Problem Statement

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.

Input

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
$A_1 A_2 \cdots A_N$

Output

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
$i_1 i_2 \cdots i_m$

Constraints

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

Sample Input 1

1
5
2 1 4 5 3

Sample Output 1

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.

Sample Input 2

2
6
2 5 3 4 3 4
5
10000 1000 100 1 10

Sample Output 2

5
1 3 4 5 6
2
4 5

见题面 Input 部分

见题面 Output 部分