C. Dominoes Covering
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Baozii presents to you a strip of $$$n$$$ cells, all initially white. You are given a target pattern consisting of $$$n$$$ cells, where each cell is either white or black. Your task is to determine whether it is possible to transform the strip into the given target pattern by performing a finite sequence of the following operation:

  • Choose an integer $$$i$$$ ($$$1 \le i \lt n$$$). Then color the $$$i$$$-th cell white and the $$$(i+1)$$$-th cell black, overriding their initial colors.

Determine if the transformation is achievable. If so, output a valid sequence of operations.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The first line of each test case contains an integer $$$n$$$ ($$$2 \le n \le 100$$$) — length of Baozii's strip.

The second line contains a binary string of length $$$n$$$, representing the pattern. If the $$$i$$$-th character is 1, the $$$i$$$-th cell should be colored black; otherwise, the $$$i$$$-th cell should be colored white.

Output

For each test case, output "YES" (without quotes) if there exists a finite sequence of operations which colors the strip to the given pattern, and "NO" (without quotes) otherwise.

If the answer is "YES", output the sequence in the following format:

  • On the first line, output a single integer $$$k$$$ ($$$0 \le k \le 1000$$$) — the number of operations. We can prove that if there exists a valid sequence, there exists one with no more than $$$1000$$$ operations.
  • The second line contains $$$k$$$ integers $$$a_1,a_2,\ldots,a_k$$$ ($$$1 \le a_i \lt n$$$), where $$$a_i$$$ represents the index chosen for the $$$i$$$-th operation.

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

Example
Input
4
5
01010
2
10
10
0111100100
3
000
Output
YES
2
1 3
NO
YES
9
7 7 7 7 4 3 2 1 1
YES
0