Given an integer sequence $$$a$$$ of length $$$n$$$ with values in $$$[0,2]$$$.
An operation is defined as choosing an index $$$x\in [1,n-2]$$$:
- Let $$$s=(a_x+a_{x+1}+a_{x+2})\bmod 3$$$, then set $$$a_x,a_{x+1},a_{x+2}$$$ all to $$$s$$$ simultaneously.
You need to perform some operations (possibly none) to maximize the sum of all elements in sequence $$$a$$$. Additionally, you must provide a valid operation sequence whose length does not exceed $$$\lfloor\dfrac{5}{7}n\rfloor+100$$$.
This problem has multiple test cases.
The first line contains an integer $$$T$$$ — the number of test cases.
For each test case:
The first line contains an integer $$$n$$$ — the length of sequence $$$a$$$.
The second line contains $$$n$$$ integers, where the $$$i$$$-th integer is $$$a_i$$$.
For each test case:
The first line should contain two integers $$$s$$$ and $$$K$$$ — the maximum sum of the sequence and the number of operations, respectively. You must ensure $$$0\le K\le \lfloor\dfrac{5}{7}n\rfloor+100$$$.
The next line should contain $$$K$$$ positive integers, where the $$$i$$$-th integer is the index $$$x$$$ chosen in the $$$i$$$-th operation.
330 1 050 2 1 2 271 1 1 1 1 1 1
3 1 1 10 4 2 2 3 1 14 5 1 3 4 5 1
For $$$100\%$$$ of the data, it is guaranteed that $$$1\le T\le 1000$$$, $$$\sum n\le 10^6$$$, $$$3\le n\le 10^6$$$, $$$0\le a_i\le 2$$$.
