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.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;

public class C {

    private static final boolean TEST_MODE = true;
    private static BufferedReader br;

    public static void main(String[] args) throws Exception {
        br = new BufferedReader(new InputStreamReader(System.in));
        int T = getInt(br);
        for (int t=0; t<T; t++) {
            int N = getInt(br);
            process(N);
        }
    }

    private static void process(int N) throws Exception {
        int[] arr = new int[N + 1];
        Arrays.fill(arr, -1);
        int nIndex = determineN(N);
        arr[nIndex] = N;

        // Now that we know N, we can use it to fill all the other positions.
        for (int i=1; i<=N; i++) {
            if (arr[i] > 0) {
                continue;
            }

            int resN = invokeOp2(1, i, nIndex);
            // resN is nothing but the answer.
            arr[i] = resN;
        }
        printArray(arr);
    }

    private static int determineN(int N) throws Exception {
        int first = 1;
        int second = 2;
        while (first <= N) {
            if (second == N+1) {
                second = 1;
            }
            int res = invokeOp1(N-1, first, second);
            if (res == N) {
                return second;
            }
            if (res == N-1) {
                int revRes = invokeOp1(N-1, second, first);
                if (revRes == N) {
                    return first;
                }
            }
            first += 2;
            second += 2;
        }
        throw new RuntimeException();
    }

    private static int invokeOp1(int x, int i, int j) throws Exception {
        StringBuilder op = new StringBuilder("? 1 ")
                .append(i).append(" ")
                .append(j).append(" ")
                .append(x);
        System.out.println(op);
        System.out.flush();
        int res = getInt(br);
        if (res == -1) {
            System.exit(1);
        }
        return res;
    }

    private static int invokeOp2(int x, int i, int j) throws Exception {
        StringBuilder op = new StringBuilder("? 2 ")
                .append(i).append(" ")
                .append(j).append(" ")
                .append(x);
        System.out.println(op);
        System.out.flush();
        int res = getInt(br);
        if (res == -1) {
            System.exit(1);
        }
        return res;
    }

    private static Integer getInt(BufferedReader br) throws Exception {
        return Integer.parseInt(br.readLine());
    }

    private static Long getLong(BufferedReader br) throws Exception {
        return Long.parseLong(br.readLine());
    }

    private static int[] getIntArray(int N, BufferedReader br) throws Exception {
        String s = br.readLine();
        String[] tokens = s.split(" ");
        int[] result = new int[N+1];

        for (int i=0; i<N; i++) {
            result[i+1] = Integer.parseInt(tokens[i]);
        }
        return result;
    }

    private static long[] getLongArray(int N, BufferedReader br) throws Exception {
        String s = br.readLine();
        String[] tokens = s.split(" ");
        long[] result = new long[N+1];

        for (int i=0; i<N; i++) {
            result[i+1] = Long.parseLong(tokens[i]);
        }
        return result;
    }

    private static void printArray(int[] arr) {
        StringBuilder res = new StringBuilder("! ");
        for (int i=1; i<arr.length; i++) {
            res.append(arr[i]).append(" ");
        }
        System.out.println(res);
    }
}