B. Beautiful String

You are given a binary

∗

 string 𝑠

 of length 𝑛

.

Your task is to find any subsequence

†

 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
• ‡
• .

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.

∗

A binary string is a string consisting of characters '0' and '1'.

†

A subsequence of a string 𝑠=𝑠

1

𝑠

2

…𝑠

𝑛

 is a sequence 𝑝=𝑠

𝑖

1

𝑠

𝑖

2

…𝑠

𝑖

𝑘

 such that 1≤𝑖

1

<𝑖

2

<…<𝑖

𝑘

≤𝑛

. The characters are selected in order, but not necessarily contiguously. Note that an empty string is a subsequence of any string.

‡

A string 𝑡=𝑡

1

𝑡

2

…𝑡

𝑚

 is a palindrome if 𝑡

𝑖

=𝑡

𝑚−𝑖+1

 for all 1≤𝑖≤𝑚

. In other words, the string reads the same forward and backward.

Input

The first line contains a single integer 𝑡

 (1≤𝑡≤3000

) — the number of test cases.

The first line of each test case contains a single integer 𝑛

 (1≤𝑛≤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≤𝑘≤𝑛
• ) — the length of the subsequence 𝑝
• .
• On the second line, print 𝑘
•  distinct integers 𝑖
• 1
• ,𝑖
• 2
• ,…,𝑖
• 𝑘
•  (1≤𝑖
• 1
• <𝑖
• 2
• <⋯<𝑖
• 𝑘
• ≤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

.

Example

Input

Copy

5
3
010
3
001
5
00111
8
11010011
6
100101

Output

Copy

0

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

Note

In the first test case, we remove an empty string, resulting in 𝑥=𝟶𝟷𝟶

, which is a palindrome.

In the second test case, we remove 𝑝=𝟶𝟷

 (indices 2

, 3

), resulting in 𝑥=𝟶

, which is a palindrome.

In the third test case, we remove 𝑝=𝟶𝟶𝟷𝟷𝟷

 (indices 1

 to 5

), resulting in an empty string, which is trivially a palindrome.

In the fourth test case, we remove 𝑝=𝟶𝟷

 (indices 3

, 4

), resulting in 𝑥=𝟷𝟷𝟶𝟶𝟷𝟷

, which is a palindrome.

In the fifth test case, we remove 𝑝=𝟶𝟷

 (indices 5

, 6

), resulting in 𝑥=𝟷𝟶𝟶𝟷

, which is a palindrome.