Description:
This is an interactive problem.
There is a secret sequence $$$p_0, p_1, \ldots, p_{n-1}$$$, which is a permutation of $$$\{0,1,\ldots,n-1\}$$$.
You need to find any two indices $$$i$$$ and $$$j$$$ such that $$$p_i \oplus p_j$$$ is maximized, where $$$\oplus$$$ denotes the bitwise XOR operation.
To do this, you can ask queries. Each query has the following form: you pick arbitrary indices $$$a$$$, $$$b$$$, $$$c$$$, and $$$d$$$ ($$$0 \le a,b,c,d < n$$$). Next, the jury calculates $$$x = (p_a \mid p_b)$$$ and $$$y = (p_c \mid p_d)$$$, where $$$|$$$ denotes the bitwise OR operation. Finally, you receive the result of comparison between $$$x$$$ and $$$y$$$. In other words, you are told if $$$x < y$$$, $$$x > y$$$, or $$$x = y$$$.
Please find any two indices $$$i$$$ and $$$j$$$ ($$$0 \le i,j < n$$$) such that $$$p_i \oplus p_j$$$ is maximum among all such pairs, using at most $$$3n$$$ queries. If there are multiple pairs of indices satisfying the condition, you may output any one of them.
Input Format:
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^3$$$). The description of the test cases follows.
Output Format:
None
Note:
In the first test case, the hidden permutation is $$$p=[0,3,1,2]$$$.
For the query "? 0 2 3 1", the jury return "<" because $$$(p_0 \mid p_2) = (0 \mid 1) =1 < (p_3 \mid p_1) = (2 \mid 3) = 3$$$.
For the query "? 1 1 2 3", the jury return "=" because $$$(p_1 \mid p_1) = (3\mid 3)= 3 = (p_2 \mid p_3) = (1 \mid 2)=3$$$.
For the query "? 1 2 0 3", the jury return ">" because $$$(p_1 \mid p_2) = (3 \mid 1) = 3 > (p_0 \mid p_3) = (0\mid 2)=2$$$.
The answer $$$i = 3$$$ and $$$j = 2$$$ is valid: $$$(p_3 \oplus p_2) = (2 \oplus 1) = 3$$$ is indeed equal to the maximum possible value of $$$p_i \oplus p_j$$$. Another valid answer would be $$$i=0$$$ and $$$j=1$$$. As the number of queries does not exceed $$$3n=12$$$, the answer is considered correct.
In the second test case, $$$n = 2$$$, so $$$p$$$ is either $$$[0, 1]$$$ or $$$[1, 0]$$$. In any case, $$$p_0 \oplus p_1 = 1$$$ is maximum possible.