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.DataInputStream;
import java.io.IOException;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.*;
import java.util.function.ToIntFunction;

public class Main {

    private static int n;

    private static void run() throws IOException {
        n = in.nextInt();
//        init_test();
        int[] ans = new int[n];

        for (int i = 0; i + 1 < n; i += 2) {
            int max = query(1, i, i + 1, n - 1);
            int min = query(2, i, i + 1, 1);

            int min_is_first = query(2, i, i + 1, min);
            if (min_is_first == min) {
                ans[i] = min;
                ans[i + 1] = max;
            } else {
                ans[i + 1] = min;
                ans[i] = max;
            }

            if (min == 2) {
                int reverse = query(2, i + 1, i, 1);
                if (reverse == 1) {
                    ans[i + 1] = 1;
                }
            }

            if (max == n - 1) {
                int max_is_second = query(1, i, i + 1, max - 1);
                if (max_is_second == max) {
                    ans[i + 1] = max_is_second;
                    ans[i] = min;
                }

                int reverse = query(1, i + 1, i, n - 1);
                if (reverse == n) {
                    ans[i] = n;
                }
            }
        }

        handle_last(ans);

//        judge(ans);
        out.print("! ");
        print_array(ans);
        out.flush();
    }

    private static void handle_last(int[] ans) {
        int last = -1;
        for (int i = 0; i < ans.length; i++) {
            if (ans[i] == 0) last = i;
        }
        if (last == -1) return;
        boolean[] already = new boolean[ans.length + 1];
        for (int now : ans) {
            already[now] = true;
        }
        for (int i = 1; i <= ans.length; i++) {
            if (!already[i]) {
                ans[last] = i;
            }
        }
    }

//    static int test_c = 0;
//    static int[] test;
//    static Random random = new Random();
//
//    static class Node {
//        int value;
//        double order;
//
//        public Node(int value) {
//            this.value = value;
//            this.order = random.nextDouble();
//        }
//    }

//    static void init_test() {
//        test_c = 0;
//        test = new int[n];
//
//        Node[] nodes = new Node[n];
//        for (int i = 0; i < n; i++) {
//            nodes[i] = new Node(i + 1);
//        }
//        Arrays.sort(nodes, Comparator.comparingDouble(o -> o.order));
//
//        for (int i = 0; i < n; i++) {
//            test[i] = nodes[i].value;
//        }
//
////        test = new int[]{9, 2, 1, 3, 4, 5, 6, 7, 8, 10};
//    }
//
//    static void judge(int[] ans) {
//        for (int i = 0; i < n; i++) {
//            if (ans[i] != test[i]) {
//                out.println("error");
//                print_array(test);
//                print_array(ans);
//                out.println(i + " " + test[i] + " " + ans[i]);
//                out.flush();
//                System.exit(0);
//            }
//        }
//        int max = 3 * n / 2 + 30;
//        if (test_c > max) {
//            out.println("too many query " + max + " " + test_c);
//        }
//    }

    private static int query(int type, int pos1, int pos2, int x) throws IOException {
//        test_c++;
//        if (type == 1) {
//            return Math.max(Math.min(x, test[pos1]), Math.min(x + 1, test[pos2]));
//        } else {
//            return Math.min(Math.max(x, test[pos1]), Math.max(x + 1, test[pos2]));
//        }
        out.printf("? %d %d %d %d\n", type, pos1 + 1, pos2 + 1, x);
        out.flush();
        return in.nextInt();
    }

    public static void main(String[] args) throws IOException {
        in = new Reader();
        out = new PrintWriter(new OutputStreamWriter(System.out));

        int t = in.nextInt();
//        int t = 1000;
        for (int i = 0; i < t; i++) {
            run();
        }

        out.flush();
        in.close();
        out.close();
    }

    private static int gcd(int a, int b) {
        if (a == 0 || b == 0)
            return 0;
        while (b != 0) {
            int tmp;
            tmp = a % b;
            a = b;
            b = tmp;
        }
        return a;
    }

    static final long mod = 1000000007;

    static long pow_mod(long a, long b) {
        long result = 1;
        while (b != 0) {
            if ((b & 1) != 0) result = (result * a) % mod;
            a = (a * a) % mod;
            b >>= 1;
        }
        return result;
    }

    private static long multiplied_mod(long... longs) {
        long ans = 1;
        for (long now : longs) {
            ans = (ans * now) % mod;
        }
        return ans;
    }

    @SuppressWarnings("FieldCanBeLocal")
    private static Reader in;
    private static PrintWriter out;

    private static int[] read_int_array(int len) throws IOException {
        int[] a = new int[len];
        for (int i = 0; i < len; i++) {
            a[i] = in.nextInt();
        }
        return a;
    }

    private static long[] read_long_array(int len) throws IOException {
        long[] a = new long[len];
        for (int i = 0; i < len; i++) {
            a[i] = in.nextLong();
        }
        return a;
    }

    private static void print_array(int[] array) {
        for (int now : array) {
            out.print(now);
            out.print(' ');
        }
        out.println();
    }

    private static void print_array(long[] array) {
        for (long now : array) {
            out.print(now);
            out.print(' ');
        }
        out.println();
    }

    static class Reader {
        private static final int BUFFER_SIZE = 1 << 16;
        private final DataInputStream din;
        private final byte[] buffer;
        private int bufferPointer, bytesRead;

        Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            final byte[] buf = new byte[1024]; // 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 nextSign() throws IOException {
            byte c = read();
            while ('+' != c && '-' != c) {
                c = read();
            }
            return '+' == c ? 0 : 1;
        }

        private static boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }

        public int skip() throws IOException {
            int b;
            // noinspection ALL
            while ((b = read()) != -1 && isSpaceChar(b)) {
                ;
            }
            return b;
        }

        public char nc() throws IOException {
            return (char) skip();
        }

        public String next() throws IOException {
            int b = skip();
            final StringBuilder sb = new StringBuilder();
            while (!isSpaceChar(b)) { // when nextLine, (isSpaceChar(b) && b != ' ')
                sb.appendCodePoint(b);
                b = read();
            }
            return sb.toString();
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            final 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 nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            final 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 nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            final 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 {
            din.close();
        }

    }
}