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.IOException;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.HashSet;
import java.util.NoSuchElementException;
import java.util.Objects;
import java.util.PriorityQueue;
import java.util.TreeSet;
import java.util.function.BiFunction;

public class Main{

	public static void main(String[] args){
		FastScanner sc = new FastScanner();
		Mathplus mp = new Mathplus();
		PrintWriter out = new PrintWriter(System.out);
		
		
		int t = sc.nextInt();
		for(int i=0;i<t;i++){
			int n = sc.nextInt();
			int max = 0;
			for(int j=0;j<=8;j++){
				int p = 0;
				int q = 0;
				for(int k=1;k<=n;k++){
					if((k>>j&1)==1){
						p++;
					}else{
						q++;
					}
				}
				if(p>0&&q>0){
					System.out.print(p+" "+q+" ");
					for(int k=1;k<=n;k++){
						if((k>>j&1)==1){
							System.out.print(k+" ");
						}
					}
					for(int k=1;k<=n;k++){
						if((k>>j&1)==0){
							System.out.print(k+" ");
						}
					}
					System.out.flush();
					int d = sc.nextInt();
					max = Math.max(max, d);
				}
			}
			System.out.println(-1 + " "+max);
		}
		
	}
	
}

class SegmentTree<T,E>{
	int N;
	BiFunction<T,T,T> f;
	BiFunction<T,E,T> g;
	T d1;
	ArrayList<T> dat;
	SegmentTree(BiFunction<T,T,T> F,BiFunction<T,E,T> G,T D1,T[] v){
		int n = v.length;
		f = F;
		g = G;
		d1 = D1;
		init(n);
		build(v);
	}
	

	void init(int n) {
		N = 1;
		while(N<n)N*=2;
		dat = new ArrayList<T>();
	}
	
	void build(T[] v) {
		for(int i=0;i<2*N;i++) {
			dat.add(d1);
		}
		for(int i=0;i<v.length;i++) {
			dat.set(N+i-1,v[i]);
		}
		for(int i=N-2;i>=0;i--) {
			dat.set(i,f.apply(dat.get(i*2+1),dat.get(i*2+2)));
		}
	}
	
	void update(int k,E a) {
		k += N-1;
		dat.set(k,g.apply(dat.get(k),a));
		while(k>0){
			k = (k-1)/2;
			dat.set(k,f.apply(dat.get(k*2+1),dat.get(k*2+2)));
		}
	}
	
	T query(int a,int b, int k, int l ,int r) {
		if(r<=a||b<=l) return d1;
		if(a<=l&&r<=b) return dat.get(k);
		T vl = query(a,b,k*2+1,l,(l+r)/2);
		T vr = query(a,b,k*2+2,(l+r)/2,r);
		return f.apply(vl, vr);
	}
	T query(int a,int b){
		return query(a,b,0,0,N);
	}
	
}
	
class LazySegmentTree<T,E> extends SegmentTree<T,E>{
	BiFunction<E,E,E> h;
	BiFunction<E,Integer,E> p = (E a,Integer b) ->{return a;};
	E d0;
	ArrayList<E> laz;
	LazySegmentTree(BiFunction<T,T,T> F,BiFunction<T,E,T> G,BiFunction<E,E,E> H,T D1,E D0,T[] v){
		super(F,G,D1,v);
		int n = v.length;
		h = H;
		d0 = D0;
		Init(n);
	}
	void build() {
		
	}
	void Init(int n){
		laz = new ArrayList<E>();
		for(int i=0;i<2*N;i++) {
			laz.add(d0);
		}
	}
	
	void eval(int len,int k) {
		if(laz.get(k).equals(d0)) return;
		if(k*2+1<N*2-1) {
			laz.set(k*2+1,h.apply(laz.get(k*2+1),laz.get(k)));
			laz.set(k*2+2,h.apply(laz.get(k*2+2),laz.get(k)));
		}
		dat.set(k,g.apply(dat.get(k), p.apply(laz.get(k), len)));
		laz.set(k,d0);
	}
	
	T update(int a,int b,E x,int k,int l,int r) {
		eval(r-l,k);
		if(r<=a||b<=l) {
			return dat.get(k);
		}
		if(a<=l&&r<=b) {
			laz.set(k,h.apply(laz.get(k),x));
			return g.apply(dat.get(k),p.apply(laz.get(k),r-l));
		}
		T vl = update(a,b,x,k*2+1,l,(l+r)/2);
		T vr = update(a,b,x,k*2+2,(l+r)/2,r);
		dat.set(k,f.apply(vl,vr));
		return dat.get(k);
		
	}
	
	T update(int a,int b,E x) {
		return update(a,b,x,0,0,N);
	}
	
	T query(int a,int b,int k,int l,int r) {
		eval(r-l,k);
		if(r<=a||b<=l) return d1;
		if(a<=l&&r<=b) return dat.get(k);
		T vl = query(a,b,k*2+1,l,(l+r)/2);
		T vr = query(a,b,k*2+2,(l+r)/2,r);
		return f.apply(vl, vr);
	}
	
	T query(int a,int b){
		return query(a,b,0,0,N);
	}
	
}
class UnionFindTree {
	int[] root;
	int[] rank;
	int[] size;
	UnionFindTree(int N){
		root = new int[N];
		rank = new int[N];
		size = new int[N];
		for(int i=0;i<N;i++){
			root[i] = i;
			size[i] = 1;
		}
	}

	public int find(int x){
		if(root[x]==x){
			return x;
		}else{
			return find(root[x]);
		}
	}

	public void unite(int x,int y){
		x = find(x);
		y = find(y);
		if(x==y){
			return;
		}else{
			if(rank[x]<rank[y]){
				root[x] = y;
				size[y] += size[x];
			}else{
				root[y] = x;
				size[x] += size[y];
				if(rank[x]==rank[y]){
					rank[x]++;
				}
			}
		}
	}

	public boolean same(int x,int y){
		return find(x)==find(y);
	}
	
}

class ParticalEternalLastingUnionFindTree extends UnionFindTree{
	int[] time;
	int now;
	ParticalEternalLastingUnionFindTree(int N){
		super(N);
		time = new int[N];
		for(int i=0;i<N;i++) {
			time[i] = 1000000007;
		}
	}
	
	public int find(int t,int i) {
		if(time[i]>t) {
			return i;
		}else {
			return find(t,root[i]);
		}
	}
	
	public void unite(int x,int y,int t) {
		now = t;
		x = find(t,x);
		y = find(t,y);
		if(x==y)return;
		if(rank[x]<rank[y]){
			root[x] = y;
			size[y] += size[x];
			time[x] = t;
		}else{
			root[y] = x;
			size[x] += size[y];
			if(rank[x]==rank[y]){
				rank[x]++;
			}
			time[y] = t;
		}
	}
	
	public int sametime(int x,int y) {
		if(find(now,x)!=find(now,y)) return -1;
		int ok = now;
		int ng = 0;
		while(ok-ng>1) {
			int mid = (ok+ng)/2;
			if(find(mid,x)==find(mid,y)) {
				ok = mid;
			}else {
				ng = mid;
			}
		}
		return ok;
	}
	
	
}
class Graph {
	ArrayList<Edge>[] list;
	int size;
	
	TreeSet<LinkEdge> Edges = new TreeSet<LinkEdge>(new LinkEdgeComparator());
	
	@SuppressWarnings("unchecked")
	Graph(int N){
		size = N;
		list = new ArrayList[N];
		for(int i=0;i<N;i++){
			list[i] = new ArrayList<Edge>();
		}
	}
	
	
	void addEdge(int a,int b){
		list[a].add(new Edge(b,1));
	}

	void addWeightedEdge(int a,int b,long c){
		list[a].add(new Edge(b,c));
	}

	void addEgdes(int[] a,int[] b){
		int size = a.length;
		for(int i=0;i<size;i++){
			list[a[i]].add(new Edge(b[i],1));
		}
	}

	void addWeighterEdges(int[] a ,int[] b ,int[] c){
		int size = a.length;
		for(int i=0;i<size;i++){
			list[a[i]].add(new Edge(b[i],c[1]));
		}
	}

	long[] bfs(int s){
		long[] L = new long[size];
		for(int i=0;i<size;i++){
			L[i] = -1;
		}
		L[s] = 0;
		ArrayDeque<Integer> Q = new ArrayDeque<Integer>();
		Q.add(s);

		while(!Q.isEmpty()){
			int v = Q.poll();
			for(Edge e:list[v]){
				int w = e.to;
				long c = e.cost;
				if(L[w]==-1){
					L[w] = L[v] + c;
					Q.add(w);
				}
			}
		}

		return L;
	}
	
	

	long[] dijkstra(int s){
		long[] L = new long[size];
		for(int i=0;i<size;i++){
			L[i] = -1;
		}
		int[] visited = new int[size];
		L[s] = 0;
		PriorityQueue<Pair> Q = new PriorityQueue<Pair>(new SampleComparator());
		Q.add(new Pair(0,s));

		while(!Q.isEmpty()){

			Pair C = Q.poll();
			if(visited[(int)C.b]==0){
				L[(int)C.b] = C.a;
				visited[(int) C.b] = 1;
				for(Edge D:list[(int) C.b]){
					Q.add(new Pair(L[(int)C.b]+D.cost,D.to));
				}
			}
		}

		return L;
	}
	long[] maxtra(int s,long l){
		long[] L = new long[size];
		for(int i=0;i<size;i++){
			L[i] = -1;
		}
		int[] visited = new int[size];
		L[s] = -1;
	;
		PriorityQueue<Pair> Q = new PriorityQueue<Pair>(new SampleComparator());
		Q.add(new Pair(l,s));

		while(!Q.isEmpty()){

			Pair C = Q.poll();
			if(visited[(int)C.b]==0){
				L[(int)C.b] = C.a;
				visited[(int) C.b] = 1;
				for(Edge D:list[(int) C.b]){
					Q.add(new Pair(Math.max(L[(int)C.b],D.cost),D.to));
				}
			}
		}

		return L;
	}
	long Kruskal(){
		long ans = 0;
		for(int i=0;i<size;i++) {
			for(Edge e:list[i]) {
				Edges.add(new LinkEdge(e.cost,i,e.to));
			}
		}
		UnionFindTree UF = new UnionFindTree(size);
		for(LinkEdge e:Edges){
			if(e.a>=0&&e.b>=0) {
				if(!UF.same(e.a,e.b)){
					ans += e.L;
					UF.unite(e.a,e.b);
				}
			}
		}

		return ans;
	}
	
	ArrayList<Integer> Kahntsort(){

		ArrayList<Integer> ans = new ArrayList<Integer>();
		PriorityQueue<Integer> q = new PriorityQueue<Integer>();
		int[] in = new int[size];
		for(int i=0;i<size;i++) {
			for(Edge e:list[i]) {
				in[e.to]++;
			}
		}
		for(int i=0;i<size;i++) {
			if(in[i]==0) {
				q.add(i);
			}
		}
		while(!q.isEmpty()) {
			int v = q.poll();
			ans.add(v);
			for(Edge e:list[v]) {
				in[e.to]--;
				if(in[e.to]==0) {
					q.add(e.to);
				}
			}
		}
		for(int i=0;i<size;i++) {
			if(in[i]>0)return new ArrayList<Integer>();
		}
		return ans;
	}
	
	RootedTree dfsTree(int i) {
		int[] used = new int[size];
		RootedTree r = new RootedTree(size);
		dfsTree(i,used,r);
		return r;
		
	}


	private void dfsTree(int i, int[] used, RootedTree r) {
		used[i] = 1;
		for(Edge e:list[i]) {
			if(used[e.to]==0) {
				r.list[i].add(e);
				used[e.to] = 1;
				dfsTree(i,used,r);
			}
		}
		
	}
}


class Tree extends Graph{
	
	public Tree(int N) {
		super(N);
	}
	
	long[] tyokkei(){
		long[] a = bfs(0);
		
		System.out.println();
		int maxdex = -1;
		long max = 0;
		for(int i=0;i<size;i++){
			if(max<a[i]){
				max = a[i];
				maxdex = i;
			}
		}
 
		long[] b = bfs(maxdex);
		System.out.println();
		int maxdex2 = -1;
		long max2 = 0;
		for(int i=0;i<size;i++){
			if(max2<b[i]){
				max2 = b[i];
				maxdex2 = i;
			}
		}
		long[] ans = {max2,maxdex,maxdex2};
		return ans;
	}
 
}

class RootedTree extends Graph{
	
	RootedTree(int N){
		super(N);
	}
	
}
class LinkEdge{
	long L;
	int a ;
	int b;
	LinkEdge(long l,int A,int B){
		L = l;
		a = A;
		b = B;
	}
	public boolean equals(Object o){
		LinkEdge O = (LinkEdge) o;
		if(O.a==this.a&&O.b==this.b&&O.L==this.L){
			return true;
		}else{
			return false;
		}


	}

	public int hashCode(){
		return Objects.hash(L,a,b);
	}

}

class Edge{
	int to;
	long cost;

	Edge(int a,long b){
		to = a;
		cost = b;
	}

}
class LinkEdgeComparator implements Comparator<LinkEdge>{
	public int compare(LinkEdge P, LinkEdge Q) {
		long temp = P.L-Q.L;
		if(temp==0){
			if(P.a>Q.a){
				return 1;
			}else{
				if(P.b>Q.b){
					return 1;
				}else{
					return -1;
				}
			}

		}
		if(temp>=0){
			return 1;
		}else{
			return -1;
		}
	}

}
class Pair{
	long a;
	long b;

	Pair(long p,long q){
		this.a = p;
		this.b = q;
	}

	public boolean equals(Object o){
		Pair O = (Pair) o;
		if(O.a==this.a&&O.b==this.b){
			return true;
		}else{
			return false;
		}


	}

	public int hashCode(){
		return Objects.hash(a,b);
	}

}

class SampleComparator implements Comparator<Pair>{
	public int compare(Pair P, Pair Q) {
		long temp = P.a-Q.a;
		if(temp==0){
			if(P.b>Q.b){
				return 1;
			}else{
				return -1;
			}

		}
		if(temp>=0){
			return 1;
		}else{
			return -1;
		}
	}

}

class LongIntPair{
	long a;
	int b;

	LongIntPair(long p,int q){
		this.a = p;
		this.b = q;
	}

	public boolean equals(Object o){
		Pair O = (Pair) o;
		if(O.a==this.a&&O.b==this.b){
			return true;
		}else{
			return false;
		}


	}

	public int hashCode(){
		return Objects.hash(a,b);
	}

}

class LongIntSampleComparator implements Comparator<LongIntPair>{
	public int compare(LongIntPair P, LongIntPair Q) {
		long temp = P.a-Q.a;
		if(temp==0){
			if(P.b>Q.b){
				return 1;
			}else{
				return -1;
			}

		}
		if(temp>=0){
			return 1;
		}else{
			return -1;
		}
	}

}

class FastScanner {
    private final java.io.InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    private void skipUnprintable() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;}
    public boolean hasNext() { skipUnprintable(); return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return (minus ? -n : n);
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return (int) (minus ? -n : n);
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
}

class Mathplus{
	int mod = 1000000007;
	long[] fac = new long[1000001];
	long[][] combt = new long[2001][2001];
	long[][] permt = new long[2001][2001];
	boolean isBuild = false;
	boolean isBuildc = false;
	boolean isBuildp = false;
	int mindex = -1;
	int maxdex = -1;


	void buildFac(){
		fac[0] = 1;
		for(int i=1;i<=1000000;i++){
			fac[i] = (fac[i-1] * i)%mod;
		}
		isBuild = true;
	}
	
	void buildComb() {
		for(int i=0;i<=2000;i++) {
			combt[i][0] = 1;
		}
		for(int j=1;j<=2000;j++) {
			combt[j][j] = 1;
			for(int i=j+1;i<=2000;i++) {
				combt[i][j] = combt[i-1][j-1] + combt[i-1][j];
				if(combt[i][j]>=mod)combt[i][j]-=mod;
			}
			
		}
		isBuildc = false;
	}
	
	void buildPerm() {
		for(int i=0;i<=2000;i++) {
			permt[i][0] = 1;
		}
		if(!isBuild)buildFac();
		for(int i=1;i<=2000;i++) {
			for(int j=1;j<=i;j++) {
				permt[i][j] = permt[i][j-1]*(i-j+1);
				permt[i][j] %= mod;
			}
		}
		isBuildp = true;
	}
	
	
	
	public int isBigger(int[] d, int i) {
		int ok = d.length;
		int ng = -1;
		while(Math.abs(ok-ng)>1) {
			int mid = (ok+ng)/2;
			if(d[mid]>i) {
				ok = mid;
			}else {
				ng = mid;
			}
		}
		return ok;
	}
	
	public int isSmaller(int[] d, int i) {
		int ok = -1;
		int ng = d.length;
		while(Math.abs(ok-ng)>1) {
			int mid = (ok+ng)/2;
			if(d[mid]<i) {
				ok = mid;
			}else {
				ng = mid;
			}
		}
		return ok;
	}

	public HashSet<Integer> primetable(int m) {
		HashSet<Integer> pt = new HashSet<Integer>();
		for(int i=2;i<=m;i++) {
			boolean b = true;
			for(int d:pt) {
				if(i%d==0) {
					b = false;
					break;
				}
			}
			if(b) {
				pt.add(i);
			}
		}
		return pt;
	}

	long max(long[] a){
		long max = 0;
		for(int i=0;i<a.length;i++){
			if(max<a[i]){
				max =a[i];
				maxdex = i;
			}
		}
		return max;
	}
	int max(int[] a){
		int max = 0;
		for(int i=0;i<a.length;i++){
			if(max<a[i]){
				max =a[i];
				maxdex = i;
			}
		}
		return max;
	}
	long min(long[] a){
		long min = Long.MAX_VALUE;
		for(int i=0;i<a.length;i++){
			if(min>a[i]){
				min =a[i];
				mindex = i;
			}
		}
		return min;
	}
	int min(int[] a){
		int min = Integer.MAX_VALUE;
		for(int i=0;i<a.length;i++){
			if(min>a[i]){
				min =a[i];
				mindex = i;
			}
		}
		return min;
	}
	long sum(long[] a){
		long sum = 0;
		for(int i=0;i<a.length;i++){
			sum += a[i];
		}
		return sum;
	}
	long sum(int[] a){
		long sum = 0;
		for(int i=0;i<a.length;i++){
			sum += a[i];
		}
		return sum;
	}

	long gcd(long a, long b){
		if(a<b){
			a^=b;
			b^=a;
			a^=b;
		}
		if(a%b==0){
			return b;
		}else{
			return gcd(b,a%b);
		}
	}

	long lcm(long a, long b){
		return a / gcd(a,b) * b;
	}
	
	public long perm(int a,int num) {
		if(a<2000&&num<2000) {
			if(!isBuildp) {
				buildPerm();
				isBuildp = true;
 			}
			return permt[a][num];
		}
		if(!isBuild) {
			buildFac();
		}
		return fac[a] * (rev(fac[a-num]))%mod;
	}
	public long comb(int a,int num){
		if(a<2000&&num<2000) {
			if(!isBuildc) {
				buildComb();
				isBuildc = true;
 			}
			return combt[a][num];
		}
		if(!isBuild){
			buildFac();
		}
		return fac[a] * (rev(fac[num])*rev(fac[a-num])%mod)%mod;
	}

	long rev(long l) {
		return pow(l,mod-2);
	}
	
	long pow(long l, int i) {
		if(i==0){
			return 1;
		}else{
			if(i%2==0){
				long val = pow(l,i/2);
				return val * val % mod;
			}else{
				return pow(l,i-1) * l % mod;
			}
		}
	}


}