Problem: Fishing Prince loves trees, and he especially loves trees with only one centroid. The tree is a connected graph without cycles.

A vertex is a centroid of a tree only when you cut this vertex (remove it and remove all edges from this vertex), the size of the largest connected component of the remaining graph is the smallest possible.

For example, the centroid of the following tree is 2, because when you cut it, the size of the largest connected component of the remaining graph is 2 and it can't be smaller.

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However, in some trees, there might be more than one centroid, for example:

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Both vertex 1 and vertex 2 are centroids because the size of the largest connected component is 3 after cutting each of them.

Now Fishing Prince has a tree. He should cut one edge of the tree (it means to remove the edge). After that, he should add one edge. The resulting graph after these two operations should be a tree. He can add the edge that he cut.

He wants the centroid of the resulting tree to be unique. Help him and find any possible way to make the operations. It can be proved, that at least one such way always exists.

Input

The input consists of multiple test cases. The first line contains an integer t (1≤ t≤ 10^4) — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer n (3≤ n≤ 10^5) — the number of vertices.

Each of the next n-1 lines contains two integers x, y (1≤ x,y≤ n). It means, that there exists an edge connecting vertices x and y.

It's guaranteed that the given graph is a tree.

It's guaranteed that the sum of n for all test cases does not exceed 10^5.

Output

For each test case, print two lines.

In the first line print two integers x_1, y_1 (1 ≤ x_1, y_1 ≤ n), which means you cut the edge between vertices x_1 and y_1. There should exist edge connecting vertices x_1 and y_1.

In the second line print two integers x_2, y_2 (1 ≤ x_2, y_2 ≤ n), which means you add the edge between vertices x_2 and y_2.

The graph after these two operations should be a tree.

If there are multiple solutions you can print any.

Example

Input


2
5
1 2
1 3
2 4
2 5
6
1 2
1 3
1 4
2 5
2 6


Output


1 2
1 2
1 3
2 3

Note

Note that you can add the same edge that you cut.

In the first test case, after cutting and adding the same edge, the vertex 2 is still the only centroid.

In the second test case, the vertex 2 becomes the only centroid after cutting the edge between vertices 1 and 3 and adding the edge between vertices 2 and 3.

Solution (in JAVA):

Solution:
// package cf.cf1406;

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.util.function.IntConsumer;

public class CFC {
    private static final String INPUT = "2\n" +
            "5\n" +
            "1 2\n" +
            "1 3\n" +
            "2 4\n" +
            "2 5\n" +
            "6\n" +
            "1 2\n" +
            "1 3\n" +
            "1 4\n" +
            "2 5\n" +
            "2 6\n";
    private static final int MOD = 1_000_000_007;

    FastScanner sc;
    PrintWriter out;

    public static void main(String[] args) {
        new CFC().run();
    }

    public CFC() {
        sc = new FastScanner(oj ? System.in : new ByteArrayInputStream(INPUT.getBytes()));
        out = new PrintWriter(System.out);
    }

    public void run() {
        long start = System.currentTimeMillis();
        times(sc.nextInt(), this::solve);
        out.flush();
        tr(System.currentTimeMillis() - start + "ms");
    }

    static class Node {
        int n;
        int cv = -1;
        List<Edge> edges = new ArrayList<>();

        public Node(int n) {
            this.n = n;
        }

        @Override
        public String toString() {
            return "Node{" +
                    "n=" + n +
                    '}';
        }
    }

    static class Edge {
        int power = -1;
        Node node;

        public Edge(Node node) {
            this.node = node;
        }
    }

    int n;
    public void solve(int time) {
        n = sc.nextInt();
        Node[] nodes = new Node[n+1];
        for (int i = 1; i <= n; i++) {
            nodes[i] = new Node(i);
        }
        for (int i = 1; i < n; i++) {
            Node n1 = nodes[sc.nextInt()];
            Node n2 = nodes[sc.nextInt()];
            n1.edges.add(new Edge(n2));
            n2.edges.add(new Edge(n1));
        }

        dfs(nodes[1], null);
        int cv = Integer.MAX_VALUE;
        List<Node> cvs = new ArrayList<>();
        for (int i = 1; i <= n; i++) {
            Node node = nodes[i];
            node.cv = node.edges.stream().mapToInt(edge -> edge.power).max().orElse(0);
            if (node.cv < cv) {
                cvs.clear();
                cv = node.cv;
            }
            if (node.cv == cv) {
                cvs.add(node);
            }
        }

        if (cvs.size() == 1) {
            Node node = cvs.get(0);
            Edge edge = node.edges.get(0);
            writeln(node.n + " " + edge.node.n);
            writeln(node.n + " " + edge.node.n);
        } else {
            Node node = cvs.get(0);
            Node node2 = cvs.get(1);
            Edge edge = node2.edges.stream().filter(e -> e.power < node.cv).findAny().orElse(null);
            writeln(node2.n + " " + edge.node.n);
            writeln(node.n + " " + edge.node.n);
        }
    }

    private int dfs(Node root, Node bnode) {
        int power = 1;
        Edge back = null;
        for (Edge edge : root.edges) {
            if (edge.node == bnode) {
                back = edge;
            } else {
                int cpower = dfs(edge.node, root);
                edge.power = cpower;
                power += cpower;
            }
        }

        if (back != null) back.power = n - power;
        return power;
    }


    //---------------------------------------------------------------------------------------------------

    /**
     * If searched element doesn't exist, returns index of first element which is bigger than searched value.<br>
     * If searched element is bigger than any array element function returns first index after last element.<br>
     * If searched element is lower than any array element function returns index of first element.<br>
     * If there are many values equals searched value function returns first occurrence.<br>
     */
    private static int lowerBound(long[] arr, long key) {
        int lo = 0;
        int hi = arr.length - 1;
        while (lo < hi) {
            int mid = (lo + hi) / 2;
            if (key <= arr[mid]) {
                hi = mid - 1;
            } else {
                lo = mid + 1;
            }
        }
        return arr[lo] < key ? lo + 1 : lo;
    }

    /**
     * Returns index of first element which is grater than searched value.
     * If searched element is bigger than any array element, returns first index after last element.
     */
    private static int upperBound(long[] arr, long key) {
        int lo = 0;
        int hi = arr.length - 1;
        while (lo < hi) {
            int mid = (lo + hi) / 2;
            if (key >= arr[mid]) {
                lo = mid + 1;
            } else {
                hi = mid;
            }
        }
        return arr[lo] <= key ? lo + 1 : lo;
    }

    private long[] prefixSum(long[] array) {
        long[] result = new long[array.length];
        result[0] = array[0];
        for (int i = 1; i < array.length; i++) result[i] = result[i - 1] + array[i];
        return result;
    }

    private int[] sort(int[] array) {
        shuffle(array);
        Arrays.sort(array);
        return array;
    }

    private static void shuffle(int[] array) {
        Random random = new Random();
        for (int i = array.length - 1; i > 0; i--) {
            int index = random.nextInt(i + 1);
            {
                int tmp = array[index];
                array[index] = array[i];
                array[i] = tmp;
            }
        }
    }

    private long[] sort(long[] array) {
        shuffle(array);
        Arrays.sort(array);
        return array;
    }

    private static void shuffle(long[] array) {
        Random random = new Random();
        for (int i = array.length - 1; i > 0; i--) {
            int index = random.nextInt(i + 1);
            {
                long tmp = array[index];
                array[index] = array[i];
                array[i] = tmp;
            }
        }
    }

    static class ExitException extends RuntimeException {
    }

    private int iread() {
        int res = sc.nextInt();
        if (res <= 0) {
            throw new ExitException();
        }
        return res;
    }

    private void iwrite(char[] chars) {
        for (char chr : chars) {
            out.print(chr);
        }
        out.println();
        out.flush();
    }

    private void write(Object obj) {
        out.print(obj);
    }

    private void writeln(Object obj) {
        out.println(obj);
    }

    private void writeln() {
        out.println();
    }

    private void answer(Object ans) {
        out.println(ans);
        throw new ExitException();
    }

    private void times(int n, IntConsumer consumer) {
        for (int i = 0; i < n; i++) {
            try {
                consumer.accept(i);
            } catch (ExitException ignored) {
            }
        }
    }

    private int[] readIntArray(int n) {
        int[] res = new int[n];
        for (int i = 0; i < n; i++) {
            res[i] = sc.nextInt();
        }
        return res;
    }

    private long[] readLongArray(int n) {
        long[] res = new long[n];
        for (int i = 0; i < n; i++) {
            res[i] = sc.nextLong();
        }
        return res;
    }

    static class FastScanner {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        FastScanner(InputStream stream) {
            this.stream = stream;
        }

        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++];
        }

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

        boolean isEndline(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

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

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

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

        public String next() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public String nextLine() {
            int c = read();
            while (isEndline(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndline(c));
            return res.toString();
        }

    }

    private boolean oj = System.getProperty("ONLINE_JUDGE") != null;

    private void tr(Object... o) {
        if (!oj) System.out.println(Arrays.deepToString(o));
    }
}