from = from;
            root.jump = new Node[20];
            root.depth = depth;
            if (root.from != null) {
                root.jump[0] = from.other(root);
                for (int i = 0; root.jump[i] != null; i++) {
                    root.jump[i + 1] = root.jump[i].jump[i];
                }
            }
            for (Edge e : root.next) {
                if (e == from) {
                    continue;
                }
                dfsT1(e.other(root), e, depth + 1);
            }
        }

        public void dfsT2(Node root, Edge from) {
            for (Edge e : root.next) {
                if (e == from) {
                    continue;
                }
                dfsT2(e.other(root), e);
            }
            for (Edge e : root.next) {
                if (e == from) {
                    continue;
                }
                Edge partner = findPartner(e.other(root), root);
                answer(partner, e);
                Node.merge(t2[partner.a.id], t2[partner.b.id]);
            }
        }

        public boolean sameComponent(Node leaf, Node x) {
            return leaf.find() == t2[x.id].find();
        }

        public Edge findPartner(Node leaf, Node p) {
            Node b = t1[lcaOnTree.lca(leaf.id, p.id)];
            Node a;
            if (sameComponent(leaf, b)) {
                a = t1[p.id];
            } else {
                a = t1[leaf.id];
            }

            for (int i = 20 - 1; i >= 0; i--) {
                if (a.jump[i] == null || a.jump[i].depth <= b.depth) {
                    continue;
                }
                boolean sameWithA;
                if (sameComponent(leaf, a)) {
                    sameWithA = sameComponent(leaf, a.jump[i]);
                } else {
                    sameWithA = !sameComponent(leaf, a.jump[i]);
                }
                if (sameWithA) {
                    a = a.jump[i];
                }
            }

            return a.from;
        }

        public void answer(Edge e1, Edge e2) {
            out.append(e1.a.id).append(' ').append(e1.b.id).append(' ')
                    .append(e2.a.id).append(' ').append(e2.b.id).println();
        }

        public void addEdge(Node a, Node b) {
            Edge e = new Edge();
            e.a = a;
            e.b = b;
            a.next.add(e);
            b.next.add(e);
        }

    }

    static interface IntegerIterator {
        boolean hasNext();

        int next();

    }

    static class LcaOnTree {
        int[] parent;
        int[] preOrder;
        int[] i;
        int[] head;
        int[] a;
        int time;

        void dfs1(MultiWayIntegerStack tree, int u, int p) {
            parent[u] = p;
            i[u] = preOrder[u] = time++;
            for (IntegerIterator iterator = tree.iterator(u); iterator.hasNext(); ) {
                int v = iterator.next();
                if (v == p) continue;
                dfs1(tree, v, u);
                if (Integer.lowestOneBit(i[u]) < Integer.lowestOneBit(i[v])) {
                    i[u] = i[v];
                }
            }
            head[i[u]] = u;
        }

        void dfs2(MultiWayIntegerStack tree, int u, int p, int up) {
            a[u] = up | Integer.lowestOneBit(i[u]);
            for (IntegerIterator iterator = tree.iterator(u); iterator.hasNext(); ) {
                int v = iterator.next();
                if (v == p) continue;
                dfs2(tree, v, u, a[u]);
            }
        }

        public LcaOnTree(MultiWayIntegerStack tree, int root) {
            int n = tree.stackNumber();
            preOrder = new int[n];
            i = new int[n];
            head = new int[n];
            a = new int[n];
            parent = new int[n];

            dfs1(tree, root, -1);
            dfs2(tree, root, -1, 0);
        }

        private int enterIntoStrip(int x, int hz) {
            if (Integer.lowestOneBit(i[x]) == hz)
                return x;
            int hw = 1 << CachedLog2.floorLog(a[x] & (hz - 1));
            return parent[head[i[x] & -hw | hw]];
        }

        public int lca(int x, int y) {
            int hb = i[x] == i[y] ? Integer.lowestOneBit(i[x]) : (1 << CachedLog2.floorLog(i[x] ^ i[y]));
            int hz = Integer.lowestOneBit(a[x] & a[y] & -hb);
            int ex = enterIntoStrip(x, hz);
            int ey = enterIntoStrip(y, hz);
            return preOrder[ex] < preOrder[ey] ? ex : ey;
        }

    }

    static class CachedLog2 {
        private static final int BITS = 16;
        private static final int LIMIT = 1 << BITS;
        private static final byte[] CACHE = new byte[LIMIT];

        static {
            int b = 0;
            for (int i = 0; i < LIMIT; i++) {
                while ((1 << (b + 1)) <= i) {
                    b++;
                }
                CACHE[i] = (byte) b;
            }
        }

        public static int floorLog(int x) {
            return x < LIMIT ? CACHE[x] : (BITS + CACHE[x >>> BITS]);
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }

    static class Edge {
        Node a;
        Node b;

        Node other(Node x) {
            return a == x ? b : a;
        }

    }

    static class Node {
        List<Edge> next = new ArrayList<>();
        int id;
        Node[] jump;
        Edge from;
        Node p = this;
        int rank = 0;
        int depth;

        public Node find() {
            return p == p.p ? p : (p = p.find());
        }

        public static void merge(Node a, Node b) {
            a = a.find();
            b = b.find();
            if (a == b) {
                return;
            }
            if (a.rank == b.rank) {
                a.rank++;
            }
            if (a.rank > b.rank) {
                b.p = a;
            } else {
                a.p = b;
            }
        }

        public String toString() {
            return "" + id;
        }

    }

    static class FastOutput implements AutoCloseable, Closeable {
        private StringBuilder cache = new StringBuilder(10 << 20);
        private final Writer os;

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            return this;
        }

        public FastOutput append(int c) {
            cache.append(c);
            return this;
        }

        public FastOutput println(int c) {
            cache.append(c).append('\n');
            return this;
        }

        public FastOutput println() {
            cache.append('\n');
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }

    static class MultiWayIntegerStack {
        private int[] values;
        private int[] next;
        private int[] heads;
        private int alloc;
        private int stackNum;

        public IntegerIterator iterator(final int queue) {
            return new IntegerIterator() {
                int ele = heads[queue];


                public boolean hasNext() {
                    return ele != 0;
                }


                public int next() {
                    int ans = values[ele];
                    ele = next[ele];
                    return ans;
                }
            };
        }

        private void doubleCapacity() {
            int newSize = Math.max(next.length + 10, next.length * 2);
            next = Arrays.copyOf(next, newSize);
            values = Arrays.copyOf(values, newSize);
        }

        public void alloc() {
            alloc++;
            if (alloc >= next.length) {
                doubleCapacity();
            }
            next[alloc] = 0;
        }

        public int stackNumber() {
            return stackNum;
        }

        public MultiWayIntegerStack(int qNum, int totalCapacity) {
            values = new int[totalCapacity + 1];
            next = new int[totalCapacity + 1];
            heads = new int[qNum];
            stackNum = qNum;
        }

        public void addLast(int qId, int x) {
            alloc();
            values[alloc] = x;
            next[alloc] = heads[qId];
            heads[qId] = alloc;
        }

        public String toString() {
            StringBuilder builder = new StringBuilder();
            for (int i = 0; i < stackNum; i++) {
                builder.append(i).append(": ");
                for (IntegerIterator iterator = iterator(i); iterator.hasNext(); ) {
                    builder.append(iterator.next()).append(",");
                }
                if (builder.charAt(builder.length() - 1) == ',') {
                    builder.setLength(builder.length() - 1);
                }
                builder.append('\n');
            }
            return builder.toString();
        }

    }
}