This is an interactive problem. The only difference between the easy and hard version is the limit on number of questions.

There are n players labelled from 1 to n. It is guaranteed that n is a multiple of 3.

Among them, there are k impostors and n-k crewmates. The number of impostors, k, is not given to you. It is guaranteed that n/3 < k < 2n/3.

In each question, you can choose three distinct integers a, b, c (1 ≤ a, b, c ≤ n) and ask: "Among the players labelled a, b and c, are there more impostors or more crewmates?" You will be given the integer 0 if there are more impostors than crewmates, and 1 otherwise.

Find the number of impostors k and the indices of players that are impostors after asking at most n+6 questions.

The jury is adaptive, which means the indices of impostors may not be fixed beforehand and can depend on your questions. It is guaranteed that there is at least one set of impostors which fulfills the constraints and the answers to your questions at any time.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 100). Description of the test cases follows.

The first and only line of each test case contains a single integer n (6 ≤ n < 10^4, n is a multiple of 3) — the number of players.

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^4.

Interaction

For each test case, the interaction starts with reading n.

Then you are allowed to make at most n+6 questions in the following way:

"? a b c" (1 ≤ a, b, c ≤ n, a, b and c are pairwise distinct).

After each one, you should read an integer r, which is equal to 0 if there are more impostors than crewmates among players labelled a, b and c, and equal to 1 otherwise.

Answer -1 instead of 0 or 1 means that you made an invalid query. Exit immediately after receiving -1 and you will see Wrong answer verdict. Otherwise you can get an arbitrary verdict because your solution will continue to read from a closed stream.

When you have found the indices of all impostors, print a single line "! " (without quotes), followed by the number of impostors k, followed by k integers representing the indices of the impostors. Please note that you must print all this information on the same line. 

After printing the answer, your program must then continue to solve the remaining test cases, or exit if all test cases have been solved.

After printing the queries and answers do not forget to output end of line and flush the output buffer. Otherwise, you will get the Idleness limit exceeded verdict. To do flush use:

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



Hacks

You cannot make hacks in this problem.

Example

Input


2
6

0

1

9

1

Output


? 1 2 3

? 3 4 5

! 3 4 1 2

? 7 1 9

! 4 2 3 6 8

Note

Explanation for example interaction (note that this example only exists to demonstrate the interaction procedure and does not provide any hint for the solution):

For the first test case:

Question "? 1 2 3" returns 0, so there are more impostors than crewmates among players 1, 2 and 3.

Question "? 3 4 5" returns 1, so there are more crewmates than impostors among players 3, 4 and 5.

Outputting "! 3 4 1 2" means that one has found all the impostors, by some miracle. There are k = 3 impostors. The players who are impostors are players 4, 1 and 2.

For the second test case:

Question "? 7 1 9" returns 1, so there are more crewmates than impostors among players 7, 1 and 9.

Outputting "! 4 2 3 6 8" means that one has found all the impostors, by some miracle. There are k = 4 impostors. The players who are impostors are players 2, 3, 6 and 8.
2
6
1
9
1
 2
153
1
5250
1

8
11
 155
5252

import java.io.*;
import java.util.*;
import java.util.concurrent.ThreadLocalRandom;
import java.math.*;

/**
 __                  __
 ( _)                ( _)
 / / \\              / /\_\_
 / /   \\            / / | \ \
 / /     \\          / /  |\ \ \
 /  /   ,  \ ,       / /   /|  \ \
 /  /    |\_ /|      / /   / \   \_\
 /  /  |\/ _ '_| \   / /   /   \    \\
 |  /   |/  0 \0\    / |    |    \    \\
 |    |\|      \_\_ /  /    |     \    \\
 |  | |/    \.\ o\o)  /      \     |    \\
 \    |     /\\`v-v  /        |    |     \\
 | \/    /_| \\_|  /         |    | \    \\
 | |    /__/_ `-` /   _____  |    |  \    \\
 \|    [__]  \_/  |_________  \   |   \    ()
 /    [___] (    \         \  |\ |   |   //
 |    [___]                  |\| \|   /  |/
 /|    [____]                  \  |/\ / / ||
 (  \   [____ /     ) _\      \  \    \| | ||
 \  \  [_____|    / /     __/    \   / / //
 |   \ [_____/   / /        \    |   \/ //
 |   /  '----|   /=\____   _/    |   / //
 __ /  /        |  /   ___/  _/\    \  | ||
 (/-(/-\)       /   \  (/\/\)/  |    /  | /
 (/\/\)           /   /   //
 _________/   /    /
 \____________/    (


 @author NTUDragons-Reborn
 */

public class C{
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(in, out);
        out.close();
    }
    // main solver
    static class Task{

        double eps= 0.00000001;
        static final int MAXN = 200015;
        static final int MOD= 998244353;

        // stores smallest prime factor for every number
        static int spf[] = new int[MAXN];

        static boolean[] prime;

        Map<Integer,Set<Integer>> dp= new HashMap<>();

        // Calculating SPF (Smallest Prime Factor) for every
        // number till MAXN.
        // Time Complexity : O(nloglogn)
        public void sieve()
        {
            spf[1] = 1;
            for (int i=2; i<MAXN; i++)

                // marking smallest prime factor for every
                // number to be itself.
                spf[i] = i;

            // separately marking spf for every even
            // number as 2
            for (int i=4; i<MAXN; i+=2)
                spf[i] = 2;

            for (int i=3; i*i<MAXN; i++)
            {
                // checking if i is prime
                if (spf[i] == i)
                {
                    // marking SPF for all numbers divisible by i
                    for (int j=i*i; j<MAXN; j+=i)

                        // marking spf[j] if it is not
                        // previously marked
                        if (spf[j]==j)
                            spf[j] = i;
                }
            }
        }

        void sieveOfEratosthenes(int n)
        {
            // Create a boolean array
            // "prime[0..n]" and
            // initialize all entries
            // it as true. A value in
            // prime[i] will finally be
            // false if i is Not a
            // prime, else true.
            prime= new boolean[n + 1];
            for (int i = 0; i <= n; i++)
                prime[i] = true;
    
            for (int p = 2; p * p <= n; p++)
            {
                // If prime[p] is not changed, then it is a
                // prime
                if (prime[p] == true)
                {
                    // Update all multiples of p
                    for (int i = p * p; i <= n; i += p)
                        prime[i] = false;
                }
            }
        }

        // A O(log n) function returning primefactorization
        // by dividing by smallest prime factor at every step
        public Set<Integer> getFactorization(int x)
        {
            if(dp.containsKey(x)) return dp.get(x);
            Set<Integer> ret = new HashSet<>();
            while (x != 1)
            {
                if(spf[x]!=2) ret.add(spf[x]);
                x = x / spf[x];
            }
            dp.put(x,ret);
            return ret;
        }
        // function to find first index >= x
        public int lowerIndex(List<Integer> arr, int n, int x)
        {
            int l = 0, h = n - 1;
            while (l <= h)
            {
                int mid = (l + h) / 2;
                if (arr.get(mid) >= x)
                    h = mid - 1;
                else
                    l = mid + 1;
            }
            return l;
        }
        public int lowerIndex(int[] arr, int n, int x)
        {
            int l = 0, h = n - 1;
            while (l <= h)
            {
                int mid = (l + h) / 2;
                if (arr[mid] >= x)
                    h = mid - 1;
                else
                    l = mid + 1;
            }
            return l;
        }

        // function to find last index <= y
        public int upperIndex(List<Integer> arr, int n, int y)
        {
            int l = 0, h = n - 1;
            while (l <= h)
            {
                int mid = (l + h) / 2;
                if (arr.get(mid) <= y)
                    l = mid + 1;
                else
                    h = mid - 1;
            }
            return h;
        }
        public int upperIndex(int[] arr, int n, int y)
        {
            int l = 0, h = n - 1;
            while (l <= h)
            {
                int mid = (l + h) / 2;
                if (arr[mid] <= y)
                    l = mid + 1;
                else
                    h = mid - 1;
            }
            return h;
        }

        // function to count elements within given range
        public int countInRange(List<Integer> arr, int n, int x, int y)
        {
            // initialize result
            int count = 0;
            count = upperIndex(arr, n, y) -
                    lowerIndex(arr, n, x) + 1;
            return count;
        }

        public int add(int a, int b){
            a+=b;
            while(a>=MOD) a-=MOD;
            while(a<0) a+=MOD;
            return a;
        }

        public int mul(int a, int b){
            long res= (long)a*(long)b;
            return (int)(res%MOD);
        }

        public int power(int a, int b) {
            int ans=1;
            while(b>0){
                if((b&1)!=0) ans= mul(ans,a);
                b>>=1;
                a= mul(a,a);
            }
            return ans;
        }

        int[] fact= new int[MAXN];
        int[] inv= new int[MAXN];

        public int Ckn(int n, int k){
            if(k<0 || n<0) return 0;
            if(n<k) return 0;
            return mul(mul(fact[n],inv[k]),inv[n-k]);
        }

        public int inverse(int a){
            return power(a,MOD-2);
        }

        public void preprocess() {
            fact[0]=1;
            for(int i=1;i<MAXN;i++) fact[i]= mul(fact[i-1],i);
            inv[MAXN-1]= inverse(fact[MAXN-1]);
            for(int i=MAXN-2;i>=0;i--){
                inv[i]= mul(inv[i+1],i+1);
            }
        }

        /**
         * return VALUE of lower bound for unsorted array
         */
        public int lowerBoundNormalArray(int[] arr, int x){
            TreeSet<Integer> set= new TreeSet<>();
            for(int num: arr) set.add(num);
            return set.lower(x);
        }
        /**
         * return VALUE of upper bound for unsorted array
         */
        public int upperBoundNormalArray(int[] arr, int x){
            TreeSet<Integer> set= new TreeSet<>();
            for(int num: arr) set.add(num);
            return set.higher(x);
        }

        public void debugArr(int[] arr){
            for(int i: arr) out.print(i+" ");
            out.println();
        }

        public int rand(){
            int min=0, max= MAXN;
            int random_int = (int)Math.floor(Math.random()*(max-min+1)+min);
            return random_int;
        }
        
        public void suffleSort(int[] arr){
            shuffleArray(arr);
            Arrays.sort(arr);
        }


        public void shuffleArray(int[] ar)
        {
            // If running on Java 6 or older, use `new Random()` on RHS here
            Random rnd = ThreadLocalRandom.current();
            for (int i = ar.length - 1; i > 0; i--)
            {
            int index = rnd.nextInt(i + 1);
            // Simple swap
            int a = ar[index];
            ar[index] = ar[i];
            ar[i] = a;
            }
        }
        
        InputReader in; PrintWriter out;
        Scanner sc= new Scanner(System.in);
        CustomFileReader cin;
        int[] xor= new int[3*100000+5];
        int[] pow2= new int[1000000+1];
        public void solve(InputReader in, PrintWriter out) {
            this.in=in; this.out=out;
            // sieve();
            // pow2[0]=1;
            // for(int i=1;i<pow2.length;i++){
            //     pow2[i]= mul(pow2[i-1],2);
            // }
            int t=sc.nextInt();
            preprocess();
            // int t=in.nextInt();
            // int t= cin.nextIntArrLine()[0];
            for(int i=1;i<=t;i++) solveD(i);
        }
    
        final double pi= Math.acos(-1);
        static Point base;

        /*
        Important observation to direct finding one crew and one imposter: if result of query (a,b,c) ≠ result of query (b,c,d), since b and c are common, players a and d have different roles. Additionally,
         if result of query (a,b,c) = 1 then player a is a crewmate (and player d is an impostor), vice versa.
        */

        Map<String, Integer> lookup= new HashMap<>();
        int n;
        
        void solveD(int t) {
            n= sc.nextInt();
            int[] res= new int[n+1];
            int[] group= new int[n+1];
            int start=-1;
            int pre=-1;
            int one=-1, zero=-1;
            // n/3 queries
            for(int k=1;k<=n;k+=3){
                int ans= query(k,k+1,k+2);
                if(pre==-1) pre= ans;
                group[k]= ans;
                if(pre!=-1 && pre!=ans && start==-1){
                    start= k-3;
                }
                if(start==-1) pre= ans;
            }
            // System.out.println(start);
            for(int k=0;k<=2;k++){
                int ans= query(start+k,start+k+1, start+k+2);
                if(ans != query(start+k+1,start+k+2, start+k+3)){
                    if(ans==1){ one= start+k; zero= start+k+3;}
                    else{ zero= start+k; one= start+k+3;}
                }
                if(zero!=-1) break;
            }
            res[zero]= 0; res[one]=1;
            for(int i=1;i<=n;i+=3){
                if(group[i]==0){
                    if(i==one || i+1==one){
                        res[i]=i==one?1:0;
                        res[i+1]=1-res[i];res[i+2]=0;
                        continue;
                    }
                    int ans= query(i,i+1,one);
                    if(ans==0){
                        res[i]=0; res[i+1]=0; 
                        if(i+2!=one && i+2!=zero) res[i+2]= query(i+2,one,zero);
                    }
                    else{
                        res[i+2]=0; 
                        if(i+1!=one && i+1!=zero) res[i+1]= query(i+1,one,zero); 
                        res[i]= 1-res[i+1];
                    }
                }
                else {
                    if(i==zero || i+1==zero){
                        res[i]=i==zero?0:1;
                        res[i+1]=1-res[i];res[i+2]=1;
                        continue;
                    }
                    int ans= query(i,i+1,zero);
                    if(ans==1){
                        res[i]=1; res[i+1]=1; 
                        if(i+2!=one && i+2!=zero) res[i+2]= query(i+2,one,zero);
                    }
                    else{
                        res[i+2]=1; 
                        if(i+1!=one && i+1!=zero) res[i+1]= query(i+1,one,zero); 
                        res[i]= 1-res[i+1];
                    }
                }
            }

            List<Integer> idx= new ArrayList<>();
            for(int i=1;i<=n;i++) {
                if(res[i]==0) idx.add(i);
            }
            String ans="! ";
            ans+= idx.size()+" ";
            for(int i: idx) ans+=i+" ";
            ans= ans.trim();
            System.out.println(ans);
            System.out.flush();


            
        }
        
        int query(int a, int b, int c){
            assert (a>=1 && a<=n);
            assert (b>=1 && b<=n);
            assert (c>=1 && c<=n);
            int[] idx= new int[]{a,b,c};
            Arrays.sort(idx);
            a= idx[0]; b= idx[1]; c= idx[2];
            String s= a+"-"+b+"-"+c;
            if(lookup.containsKey(s)) return lookup.get(s);
            System.out.println("? "+a+" "+b+" "+c);
            System.out.flush();
            int ans= sc.nextInt();
            lookup.put(s,ans);
            return ans;
        }

        



        static class Node implements Comparable<Node>{
            char op;
            int s;
            public Node (char op, int s) {
                this.op= op;
                this.s= s;
            }
            @Override
            public int compareTo(Node o) {
                if (this.s==o.s) return (int)(this.op-o.op);
                return this.s-o.s;
            }

        }

        private long distance(Point p1, Point p2) {
            long x= p1.x-p2.x, y= p1.y-p2.y;
            return x*x+y*y;
        }


        private boolean eqPoint(Point p1, Point p2){
            return p1.x==p2.x && p1.y==p2.y;
        }

        private double polarAngle(Point p1, Point p2) {
            // p1 -> p2
            if (p1.x==p2.x) return pi/2;
            else if (p1.y==p2.y){
                if(p1.x<p2.x) return 0;
                else return pi;
            }
            else {
                double y= (double)p2.y-(double)p1.y;
                double x= (double)p2.x-(double)p1.x;
                BigDecimal alpha1= new BigDecimal(y);
                BigDecimal alpha2= new BigDecimal(x);
                BigDecimal val= alpha1.divide(alpha2);

                double angle= Math.atan(val.doubleValue());
                if (angle<0) angle+= pi;
                out.println("angle: "+angle);
                return angle;
            }
        }

        private boolean isRightTurn(Point p1, Point p2, Point p3){
            Vector v1= new Vector(p1,p2), v2= new Vector(p1,p3);
            if(crossProd(v1,v2)<0) return true;
            else return false;
        }

        private long crossProd(Vector v1, Vector v2){
            //x1*y2-x2*y1
            return v1.x*v2.y - v2.x*v1.y;
        }

        static class PointAngle implements Comparable<PointAngle>{
            Point p;
            double angle;
            long dis;
            public PointAngle(Point p, double angle, long dis) {
                this.p= p;
                this.angle= angle;
                this.dis= dis;

            }

            @Override
            public int compareTo(PointAngle o) {
                double dif= this.angle-o.angle;
                if (dif <0) return -1;
                else if(dif >0) return 1;
                else {
                    long dif2r= this.dis-o.dis;
                    long dif2l= o.dis-this.dis;

                    if (base.x < this.p.x) return intDif(dif2r);
                    else return intDif(dif2l); 
                    
                }
            }

            private int intDif(long a){
                if (a>0) return 1;
                else if(a<0) return -1;
                else return 0;
            }
        }


    
        
        public long _gcd(long a,  long b)
        {

            if(b == 0) {
                return a;
            }
            else {
                return _gcd(b, a % b);
            }
        }
        public long _lcm(long a, long b){
            return (a*b)/_gcd(a,b);
        }

    }


    // static class SEG {

    //     Pair[] segtree;
        
    //     public SEG(int n){
            
    //         segtree= new Pair[4*n];
    //         Arrays.fill(segtree, new Pair(-1,Long.MAX_VALUE));
    //     }
    //     // void buildTree(int l, int r, int index) {
    //     //     if (l == r) {
    //     //         segtree[index].y = a[l];
    //     //         return;
    //     //     }
    //     //     int mid = (l + r) / 2;
    //     //     buildTree(l, mid, 2 * index + 1);
    //     //     buildTree(mid + 1, r, 2 * index + 2);
    //     //     segtree[index].y = Math.min(segtree[2 * index + 1].y, segtree[2 * index + 2].y);
    //     // }
        
    //     void update(int l, int r, int index, int pos, Pair val) {
    //         if (l == r) {
    //             segtree[index] = val;
    //             return;
    //         }
    //         int mid = (l + r) / 2;
    //         if (pos <= mid) update(l, mid, 2 * index + 1, pos, val);
    //         else update(mid + 1, r, 2 * index + 2, pos, val);
    //         if(segtree[2 * index + 1].y < segtree[2 * index + 2].y){
    //             segtree[index]= segtree[2 * index + 1];
    //         }
    //         else {
    //             segtree[index]= segtree[2 * index + 2];
    //         }
    //     }
        
    //     // Pair query(int l, int r, int from, int to, int index) {
    //     //     if (from <= l && r <= to)
    //     //         return segtree[index];
    //     //     if (r < from | to < l)
    //     //         return 0;
    //     //     int mid = (l + r) / 2;
    //     //     Pair left= query(l, mid, from, to, 2 * index + 1);
    //     //     Pair right= query(mid + 1, r, from, to, 2 * index + 2);
    //     //     if(left.y < right.y) return left;
    //     //     else return right;
            
    //     // }
        
        
    // }

    static class Venice{
        public Map<Long,Long> m= new HashMap<>();
        public long base=0;
        public long totalValue=0;
        private int M= 1000000007;

        private long addMod(long a, long b){
            a+=b;
            if(a>=M) a-=M;
            return a;
        }

        public void reset(){
            m= new HashMap<>();
            base=0;
            totalValue=0;
        }
        public void update(long add){
            base= base+ add;
        }
        public void add(long key, long val){
            long newKey= key-base;
            m.put(newKey, addMod(m.getOrDefault(newKey,(long)0),val));
        }
    }



    static class Tuple implements Comparable<Tuple>{
        int x, y, z;
        public Tuple(int x, int y, int z){
            this.x= x;
            this.y= y;
            this.z=z;
        }
        @Override
        public int compareTo(Tuple o){
            return this.z-o.z;
        }
    }

    static class Point implements Comparable<Point>{
        public long x;
        public long y;
        public Point(long x, long y){
            this.x= x;
            this.y= y;
        }

        @Override
        public int compareTo(Point o) {
            if(this.y!=o.y) return (int)(this.y-o.y);
            return (int)(this.x-o.x);
        }
    }

    static class Vector {
        public long x;
        public long y;

        // p1 -> p2
        public Vector(Point p1, Point p2){
            this.x= p2.x-p1.x;
            this.y= p2.y-p1.y;
        }
    }

    static class Pair implements Comparable<Pair>{
        public int x;
        public int y;
        public Pair(int x, int y){
            this.x= x;
            this.y= y;
        }

        @Override
        public int compareTo(Pair o) {
            if(this.x!=o.x) return this.x-o.x;
            return (int)(this.y-o.y);
        }
    }

    // public static class compareL implements Comparator<Tuple>{
    //     @Override
    //     public int compare(Tuple t1, Tuple t2) {
    //         return t2.l - t1.l;
    //     }
    // }

    // fast input reader class;
    static class InputReader {
        BufferedReader br;
        StringTokenizer st;

        public InputReader(InputStream stream) {
            br = new BufferedReader(new InputStreamReader(stream));
        }

        public String nextToken() {
            while (st == null || !st.hasMoreTokens()) {
                String line = null;
                try {
                    line = br.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (line == null) {
                    return null;
                }
                st = new StringTokenizer(line);
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(nextToken());
        }
        public double nextDouble(){
            return Double.parseDouble(nextToken());
        }
        public long nextLong(){
            return Long.parseLong(nextToken());
        }
        public int[] nextIntArr(int n){
            int[] arr= new int[n];
            for(int i=0;i<n;i++) arr[i]= nextInt();
            return arr;
        }
        public long[] nextLongArr(int n){
            long[] arr= new long[n];
            for(int i=0;i<n;i++) arr[i]= nextLong();
            return arr;
        }
        public List<Integer> nextIntList(int n){
            List<Integer> arr= new ArrayList<>();
            for(int i=0;i<n;i++) arr.add(nextInt());
            return arr;
        }
        public int[][] nextIntMatArr(int n, int m){
            int[][] mat= new int[n][m];
            for(int i=0;i<n;i++) for(int j=0;j<m;j++) mat[i][j]= nextInt();
            return mat;
        }
        public List<List<Integer>> nextIntMatList(int n, int m){
            List<List<Integer>> mat= new ArrayList<>();
            for(int i=0;i<n;i++){
                List<Integer> temp= new ArrayList<>();
                for(int j=0;j<m;j++) temp.add(nextInt());
                mat.add(temp);
            }
            return mat;
        }
        public char[] nextStringCharArr(){
            return nextToken().toCharArray();
        }
    }

    static class CustomFileReader{
        String path="";
        Scanner sc;
        public CustomFileReader(String path){
            this.path=path;
            try{
                sc= new Scanner(new File(path));
            }
            catch(Exception e){}
        }
        public String nextLine(){
            return sc.nextLine();
        }
        public int[] nextIntArrLine(){
            String line= sc.nextLine();
            String[] part= line.split("[\\s+]");
            int[] res= new int[part.length];
            for(int i=0;i<res.length;i++) res[i]= Integer.parseInt(part[i]);
            return res;
        }
    }
}