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.util.*;
import java.io.*;
import java.util.stream.IntStream;

public class Main {

    static long startTime = System.currentTimeMillis();

    // for global initializations and methods starts here

    // global initialisations and methods end here

    static void run(){
    boolean tc = true;
    AdityaFastIO r = new AdityaFastIO();
    //FastReader r = new FastReader();

    try (OutputStream out = new BufferedOutputStream(System.out)) {

        //long startTime = System.currentTimeMillis();

        int testcases = tc ? r.ni() : 1;
        int tcCounter = 1;
        // Hold Here Sparky------------------->>>
        // Solution Starts Here

        start : while (testcases --> 0) {

            int n = r.ni();
            int[] arr = new int[n];
            int ind = n-1;
            {
                int i=0;
                while (i<n-1) {
                    out.write((("? 1") + " " + (i + 1) + " " + (i + 2) + " " + (n - 1) + " ").getBytes());
                    out.write(("\n").getBytes());
                    out.flush();
                    int present = r.ni();
                    if (present != n) {
                        if (present == n-1){
                            out.write((("? 1") + " " + (i + 2) + " " + (i + 1) + " " + (n - 1) + " ").getBytes());
                            out.write(("\n").getBytes());
                            out.flush();
                            int ele = r.ni();
                            if (ele == n){
                                ind = i;
                                break ;
                            }
                        }
                    } else {ind = i+1;break ;}
                    i+=2;
                }
            }

            arr[ind] = n;
            for (int is = 0;is <n;is ++){
                if (is  == ind){
                    continue ;
                }

                out.write((("? 2") + " " + (is  + 1) + " " + (ind + 1) + " " + (1) + " ").getBytes());
                out.write(("\n").getBytes());
                out.flush();
                arr[is ] = r.ni();
            }

            out.write((("! ") + " ").getBytes());
            for (int ele : arr) out.write((ele + " ").getBytes());
            out.write(("\n").getBytes());
            out.flush();

        }
        // Solution Ends Here
    } catch (IOException e) {
        e.printStackTrace();
    }
}

    static class AdityaFastIO{
        final private int BUFFER_SIZE = 1<<16;
        private final DataInputStream din;
        private final byte[] buffer;
        private int bufferPointer, bytesRead;
        public BufferedReader br;
        public StringTokenizer st;

        public AdityaFastIO() {
            br = new BufferedReader(new InputStreamReader(System.in));
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public AdityaFastIO(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

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

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

        public String readLine() throws IOException {
            byte[] buf = new byte[100000001]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n') break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int ni() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do { ret = ret * 10 + c - '0'; }
            while ((c = read()) >= '0' && c <= '9');
            if (neg) return -ret;
            return ret;
        }

        public long nl() throws IOException {
            long ret = 0;byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do { ret = ret * 10 + c - '0'; }
            while ((c = read()) >= '0' && c <= '9');
            if (neg) return -ret;return ret;
        }

        public double nd() throws IOException {
            double ret = 0, div = 1;byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do { ret = ret * 10 + c - '0'; }
            while ((c = read()) >= '0' && c <= '9');
            if (c == '.') while ((c = read()) >= '0' && c <= '9') ret += (c - '0') / (div *= 10);
            if (neg) return -ret;return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1) buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead) fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null) return;
            din.close();
        }
    }
    public static void main(String[] args) throws Exception {run();}

    static long mod = 998244353;
    static long modInv(long base, long e) {
    long result = 1;
    base %= mod;
    while (e>0) {
        if ((e & 1)>0) result = result * base % mod;
        base = base * base % mod;
        e >>= 1;
    }
    return result;
}

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;
        public FastReader() { br = new BufferedReader(new InputStreamReader(System.in)); }
        String word() {
            while (st == null || !st.hasMoreElements()) {
                try { st = new StringTokenizer(br.readLine()); }
                catch (IOException e) { e.printStackTrace(); }
            }
            return st.nextToken();
        }
        String line() {
            String str = "";
            try { str = br.readLine(); }
            catch (IOException e) { e.printStackTrace(); }
            return str;
        }
        int ni() { return Integer.parseInt(word()); }
        long nl() { return Long.parseLong(word()); }
        double nd() { return Double.parseDouble(word()); }
    }

    static int MOD = (int) (1e9 + 7);

    static long powerLL(long x, long n) {
    long result = 1;
    while (n > 0) {
        if (n % 2 == 1) result = result * x % MOD;
        n = n / 2;x = x * x % MOD;
    }
    return result;
}

    static long powerStrings(int i1, int i2) {
    String sa = String.valueOf(i1);
    String sb = String.valueOf(i2);
    long a = 0, b = 0;
    for (int i = 0; i < sa.length(); i++) a = (a * 10 + (sa.charAt(i) - '0')) % MOD;
    for (int i = 0; i < sb.length(); i++) b = (b * 10 + (sb.charAt(i) - '0')) % (MOD - 1);
    return powerLL(a, b);
}

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

    static long lower_bound(List<Long> list, long k) {
    int s = 0;
    int e = list.size();
    while (s != e) {
        int mid = (s + e) >> 1;
        if (list.get(mid) < k) s = mid + 1;
        else e = mid;
    }
    if (s == list.size()) return -1;
    return s;
}

    static int upper_bound(List<Long> list, long k) {
    int s = 0;
    int e = list.size();
    while (s != e) {
        int mid = (s + e) >> 1;
        if (list.get(mid) <= k) s = mid + 1;
        else e = mid;
    }
    if (s == list.size()) return -1; return s;
}

    static void addEdge(ArrayList<ArrayList<Integer>> graph, int edge1, int edge2) {
    graph.get(edge1).add(edge2);graph.get(edge2).add(edge1);
}

    public static class Pair implements Comparable<Pair> {
        int first;int second;
        public Pair(int first, int second) { this.first = first;this.second = second; }
        public String toString() { return "(" + first + "," + second + ")"; }
        public int compareTo(Pair o) {
            // TODO Auto-generated method stub
            if(this.first!=o.first)
                return (int) (this.first - o.first);
            else return(int)(this.second-o.second);
        }
    }

    public static class PairC<X,Y> implements Comparable<PairC> {
        X first;Y second;
        public PairC(X first, Y second) { this.first = first;this.second = second; }
        public String toString() { return "(" + first + "," + second + ")"; }
        public int compareTo(PairC o) {
            // TODO Auto-generated method stub
            return o.compareTo((PairC) first);
        }
    }

    static boolean isCollectionsSorted(List<Long> list) {
    if (list.size() == 0 || list.size() == 1) return true;
    for (int i = 1; i < list.size(); i++) if (list.get(i) <= list.get(i - 1)) return false;
    return true;
}

    static boolean isCollectionsSortedReverseOrder(List<Long> list) {
    if (list.size() == 0 || list.size() == 1) return true;
    for (int i = 1; i < list.size(); i++) if (list.get(i) >= list.get(i - 1)) return false;
    return true;
}

}