You have a sequence $$$a_1, a_2, \ldots, a_n$$$ of length $$$n$$$, each element of which is either $$$0$$$ or $$$1$$$, and a sequence $$$b$$$, which is initially empty.

You are going to perform $$$n$$$ operations. On each of them you will increase the length of $$$b$$$ by $$$1$$$.

On the $$$i$$$-th operation you choose an integer $$$p$$$ between $$$0$$$ and $$$i-1$$$. You insert $$$0$$$ in the sequence $$$b$$$ on position $$$p+1$$$ (after the first $$$p$$$ elements), and then you invert the first $$$p$$$ elements of $$$b$$$.
More formally: let's denote the sequence $$$b$$$ before the $$$i$$$-th ($$$1 \le i \le n$$$) operation as $$$b_1, b_2, \ldots, b_{i-1}$$$. On the $$$i$$$-th operation you choose an integer $$$p$$$ between $$$0$$$ and $$$i-1$$$ and replace $$$b$$$ with $$$\overline{b_1}, \overline{b_2}, \ldots, \overline{b_{p}}, 0, b_{p+1}, b_{p+2}, \ldots, b_{i-1}$$$. Here, $$$\overline{x}$$$ denotes the binary inversion. Hence, $$$\overline{0} = 1$$$ and $$$\overline{1} = 0$$$.

You can find examples of operations in the Notes section.

Determine if there exists a sequence of operations that makes $$$b$$$ equal to $$$a$$$. If such sequence of operations exists, find it.

Input

Each test contains multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

The first line of each test case contains one integer $$$n$$$ ($$$1 \le n \le 10^5$$$) — the length of the sequence $$$a$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 1$$$) — the sequence $$$a$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.

Output

For each test case:

output "NO", if it is impossible to make $$$b$$$ equal to $$$a$$$ using the given operations;
otherwise, output "YES" in the first line and $$$n$$$ integers $$$p_1, p_2, \ldots, p_n$$$ ($$$0 \le p_i \le i-1$$$) in the second line — the description of sequence of operations that makes $$$b$$$ equal to $$$a$$$. Here, $$$p_i$$$ should be the integer you choose on the $$$i$$$-th operation. If there are multiple solutions, you can output any of them.

Note

In the first test case,

Before the first operation, $$$b = [\,]$$$. You choose $$$p = 0$$$ and replace $$$b$$$ with $$$[\, \underline{0} \,]$$$
On the second operation you choose $$$p = 0$$$ and replace $$$b$$$ with $$$[\, \underline{0}, 0 \,]$$$.
On the third operation you choose $$$p = 2$$$ and replace $$$b$$$ with $$$[\, 1, 1, \underline{0} \,]$$$.
On the fourth operation you choose $$$p = 1$$$ and replace $$$b$$$ with $$$[\, 0, \underline{0}, 1, 0 \,]$$$.
On the fifth operation you choose $$$p = 3$$$ and replace $$$b$$$ with $$$[\, 1, 1, 0, \underline{0}, 0 \,]$$$.

Hence, sequence $$$b$$$ changes in the following way: $$$[\,]$$$ $$$\xrightarrow{p \, = \, 0}$$$ $$$[\, \underline{0} \,]$$$ $$$\xrightarrow{p \, = \, 0}$$$ $$$[\, \underline{0}, 0 \,]$$$ $$$\xrightarrow{p \, = \, 2}$$$ $$$[\, 1, 1, \underline{0} \,]$$$ $$$\xrightarrow{p \, = \, 1}$$$ $$$[\, 0, \underline{0}, 1, 0 \,]$$$ $$$\xrightarrow{p \, = \, 3}$$$ $$$[\, 1, 1, 0, \underline{0}, 0 \,]$$$. In the end the sequence $$$b$$$ is equal to the sequence $$$a$$$, so this way to perform operations is one of the correct answers.

In the second test case, $$$n = 1$$$ and the only achiveable sequence $$$b$$$ is $$$[\, 0 \, ]$$$.

In the third test case, there are six possible sequences of operations:

$$$[\,]$$$ $$$\xrightarrow{p \, = \, 0}$$$ $$$[\, \underline{0} \,]$$$ $$$\xrightarrow{p \, = \, 0}$$$ $$$[\, \underline{0}, 0 \,]$$$ $$$\xrightarrow{p \, = \, 0}$$$ $$$[\, \underline{0}, 0, 0 \,]$$$.
$$$[\,]$$$ $$$\xrightarrow{p \, = \, 0}$$$ $$$[\, \underline{0} \,]$$$ $$$\xrightarrow{p \, = \, 0}$$$ $$$[\, \underline{0}, 0 \,]$$$ $$$\xrightarrow{p \, = \, 1}$$$ $$$[\, 1, \underline{0}, 0 \,]$$$.
$$$[\,]$$$ $$$\xrightarrow{p \, = \, 0}$$$ $$$[\, \underline{0} \,]$$$ $$$\xrightarrow{p \, = \, 0}$$$ $$$[\, \underline{0}, 0 \,]$$$ $$$\xrightarrow{p \, = \, 2}$$$ $$$[\, 1, 1, \underline{0} \,]$$$.
$$$[\,]$$$ $$$\xrightarrow{p \, = \, 0}$$$ $$$[\, \underline{0} \,]$$$ $$$\xrightarrow{p \, = \, 1}$$$ $$$[\, 1, \underline{0} \,]$$$ $$$\xrightarrow{p \, = \, 0}$$$ $$$[\, \underline{0}, 1, 0 \,]$$$.
$$$[\,]$$$ $$$\xrightarrow{p \, = \, 0}$$$ $$$[\, \underline{0} \,]$$$ $$$\xrightarrow{p \, = \, 1}$$$ $$$[\, 1, \underline{0} \,]$$$ $$$\xrightarrow{p \, = \, 1}$$$ $$$[\, 0, \underline{0}, 0 \,]$$$.
$$$[\,]$$$ $$$\xrightarrow{p \, = \, 0}$$$ $$$[\, \underline{0} \,]$$$ $$$\xrightarrow{p \, = \, 1}$$$ $$$[\, 1, \underline{0} \,]$$$ $$$\xrightarrow{p \, = \, 2}$$$ $$$[\, 0, 1, \underline{0} \,]$$$.

None of them makes $$$b$$$ equal to $$$[\, 0, 1, 1 \,]$$$, so the answer is "NO".

Insert Zero and Invert Prefix

Examples