Description: You are given a binary string $$$s$$$ of length $$$n$$$ (a string that consists only of $$$0$$$ and $$$1$$$). A number $$$x$$$ is good if there exists a binary string $$$l$$$ of length $$$n$$$, containing $$$x$$$ ones, such that if each symbol $$$s_i$$$ is replaced by $$$s_i \oplus l_i$$$ (where $$$\oplus$$$ denotes the bitwise XOR operation), then the string $$$s$$$ becomes a palindrome. You need to output a binary string $$$t$$$ of length $$$n+1$$$, where $$$t_i$$$ ($$$0 \leq i \leq n$$$) is equal to $$$1$$$ if number $$$i$$$ is good, and $$$0$$$ otherwise. A palindrome is a string that reads the same from left to right as from right to left. For example, 01010, 1111, 0110 are palindromes. Input Format: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^5$$$). The description of the test cases follows. The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 10^5$$$). The second line of each test case contains a binary string $$$s$$$ of length $$$n$$$. It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$. Output Format: For each test case, output a single line containing a binary string $$$t$$$ of length $$$n+1$$$ - the answer to the problem. Note: Consider the first example. - $$$t_2 = 1$$$ because we can choose $$$l = $$$ 010100, then the string $$$s$$$ becomes 111111, which is a palindrome. - $$$t_4 = 1$$$ because we can choose $$$l = $$$ 101011. - It can be shown that for all other $$$i$$$, there is no answer, so the remaining symbols are $$$0$$$.