This is an interactive problem. You are given an unknown binary string (s)(^{\text{∗}}) of length (n). The function (f(l, r)) is defined as the number of distinct elements in the array (a) formed by the following operation: Let (S) be the substring (s_l s_{l+1} \ldots s_r). Let (m) be the length of the substring. We start with an empty array (a). For the (i)-th ((0 \le i \lt m)) left cyclic rotation(^{\text{†}}) of (S), let's denote the number of inversions(^{\text{‡}}) as (x_{i}). For every (i) such that (0 \le i \lt m), append (x_{i} \mbox{ mod } m) to the array (a), where (u \mbox{ mod } v) denotes the remainder of dividing (u) by (v). To determine (s), you can ask some questions. In each question, you can choose (2) integers (l) and (r) ((1 \le l \le r \le n)) and get the value of (f(l, r)). Asking each query incurs a cost of (\dfrac{n}{r-l+1}). Note that the cost does not necessarily have to be an integer. You have to determine the hidden binary string while keeping the total cost of queries atmost (\mathbf{max(30,3\cdot n)}). You are allowed to make at most (\mathbf{2}) guesses. (^{\text{∗}})A binary string only contains characters (0) and (1). (^{\text{†}})Let there be a binary string (s \; = \; s_{1}s_{2}\cdots s_{n}). The (k)-th left cyclic rotation of (s) is defined as (t_{k} \; = \; s_{k+1}s_{k+2}\cdots s_{n}s_{1}s_{2}\cdots s_{k}). (^{\text{‡}})Let there be a string (s \; = \; s_{1}s_{2}\cdots s_{n}). The number of inversions of (s) is defined as the number of pairs of indices (i,j \; (1 \le i \lt j \le n)), such that (s_{i} \gt s_{j}). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 100)). The description of the test cases follows. The first line of each test case contains a single integ