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. 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). For each test case, output a single line containing a binary string (t) of length (n+1) - the answer to the problem. 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).