## Unordered Subsequence

• 문제 ID
• 시간 제한
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• 제출 횟수
• 정답 횟수 (비율)
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#### 문제

The sequence is called ordered if it is non-decreasing (i.e. Ai <= Ai+1 for 1 <= i < N) or non-increasing (i.e. Ai >= Ai+1 for 1 <= i < N). Therefore, the sequence [1, 3, 3, 1] is not ordered.

You are given a sequence of numbers. You are to find its shortest subsequence which is not ordered. Note that subsequence does not need to be consecutive.

#### 입력

The first line of the input contains one integer T, the number of test cases.

The first line of each test case contains one integer N (1 <= N <= 10^5).
The second line contains N space-seperated integers - the given sequence.
Absolute values of numbers in input sequences do not exceed 10^6.

#### 출력

If the given sequence does not contain any unordered subsequences, output 0.

Otherwise, output the length K of the shortest such subsequence.
Then output K integers on the next line, representing indexes of the subsequence from the input sequence.

If there are several solutions, output the lexicographically earlist one.
Sequence A is lexicographically earlier than sequence B if Ai < Bi for the smallest index i such that Ai != Bi.

#### 예제 입력

3
5
67 499 600 42 23
3
1 2 3
3
2 3 1

#### 예제 출력

3
1 2 4
0
3
1 2 3