You are given a binary$^{\text{∗}}$ string $s$ of length $n$.

Your task is to find any subsequence$^{\text{†}}$ $p$ of $s$ such that:

• The subsequence $p$ is non-decreasing. That is, each character in $p$ is not greater than the next one.
• Let $x$ denote the string obtained by removing all characters of $p$ from $s$, while preserving the order of the remaining characters. Then $x$ must be a palindrome$^{\text{‡}}$.

You only need to output any valid subsequence $p$ that satisfies both conditions. If no such subsequence exists, output $-1$.

Note that an empty string is both non-decreasing and a palindrome.

$^{\text{∗}}$A binary string is a string consisting of characters '0' and '1'.

$^{\text{†}}$A subsequence of a string $s = s_1s_2\ldots s_n$ is a sequence $p = s_{i_1}s_{i_2}\ldots s_{i_k}$ such that $1 \leq i_1 \lt i_2 \lt \ldots \lt i_k \leq n$. The characters are selected in order, but not necessarily contiguously. Note that an empty string is a subsequence of any string.

$^{\text{‡}}$A string $t = t_1t_2\ldots t_m$ is a palindrome if $t_i = t_{m - i + 1}$ for all $1 \leq i \leq m$. In other words, the string reads the same forward and backward.

Input

The first line contains a single integer $t$ ($1 \le t \le 3000$) — the number of test cases.

The first line of each test case contains a single integer $n$ ($1 \le n \le 10$) — the length of the string.

The second line contains a binary string $s$ of length $n$.

Output

If a solution exists:

• On the first line, print a single integer $k$ ($0 \le k \le n$) — the length of the subsequence $p$.
• On the second line, print $k$ distinct integers $i_1, i_2, \dots, i_k$ ($1 \le i_1 \lt i_2 \lt \dots \lt i_k \le n$) — the indices of the characters in $s$ that form $p$ (in order as they appear in $s$).

Otherwise, print a single line containing $-1$.

Note

In the first test case, we remove an empty string, resulting in $x = \texttt{010}$, which is a palindrome.

In the second test case, we remove $p = \texttt{01}$ (indices $2$, $3$), resulting in $x = \texttt{0}$, which is a palindrome.

In the third test case, we remove $p = \texttt{00111}$ (indices $1$ to $5$), resulting in an empty string, which is trivially a palindrome.

In the fourth test case, we remove $p = \texttt{01}$ (indices $3$, $4$), resulting in $x = \texttt{110011}$, which is a palindrome.

In the fifth test case, we remove $p = \texttt{01}$ (indices $5$, $6$), resulting in $x = \texttt{1001}$, which is a palindrome.

Samples

5
3
010
3
001
5
00111
8
11010011
6
100101

0

2
2 3
5
1 2 3 4 5
2
3 4
2
5 6