CF1867B.XOR Palindromes
普及/提高-
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题目描述
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 si is replaced by si⊕li (where ⊕ 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 ti ( 0≤i≤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.
输入格式
Each test contains multiple test cases. The first line contains the number of test cases t ( 1≤t≤105 ). The description of the test cases follows.
The first line of each test case contains a single integer n ( 1≤n≤105 ).
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 105 .
输出格式
For each test case, output a single line containing a binary string t of length n+1 - the answer to the problem.
输入输出样例
输入#1
5 6 101011 5 00000 9 100100011 3 100 1 1
输出#1
0010100 111111 0011111100 0110 11
说明/提示
Consider the first example.
- t2=1 because we can choose $l = $ 010100, then the string s becomes 111111, which is a palindrome.
- t4=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 .