This is an interactive problem. Kachina challenges you to guess her favorite binary string(^{\text{∗}}) (s) of length (n). She defines (f(l, r)) as the number of subsequences(^{\text{†}}) of (01) in (s_l s_{l+1} \ldots s_r). Two subsequences are considered different if they are formed by deleting characters from different positions in the original string, even if the resulting subsequences consist of the same characters. To determine (s), you can ask her some questions. In each question, you can choose two indices (l) and (r) ((1 \leq l < r \leq n)) and ask her for the value of (f(l, r)). Determine and output (s) after asking Kachina no more than (n) questions. However, it may be the case that (s) is impossible to be determined . In this case, you would need to report (IMPOSSIBLE) instead. Formally, (s) is impossible to be determined if after asking (n) questions, there are always multiple possible strings for (s), regardless of what questions are asked. Note that if you report (IMPOSSIBLE) when there exists a sequence of at most (n) queries that will uniquely determine the binary string, you will get the Wrong Answer verdict. (^{\text{∗}})A binary string only contains characters (0) and (1). (^{\text{†}})A sequence (a) is a subsequence of a sequence (b) if (a) can be obtained from (b) by the deletion of several (possibly, zero or all) elements. For example, subsequences of (\mathtt{1011101}) are (\mathtt{0}), (\mathtt{1}), (\mathtt{11111}), (\mathtt{0111}), but not (\mathtt{000}) nor (\mathtt{11100}). The first line of input contains a single integer (t) ((1 \leq t \leq 10^3)) — the number of test cases. The first line of each test case contains a single integer (n) ((2 \leq n \leq 10^4)) — the length of (s). It is guaranteed that the sum of (n)