You are given an integer sequence $A$ of length $N$.

For each $t = 1, 2, \dots, N$, determine whether $A_t$ is included in a longest increasing subsequence of $A$.

Here, $A_t$ is included in a longest increasing subsequence of $A$ if and only if the following holds:

-   Let $L$ be the length of a longest increasing subsequence of $A$. There exists a strictly increasing integer sequence $i = (i_1, i_2, \dots, i_L) \ (i_1 < i_2 < \dots < i_L)$, where each element is between $1$ and $N$, inclusive, that satisfies all of the following conditions:
    
    -   $A_{i_1} < A_{i_2} < \dots < A_{i_L}$.
    -   $i_k = t$ for some $k \ (1 \leq k \leq L)$.

You are given $T$ test cases; solve each of them.

What is a longest increasing subsequence?

A subsequence of a sequence $A$ is a sequence that can be derived by extracting some elements from $A$ without changing the order.

A longest increasing subsequence of a sequence $A$ is a subsequence of $A$ that is strictly increasing with the greatest possible length.

The input is given from Standard Input in the following format:

```
$T$
$\mathrm{case}_1$
$\mathrm{case}_2$
$\vdots$
$\mathrm{case}_T$
```

Here, $\mathrm{case_i}$ represents the input for the $i$\-th case. Each case is given in the following format:

```
$N$
$A_1$ $A_2$ $\cdots$ $A_N$
```

Print the answers in the following format:

```
$\mathrm{answer}_1$
$\mathrm{answer}_2$
$\vdots$
$\mathrm{answer}_T$
```

Here, $\mathrm{answer}_i$ represents the output for the $i$\-th case. For each case, let there be $m$ indices $t$ such that $A_t$ is included in a longest increasing subsequence of $A$, which are $i_1, i_2, \dots, i_m$ in ascending order. Print these in the following format:

```
$m$
$i_1$ $i_2$ $\cdots$ $i_m$
```

-   $1 \leq T \leq 2 \times 10^5$
-   $1 \leq N \leq 2 \times 10^5$
-   $1 \leq A_i \leq 10^9$
-   The sum of $N$ across all test cases is at most $2 \times 10^5$.

4
1 2 3 4

One of the longest increasing subsequences is (2,4,5), with a length of 3. Another longest increasing subsequence is (1,4,5). However, no longest increasing subsequence includes $A_5$.

Therefore, print 1,2,3,4.