Problem: This is an interactive problem!

Nastia has a hidden permutation p of length n consisting of integers from 1 to n. You, for some reason, want to figure out the permutation. To do that, you can give her an integer t (1 ≤ t ≤ 2), two different indices i and j (1 ≤ i, j ≤ n, i ≠ j), and an integer x (1 ≤ x ≤ n - 1). 

Depending on t, she will answer: 

  * t = 1: max{(min{(x, p_i)}, min{(x + 1, p_j)})}; 
  * t = 2: min{(max{(x, p_i)}, max{(x + 1, p_j)})}. 



You can ask Nastia at most ⌊ \frac {3 ⋅ n} { 2} ⌋ + 30 times. It is guaranteed that she will not change her permutation depending on your queries. Can you guess the permutation?

Input

The input consists of several test cases. In the beginning, you receive the integer T (1 ≤ T ≤ 10 000) — the number of test cases.

At the beginning of each test case, you receive an integer n (3 ≤ n ≤ 10^4) — the length of the permutation p.

It's guaranteed that the permutation is fixed beforehand and that the sum of n in one test doesn't exceed 2 ⋅ 10^4.

Interaction

To ask a question, print "? t i j x" (t = 1 or t = 2, 1 ≤ i, j ≤ n, i ≠ j, 1 ≤ x ≤ n - 1) Then, you should read the answer.

If we answer with −1 instead of a valid answer, that means you exceeded the number of queries or made an invalid query. Exit immediately after receiving −1 and you will see the Wrong Answer verdict. Otherwise, you can get an arbitrary verdict because your solution will continue to read from a closed stream.

To print the answer, print "! p_1 p_2 … p_{n} (without quotes). Note that answering doesn't count as one of the ⌊ \frac {3 ⋅ n} {2} ⌋ + 30 queries.

After printing a query or printing the answer, 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 the documentation for other languages. 



Hacks

To hack the solution, use the following test format.

The first line should contain a single integer T (1 ≤ T ≤ 10 000) — the number of test cases.

For each test case in the first line print a single integer n (3 ≤ n ≤ 10^4) — the length of the hidden permutation p.

In the second line print n space-separated integers p_1, p_2, …, p_n (1 ≤ p_i ≤ n), where p is permutation.

Note that the sum of n over all test cases should not exceed 2 ⋅ 10^4.

Example

Input


2
4

3

2

5

3

Output


? 2 4 1 3

? 1 2 4 2

! 3 1 4 2

? 2 3 4 2

! 2 5 3 4 1

Note

Consider the first test case.

The hidden permutation is [3, 1, 4, 2].

We print: "? 2 4 1 3" and get back min{(max{(3, p_4}), max{(4, p_1)})} = 3.

We print: "? 1 2 4 2" and get back max{(min{(2, p_2)}, min{(3, p_4)})} = 2.

Consider the second test case.

The hidden permutation is [2, 5, 3, 4, 1].

We print: "? 2 3 4 2" and get back min{(max{(2, p_3}), max{(3, p_4)})} = 3.

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.io.BufferedReader;
import java.io.InputStreamReader;

public class First {

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        //int a = 1;
        int t;
        t = in.nextInt();
        //t = 1;
        while (t > 0) {
            //out.print("Case #"+(a++)+": ");
            solver.call(in,out);
            t--;
        }
        out.close();

    }

    static class TaskA {
        public void call(InputReader in, PrintWriter out) {
            int n;
            n = in.nextInt();

            int[] arr = new int[n+1];
            int[] ans = new int[n+1];
            Set<Integer> set = new HashSet<>();

            for (int i = 1; i <= n; i++) {
                set.add(i);
            }

            int a, b, c, d;

            for (int i = 1; i <= n-1; i+=2) {
                System.out.println("? "+1+" "+i+" "+(i+1)+" "+(n-1));
                a = in.nextInt();
                System.out.flush();

                System.out.println("? "+2+" "+i+" "+(i+1)+" "+(1));
                b = in.nextInt();
                System.out.flush();

                if(a==1 || a==n-1 || a==2|| a==n || b==1 || b==n-1||b==2|| b==n){
                    System.out.println("? "+1+" "+(i+1)+" "+(i)+" "+(n-1));
                    c = in.nextInt();
                    System.out.flush();

                    System.out.println("? "+2+" "+(i+1)+" "+i+" "+(1));
                    d = in.nextInt();
                    System.out.flush();

                    arr[i] = Math.max(a,c);
                    arr[i+1] = Math.min(b,d);

                }
                else{
                    arr[i] = b;
                    arr[i+1] = a;
                }
            }
            //3 5 1 2 6 4

            for (int i = 0; i < n; i++) {
                set.remove(arr[i]);
            }
            for (Integer i : set) {
                arr[n] = i;
            }

            for (int i = 2; i < n; i+=4) {

                System.out.println("? "+1+" "+i+" "+(i+1)+" "+(n-1));
                a = in.nextInt();
                System.out.flush();

                System.out.println("? "+2+" "+i+" "+(i+1)+" "+(1));
                b = in.nextInt();
                System.out.flush();

                if(a==1 || a==n-1 || a==2|| a==n || b==1 || b==n-1||b==2|| b==n){
                    System.out.println("? "+1+" "+(i+1)+" "+(i)+" "+(n-1));
                    c = in.nextInt();
                    System.out.flush();

                    System.out.println("? "+2+" "+(i+1)+" "+i+" "+(1));
                    d = in.nextInt();
                    System.out.flush();

                    a = Math.max(a,c);
                    b = Math.min(b,d);
                }

                c = arr[i-1];
                d = arr[i];

                if(c==a){
                    ans[i] = c;
                    ans[i-1] = d;
                    if(i+1<=n)
                        ans[i+1] = b;
                    if(i+2<=n) {
                        if(arr[i+1]==b){
                            ans[i+2] = arr[i+2];
                        }
                        else{
                            ans[i+2] = arr[i+1];
                        }
                    }
                }
                else if(d==a){
                    ans[i] = d;
                    ans[i-1] = c;
                    if(i+1<=n)
                        ans[i+1] = b;
                    if(i+2<=n) {
                        if(arr[i+1]==b){
                            ans[i+2] = arr[i+2];
                        }
                        else{
                            ans[i+2] = arr[i+1];
                        }
                    }
                }
                else if(c==b){
                    ans[i] = c;
                    ans[i-1] = d;
                    if(i+1<=n)
                        ans[i+1] = a;
                    if(i+2<=n) {
                        if(arr[i+1]==a){
                            ans[i+2] = arr[i+2];
                        }
                        else{
                            ans[i+2] = arr[i+1];
                        }
                    }
                }
                else{
                    ans[i] = d;
                    ans[i-1] = c;
                    if(i+1<=n)
                        ans[i+1] = a;
                    if(i+2<=n) {
                        if(arr[i+1]==a){
                            ans[i+2] = arr[i+2];
                        }
                        else{
                            ans[i+2] = arr[i+1];
                        }
                    }
                }
            }

            if(n%4==2){
                int  i = n-2;
                System.out.println("? "+1+" "+i+" "+(i+1)+" "+(n-1));
                a = in.nextInt();
                System.out.flush();

                System.out.println("? "+2+" "+i+" "+(i+1)+" "+(1));
                b = in.nextInt();
                System.out.flush();

                if(a==1 || a==n-1 || a==2|| a==n || b==1 || b==n-1||b==2|| b==n){
                    System.out.println("? "+1+" "+(i+1)+" "+(i)+" "+(n-1));
                    c = in.nextInt();
                    System.out.flush();

                    System.out.println("? "+2+" "+(i+1)+" "+i+" "+(1));
                    d = in.nextInt();
                    System.out.flush();

                    a = Math.max(a,c);
                    b = Math.min(b,d);
                }
                
                if(a==ans[i]){
                    ans[i+1] = b;
                    if(arr[i+1]==b){
                        ans[i+2] = arr[i+2];
                    }
                    else{
                        ans[i+2] = arr[i+1];
                    }
                }
                else{
                    ans[i+1] = a;
                    if(arr[i+1]==a){
                        ans[i+2] = arr[i+2];
                    }
                    else{
                        ans[i+2] = arr[i+1];
                    }
                }
                
            }

            if(n%4==1){
                ans[n] = arr[n];
            }


            System.out.print("! ");
            for (int i = 1; i <= n; i++) {
                System.out.print(ans[i]+" ");
            }
            System.out.println();
            System.out.flush();
        }
    }

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

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

    static class answer implements Comparable<answer>{
        int a;
        int b;

        public answer(int a, int b) {
            this.a = a;
            this.b = b;
        }

        @Override
        public int compareTo(answer o) {
            return o.a - this.a;
        }

        @Override
        public boolean equals(Object o){
            if(o instanceof answer){
                answer c = (answer)o;
                return a == c.a && b == c.b;
            }
            return false;
        }
    }

    static class answer1 implements Comparable<answer1>{
        int a, b, c;

        public answer1(int a, int b, int c) {
            this.a = a;
            this.b = b;
            this.c = c;

        }

        @Override
        public int compareTo(answer1 o) {
            if(o.c==this.c){
                return this.a - o.a;
            }
            return o.c - this.c;
        }
    }

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

    static void sort(long[] a) {
        ArrayList<Long> l=new ArrayList<>();
        for (Long i:a) l.add(i);
        l.sort(Collections.reverseOrder());
        for (int i=0; i<a.length; i++) a[i]=l.get(i);
    }

    static final Random random=new Random();

    static void shuffleSort(int[] a) {
        int n=a.length;
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n), temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong(){
            return Long.parseLong(next());
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }

    }
}