You are given a binary string S of length $2\cdot N$.

A partition of string S into strings P and Q is said to be valid if:
Both P and Q are [subsequences] of S of length N;
Each character of string S belongs to exactly one subsequence out of P and Q;
Strings P and Q are NOT equal.

Let A denote the set of indices of S that belong to the subsequence P.

Find whether it is possible to make a valid partition of S.
If it is possible, print the elements of array A, in increasing order. Otherwise, print -1.

------ Input Format ------

• Each test contains multiple test cases. The first line contains the number of test cases T. Description of the test cases follows.
• The first line of each test case contains a single integer N, where $2\cdot N$ is the length of the binary string.
• The second line of each test case contains the binary string S of length $2\cdot N$.

------ Output Format ------

For each test case, if a valid partition exists, print $N distinct indices A_{1}, A_{2}, \ldots, A_{N} ($in increasing order).
If no valid partition exists, print -1.
If there are multiple solutions, print any.

------ Constraints ------

$1 ≤ T ≤ 10^{5}$
$1 ≤ N ≤ 10^{5}$
$S$ consists of $0$ and $1$ only.
- It is guaranteed that the sum of $N$ over all test cases does not exceed $10^{5}$.

----- Sample Input 1 ------
4
1
11
1
10
3
100000
3
100100

----- Sample Output 1 ------
-1
1
1 2 3
1 4 6

----- explanation 1 ------
Test case $1$: It can be proven that no valid partition exists.

Test case $2$: A valid partition is $P = 1$ and $Q = 0$. Here, $A = [1]$.

Test case $3$: A valid partition is $P = 100$ and $Q = 000$. Here, $A = [1, 2, 3]$.

Test case $4$: A valid partition is $P = 110$ and $Q = 000$. Here, $A = [1, 4, 6]$.

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