Ashish has a binary string $s$ of length $n$ that he wants to sort in non-decreasing order.

He can perform the following operation:

1. Choose a subsequence of any length such that its elements are in non-increasing order. Formally, choose any $k$ such that $1 \leq k \leq n$ and any sequence of $k$ indices $1 \le i_1 \lt i_2 \lt \ldots \lt i_k \le n$ such that $s_{i_1} \ge s_{i_2} \ge \ldots \ge s_{i_k}$.
2. Reverse this subsequence in-place. Formally, swap $s_{i_1}$ with $s_{i_k}$, swap $s_{i_2}$ with $s_{i_{k-1}}$, $\ldots$ and swap $s_{i_{\lfloor k/2 \rfloor}}$ with $s_{i_{\lceil k/2 \rceil + 1}}$ (Here $\lfloor x \rfloor$ denotes the largest integer not exceeding $x$, and $\lceil x \rceil$ denotes the smallest integer not less than $x$)

Find the minimum number of operations required to sort the string in non-decreasing order. It can be proven that it is always possible to sort the given binary string in at most $n$ operations.

Input

The first line contains a single integer $t$ $(1 \le t \le 1000)$  — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer $n$ $(1 \le n \le 1000)$  — the length of the binary string $s$.

The second line of each test case contains a binary string $s$ of length $n$ containing only $0$s and $1$s.

It is guaranteed that the sum of $n$ over all test cases does not exceed $1000$.

Output

For each test case output the following:

• The minimum number of operations $m$ in the first line ($0 \le m \le n$).
• Each of the following $m$ lines should be of the form: $k$ $i_1$ $i_2$ ... $i_{k}$, where $k$ is the length and $i_1 \lt i_2 \lt ... \lt i_{k}$ are the indices of the chosen subsequence. For them the conditions from the statement must hold.

见题面 Input 部分

见题面 Output 部分

In the first test case, the binary string is already sorted in non-decreasing order.

In the second test case, we can perform the following operation:

• $k = 4:$ choose the indices $\{1, 3, 4, 5\}$$\underline{1}$ $0$ $\underline{1}$ $\underline{0}$ $\underline{0}$ $\rightarrow $ $\underline{0}$ $0$ $\underline{0}$ $\underline{1}$ $\underline{1}$ In the third test case, we can perform the following operation: - $k = 3:$ choose the indices $\{3, 5, 6\}$$0$ $0$ $\underline{1}$ $0$ $\underline{0}$ $\underline{0}$ $\rightarrow $ $0$ $0$ $\underline{0}$ $0$ $\underline{0}$ $\underline{1}$