Jesse's Job

You had one thing to do, one thing! That is the only thing, I might add, that might have saved our lives.

• Walter White, Breaking Bad

Jesse has a permutation $p_1, p_2, \ldots, p_n$ of integers from $1$ to $n$. His job is simple: to maximize the number of positions $i$, for which $p_i = i$. To achieve that, Jesse can do the following operation exactly once:

• Color some elements of the permutation in yellow, and all the remaining elements in blue. There has to be at least one yellow and at least one blue element.
• Then, separately sort yellow and blue numbers.

For example, for permutation $(3, 5, 1, 6, 2, 4)$, Jesse can mark numbers $3, 5, 4$ yellow, and $1, 6, 2$ blue. After sorting yellow and blue elements separately, Jesse will get permutation $(3, 4, 1, 2, 6, 5)$.

Jesse's score in the end is the number of positions $i$, for which $p_i = i$. Find the maximal score Jesse can achieve and some way to achieve it.

Input data

The first line contains a single integer $t$ ($1 \le t \le 10^5$) - the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $n$ ($2 \leq n \leq 10^6$) - the length of the permutation.

The second line of each test case contains $n$ integers $p_1, p_2, \ldots, p_n$ ($1 \le p_i \le n$, all $p_i$ are distinct) - elements of the permutation.

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^6$.

Output data

For every test case, in the first line, output the maximal score Jesse can achieve.

In the second line, output a single integer $k$ ($1 \le k \le n-1$) - the number of elements Jesse should color yellow.

In the third line, output $k$ integers $pos_1, pos_2, \ldots, pos_k$ ($1 \le pos_i \le n$, all $pos_i$ are distinct) - the positions of elements that you are going to color in yellow.

If there are several ways to obtain the maximum score, output any of them.

Example

stdin

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

stdout

0
1
1 
4
2
1 2 
4
3
1 3 4 

Explanation

In the first test case, for permutation $(p_1, p_2) = (2, 1)$, Jesse can mark $p_1$ yellow and $p_2$ blue. After sorting it will remain being $(2, 1)$, with score $0$.

In the second test case, for permutation $(p_1, p_2, p_3, p_4) = (2, 1, 4, 3)$, Jesse can mark $p_1, p_2$ yellow and $p_3, p_4$ blue. After sorting the permutation will become $(1, 2, 3, 4)$, with score $4$.