B. XOR Palindromestime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputEach 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.OutputFor each test case, output a single line containing a binary string t of length n+1 - the answer to the problem.ExampleInput
561010115000009100100011310011Output
0010100
111111
0011111100
0110
11
NoteConsider 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. 
561010115000009100100011310011
0010100 111111 0011111100 0110 11 
['bitmasks', 'constructive algorithms', 'strings', '*1100']