Binary Construction

For a binary string $S$ of length $N$, define a set $f(S) = \{i + j$ $|$ $1 \le i, j \le N, S_i \ne S_j\}$. Find a binary string of length $N$ that maximizes the size of the set $f(S)$. If multiple answers are possible, all of them will be accepted. ### Input - The first line of input will contain a single integer $T$, denoting the number of test cases. - The first and only line of each test cas