Everool has a binary string $$$s$$$ of length $$$2n$$$. Note that a binary string is a string consisting of only characters $$$0$$$ and $$$1$$$. He wants to partition $$$s$$$ into two disjoint equal subsequences. He needs your help to do it.
You are allowed to do the following operation exactly once.
In other words, you can select a sequence of indices $$$b_1, b_2, \ldots, b_m$$$, where $$$1 \le b_1 < b_2 < \ldots < b_m \le 2n$$$. After that you simultaneously set $$$$$$s_{b_1} := s_{b_m},$$$$$$ $$$$$$s_{b_2} := s_{b_1},$$$$$$ $$$$$$\ldots,$$$$$$ $$$$$$s_{b_m} := s_{b_{m-1}}.$$$$$$
Can you partition $$$s$$$ into two disjoint equal subsequences after performing the allowed operation exactly once?
A partition of $$$s$$$ into two disjoint equal subsequences $$$s^p$$$ and $$$s^q$$$ is two increasing arrays of indices $$$p_1, p_2, \ldots, p_n$$$ and $$$q_1, q_2, \ldots, q_n$$$, such that each integer from $$$1$$$ to $$$2n$$$ is encountered in either $$$p$$$ or $$$q$$$ exactly once, $$$s^p = s_{p_1} s_{p_2} \ldots s_{p_n}$$$, $$$s^q = s_{q_1} s_{q_2} \ldots s_{q_n}$$$, and $$$s^p = s^q$$$.
If it is not possible to partition after performing any kind of operation, report $$$-1$$$.
If it is possible to do the operation and partition $$$s$$$ into two disjoint subsequences $$$s^p$$$ and $$$s^q$$$, such that $$$s^p = s^q$$$, print elements of $$$b$$$ and indices of $$$s^p$$$, i. e. the values $$$p_1, p_2, \ldots, p_n$$$.
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^5$$$). Description of the test cases follows.
The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 10^5$$$), where $$$2n$$$ is the length of the binary string.
The second line of each test case contains the binary string $$$s$$$ of length $$$2n$$$.
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.
For each test case, follow the following output format.
If there is no solution, print $$$-1$$$.
Otherwise,
If there are multiple solutions, print any.
4 2 1010 3 100010 2 1111 2 1110
0 1 2 2 3 5 1 2 5 3 2 3 4 1 4 -1
In the first test case, $$$b$$$ is empty. So string $$$s$$$ is not changed. Now $$$s^p = s_1 s_2 = \mathtt{10}$$$, and $$$s^q = s_3s_4 = \mathtt{10}$$$.
In the second test case, $$$b=[3,5]$$$. Initially $$$s_3=\mathtt{0}$$$, and $$$s_5=\mathtt{1}$$$. On performing the operation, we simultaneously set $$$s_3=\mathtt{1}$$$, and $$$s_5=\mathtt{0}$$$.
So $$$s$$$ is updated to 101000 on performing the operation.
Now if we take characters at indices $$$[1,2,5]$$$ in $$$s^p$$$, we get $$$s_1=\mathtt{100}$$$. Also characters at indices $$$[3,4,6]$$$ are in $$$s^q$$$. Thus $$$s^q=100$$$. We are done as $$$s^p=s^q$$$.
In fourth test case, it can be proved that it is not possible to partition the string after performing any operation.