Problem: There is a weighted tree with n nodes and n-1 edges. The nodes are conveniently labeled from 1 to n. The weights are positive integers at most 100. Define the distance between two nodes to be the sum of edges on the unique path between the nodes. You would like to find the diameter of the tree. Diameter is the maximum distance between a pair of nodes.

Unfortunately, the tree isn't given to you, but you can ask some questions about it. In one question, you can specify two nonempty disjoint sets of nodes p and q, and the judge will return the maximum distance between a node in p and a node in q. In the words, maximum distance between x and y, where x ∈ p and y ∈ q. After asking not more than 9 questions, you must report the maximum distance between any pair of nodes.

Interaction

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 1 000). Description of the test cases follows.

The first line of each test case contains an integer n (2 ≤ n ≤ 100) — the number of nodes in the tree.

To ask a question, print "k_1\ k_2\ a_1\ a_2\ …\ a_{k_1}\ b_1\ b_2\ …\ b_{k_2}" (k_1, k_2 ≥ 1 and k_1+k_2 ≤ n). These two sets must be nonempty and disjoint. The judge will respond with a single integer max_{p,q} dist(a_p, b_q). If you ever get a result of -1 (because you printed an invalid query), exit immediately to avoid getting other verdicts.

After printing a query do not forget to output end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use:

  * fflush(stdout) or cout.flush() in C++;
  * System.out.flush() in Java;
  * flush(output) in Pascal;
  * stdout.flush() in Python;
  * see documentation for other languages.



When you are ready to answer, print "-1\ d", where d is the maximum shortest distance over all pairs of nodes.

You can only ask at most 9 questions per test case.

Hack Format

To hack, use the following format. Note that you can only hack with one test case.

The first line should contain a single integer t (t=1).

The second line should contain a single integer n (2 ≤ n ≤ 100).

Each of the next n-1 lines should contain three integers a_i, b_i, c_i (1≤ a_i, b_i≤ n, 1 ≤ c_i ≤ 100). This denotes an undirected edge between nodes a_i and b_i with weight c_i. These edges must form a tree.

Example

Input


2
5
9
6
10
9
10
2
99


Output


1 4 1 2 3 4 5
1 4 2 3 4 5 1
1 4 3 4 5 1 2
1 4 4 5 1 2 3
1 4 5 1 2 3 4
-1 10
1 1 1 2
-1 99

Note

In the first example, the first tree looks as follows: <image>

In the first question, we have p = {1}, and q = {2, 3, 4, 5}. The maximum distance between a node in p and a node in q is 9 (the distance between nodes 1 and 5).

The second tree is a tree with two nodes with an edge with weight 99 between them.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.File;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedHashMap;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Random;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeSet;
import java.util.stream.Collectors;

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

    /* ======================DSU===================== */
    static class dsu {
        static int parent[], n;// min[],value[];
        static long size[];

        dsu(int n) {
            parent = new int[n + 1];
            size = new long[n + 1];
            // min=new int[n+1];
            // value=new int[n+1];
            this.n = n;
            makeSet();
        }

        static void makeSet() {
            for (int i = 1; i <= n; i++) {
                parent[i] = i;
                size[i] = 1;
                // min[i]=i;
            }
        }

        static int find(int a) {
            if (parent[a] == a)
                return a;
            else {
                return parent[a] = find(parent[a]);// Path Compression
            }
        }

        static void union(int a, int b) {
            int setA = find(a);
            int setB = find(b);
            if (setA == setB)
                return;
            if (size[setA] >= size[setB]) {
                parent[setB] = setA;
                size[setA] += size[setB];
            } else {
                parent[setA] = setB;
                size[setB] += size[setA];
            }
        }
    }

    /* ======================================================== */
    static class Pair<X extends Number, Y extends Number> implements Comparator<Pair> {
        X x;
        Y y;

        // Constructor
        public Pair(X x, Y y) {
            this.x = x;
            this.y = y;
        }

        public Pair() {

        }

        @Override
        public int compare(Main.Pair o1, Main.Pair o2) {
            return ((int) (o1.y.intValue() - o2.y.intValue()));// Ascending Order based on 'y'
        }
    }

    /* ===============================Tries================================= */
    static class TrieNode {
        private HashMap<Character, TrieNode> children = new HashMap<>();
        public int size;
        boolean endOfWord;

        public void putChildIfAbsent(char ch) {
            children.putIfAbsent(ch, new TrieNode());
        }

        public TrieNode getChild(char ch) {
            return children.get(ch);
        }
    }

    static private TrieNode root;

    public static void insert(String str) {
        TrieNode curr = root;
        for (char ch : str.toCharArray()) {
            curr.putChildIfAbsent(ch);
            curr = curr.getChild(ch);
            curr.size++;
        }
        // mark the current nodes endOfWord as true
        curr.endOfWord = true;
    }

    public static int search(String word) {
        TrieNode curr = root;

        for (char ch : word.toCharArray()) {
            curr = curr.getChild(ch);
            if (curr == null) {
                return 0;
            }
        }
        // size contains words starting with prefix- word
        return curr.size;
    }

    public boolean delete(TrieNode current, String word, int index) {
        if (index == word.length()) {
            // when end of word is reached only delete if currrent.endOfWord is true.
            if (!current.endOfWord) {
                return false;
            }
            current.endOfWord = false;
            // if current has no other mapping then return true
            return current.children.size() == 0;
        }
        char ch = word.charAt(index);
        TrieNode node = current.children.get(ch);
        if (node == null) {
            return false;
        }
        boolean shouldDeleteCurrentNode = delete(node, word, index + 1);

        // if true is returned then delete the mapping of character and trienode
        // reference from map.
        if (shouldDeleteCurrentNode) {
            current.children.remove(ch);
            // return true if no mappings are left in the map.
            return current.children.size() == 0;
        }
        return false;
    }

    /* ================================================================= */
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

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

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

    static FastReader f = new FastReader();
    static BufferedWriter w = new BufferedWriter(new OutputStreamWriter(System.out));

    static boolean isPrime(long n) {
        if (n <= 1)
            return false;
        if (n <= 3)
            return true;
        if (n % 2 == 0 || n % 3 == 0)
            return false;
        for (long i = 5; i * i <= n; i = i + 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;
        return true;
    }

    static int lowerBound(int a[], int x) { // x is the target, returns lowerBound. If not found return -1
        int l = -1, r = a.length, flag = 0;
        while (l + 1 < r) {
            int m = (l + r) >>> 1;
            if (x == a[m])
                flag = 1;
            if (a[m] >= x)
                r = m;
            else
                l = m;
        }
        return r;
    }

    static int upperBound(int a[], int x, int l, int r) {// x is the target, returns upperBound. If not found return -1
        int flag = 0;
        while (l + 1 < r) {
            int m = (l + r) >>> 1;
            if (a[m] == x)
                return m;
            if (a[m] <= x) {
                l = m;
                flag = 1;
            } else
                r = m;
        }
        return l + 1;
    }

    static long gcd(long a, long b) {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }

    static long lcm(long a, long b) {
        return (a * b) / gcd(a, b);
    }

    static long power(long x, long y) {
        long res = 1;
        while (y > 0) {
            if (y % 2 == 1)
                res = (res * x);
            y >>= 1;
            x = (x * x);
        }
        return res;
    }

    public double binPow(double x, int n) {// binary exponentiation with negative power as well
        if (n == 0)
            return 1.0;
        double binPow = binPow(x, n / 2);
        if (n % 2 == 0) {
            return binPow * binPow;
        } else {
            return n > 0 ? (binPow * binPow * x) : (binPow * binPow / x);
        }
    }

    static long ceil(long x, long y) {
        return (x % y == 0 ? x / y : (x / y + 1));
    }

    /*
     * ===========Modular Operations==================
     */
    static long modPower(long x, long y, long p) {
        long res = 1;
        x = x % p;
        while (y > 0) {
            if (y % 2 == 1)
                res = (res * x) % p;
            y = y >> 1; // y = y/2
            x = (x * x) % p;
        }
        return res;
    }

    static long modInverse(long n, long p) {
        return modPower(n, p - 2, p);
    }

    static long modAdd(long a, long b) {
        return ((a + b + mod) % mod);
    }

    static long modMul(long a, long b) {
        return ((a % mod) * (b % mod)) % mod;
    }

    static long nCrModPFermat(int n, int r) {
        if (r == 0)
            return 1;
        long[] fac = new long[n + 1];
        fac[0] = 1;
        for (int i = 1; i <= n; i++)
            fac[i] = fac[i - 1] * i % mod;
        return (fac[n] * modInverse(fac[r], mod) % mod * modInverse(fac[n - r], mod) % mod) % mod;
    }

    /*
     * ===============================================
     */

    static void ruffleSort(long[] a) {
        int n = a.length;
        Random r = new Random();
        for (int i = 0; i < a.length; i++) {
            int oi = r.nextInt(n);
            long temp = a[i];
            a[i] = a[oi];
            a[oi] = temp;
        }
        Arrays.sort(a);
    }

    static void ruffleSort(int[] a) {
        int n = a.length;
        Random r = new Random();
        for (int i = 0; i < a.length; i++) {
            int oi = r.nextInt(n);
            int temp = a[i];
            a[i] = a[oi];
            a[oi] = temp;
        }
        Arrays.sort(a);
    }

    static String binString32(int n) {
        StringBuilder str = new StringBuilder("");
        String bin = Integer.toBinaryString(n);
        if (bin.length() != 32) {
            for (int k = 0; k < 32 - bin.length(); k++) {
                str.append("0");
            }
            str.append(bin);
        }
        return str.toString();
    }

    static class sparseTable {
        public static int st[][];
        public static int log = 4;

        static int func(int a, int b) {// make func as per question(here min range query)
            return (int) gcd(a, b);
        }

        void makeTable(int n, int a[]) {

            st = new int[n][log];
            for (int i = 0; i < n; i++) {
                st[i][0] = a[i];
            }
            for (int j = 1; j < log; j++) {
                for (int i = 0; i + (1 << j) <= n; i++) {
                    st[i][j] = func(st[i][j - 1], st[i + (1 << (j - 1))][j - 1]);
                }
            }
        }

        static int query(int l, int r) {
            int length = r - l + 1;
            int k = 0;
            while ((1 << (k + 1)) <= length) {
                k++;
            }
            return func(st[l][k], st[r - (1 << k) + 1][k]);
        }

        static void printTable(int n) {
            for (int j = 0; j < log; j++) {
                for (int i = 0; i < n; i++) {
                    System.out.print(st[i][j] + " ");
                }
                System.out.println();
            }
        }
    }

    /*
     * ====================================Main=================================
     */

    // static int st[], a[];

    // static void buildTree(int treeIndex, int lo, int hi) {
    // if (hi == lo) {
    // st[treeIndex] = a[lo];
    // return;
    // }
    // int mid = (lo + hi) / 2;
    // buildTree(treeIndex * 2 + 1, lo, mid);
    // buildTree(treeIndex * 2 + 2, mid + 1, hi);
    // st[treeIndex] = merge(st[treeIndex * 2 + 1], st[treeIndex * 2 + 2]);
    // }

    // static void update(int treeIndex, int lo, int hi, int arrIndex, int val) {
    // if (hi == lo) {
    // st[treeIndex] = val;
    // a[arrIndex] = val;
    // return;
    // }
    // int mid = (hi + lo) / 2;
    // if (mid < arrIndex) {
    // update(treeIndex * 2 + 2, mid + 1, hi, arrIndex, val);
    // } else {
    // update(treeIndex * 2 + 1, lo, mid, arrIndex, val);
    // }
    // st[treeIndex] = merge(st[treeIndex * 2 + 1], st[treeIndex * 2 + 2]);
    // }

    // static int query(int treeIndex, int lo, int hi, int l, int r) {
    // if (l <= lo && r >= hi) {
    // return st[treeIndex];
    // }
    // if (l > hi || r < lo) {
    // return 0;
    // }
    // int mid = (hi + lo) / 2;
    // return query(treeIndex * 2 + 1, lo, mid, l, Math.min(mid, r));
    // }

    // static int merge(int a, int b) {
    // return a + b;
    // }

    public static long findKthPositive(long[] A, long k) {
        int l = 0, r = A.length, m;
        while (l < r) {
            m = (l + r) / 2;
            if (A[m] - 1 - m < k)
                l = m + 1;
            else
                r = m;
        }
        return l + k;
    }

    static int[] z_function(char ar[]) {
        int[] z = new int[ar.length];
        z[0] = ar.length;
        int l = 0;
        int r = 0;
        for (int i = 1; i < ar.length; i++) {
            if (r < i) {
                l = i;
                r = i;
                while (r < ar.length && ar[r - l] == ar[r])
                    r++;
                z[i] = r - l;
                r--;
            } else {
                int k = i - l;
                if (z[k] < r - i + 1) {
                    z[i] = z[k];
                } else {
                    l = i;
                    while (r < ar.length && ar[r - l] == ar[r])
                        r++;
                    z[i] = r - l;
                    r--;
                }
            }
        }
        return z;
    }

    static long dp[][][];
    static ArrayList<ArrayList<Integer>> g;
    static int minTurns = Integer.MAX_VALUE, n, m;
    static int r[] = { 1, -1, 0, 0 }, c[] = { 0, 0, 1, -1 };
    static boolean vis[][][][], ok = false;
    static Pair<Integer, Integer> start = new Pair<>(), end = new Pair<>();
    static char ch[][];

    public static void main(String args[]) throws Exception {
        // File file = new File("D:\\VS Code\\Java\\Output.txt");
        // FileWriter fw = new FileWriter("D:\\VS Code\\Java\\Output.txt");
        int t = 1;
        t = f.nextInt();
        int tc = 1;
        while (t-- != 0) {
            // BufferedReader br = new BufferedReader(new FileReader("PHOBIA.INP"));
            // PrintWriter pw = new PrintWriter(new BufferedWriter(new
            // FileWriter("PHOBIA.OUT")));
            int n = f.nextInt();
            ArrayList<Integer> a=new ArrayList<>();
            ArrayList<Integer> b=new ArrayList<>();
            a.add(1);

            for(int i=2;i<=n;i++){
                b.add(i);
            }
            int maxDistFrom1=ask(1, n-1, a, b);
            int low=2,hi=n,mid=0;
            while(hi>low){
                mid=(hi+low)>>>1;
                b.clear();
                for(int i=low;i<=mid;i++){
                    b.add(i);
                }
                int dist1=ask(1, mid-low+1, a, b);
                // b.clear();
                // for(int i=mid+1;i<=hi;i++){
                //     b.add(i);
                // }
                // int dist2=ask(1, hi-mid, a, b);
                if(dist1==maxDistFrom1){
                    hi=mid;
                }else {
                    low=mid+1;
                }
            }
            a.clear();b.clear();
            a.add(hi);
            for(int i=1;i<=n;i++){
                if(i!=hi){
                    b.add(i);
                }
            }
            int diam=ask(1, n-1, a, b);
            w.write("-1 "+diam+"\n");
            w.flush();
        }
        w.flush();
    }

    public static int ask(int k1,int k2,ArrayList<Integer> a,ArrayList<Integer> b){
        System.out.print(k1+" "+k2+" ");
        for(int i:a){
            System.out.print(i+" ");
        }
        for(int i:b){
            System.out.print(i+" ");
        }
        int q=f.nextInt();
        return q;
    }
}
/*

 */