This is an interactive problem. There are two hidden integers (k) and (c) such that (k\in \{1,2,3\}) and (1\le c\le 2^n-1). Note that (c\neq 0). Before any interaction, you need to tell the jury a non-negative integer (a\le 2^n-1). The grader will then use (a) as the initial element in the set (S), that is, initially (S = \{a\}). Next, you can make at most (n+3) queries of the following two types: Select an integer (x) such that (0\leq x\le 2^n-1). The jury will insert (f(x)) into (S) and then respond with (|S|) (i. e., the size of (S) after the insertion); Select an integer (y) such that (0\leq y\le 2^n-1). The jury will respond with the number of integers (z) such that (z\in S) and (z\geq y). The definition of (f(x)) is as follows: () f(x)= \begin{cases} x\,\&\,c & \text{if}\, k=1,\\ x\,|\,c & \text{if}\, k=2,\\ x\oplus c & \text{if}\, k=3.\\ \end{cases} () Here, (\&) denotes the bitwise AND operation , (|) denotes the bitwise OR operation , and (\oplus) denotes the bitwise XOR operation . Your task is to determine the values of (k) and (c) using at most (n+3) interactions. Please note that reporting the answer does not count towards the (n+3) interactions. Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The first line of each test case contains a single integer (n) ((2 \leq n \leq 60)). Then, interaction follows. It is guaranteed that the sum of (n) over all test cases does not exceed (10^5). First, you need to output an integer (a) ((0\leq a\le 2^n-1)) — the initial element you chose for set (S). To make an interaction, output a single line in the following format: (\mathtt{I}\;x) ((0\leq x\le 2^n-1)) — Insert (f(x)) into set (S). After that, the jury will return $$$|S|$$