distanced subsequence

Given a permutation p of length n, find its subsequence s_1, s_2, …, s_k of length at least 2 such that:

• |s_1-s_2|+|s_2-s_3|+…+|s_{k-1}-s_k| is as big as possible over all subsequences of p with length at least 2.
• Among all such subsequences, choose the one whose length, k, is as small as possible.

If multiple subsequences satisfy these conditions, you are allowed to find any of them.

A sequence a is a subsequence of an array b if a can be obtained from b by deleting some (possibly, zero or all) elements.

A permutation of length n is an array of length n in which every element from 1 to n occurs exactly once.

Input

The first line contains an integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer n (2 ≤ n ≤ 10^5) — the length of the permutation p.

The second line of each test case contains n integers p_1, p_2, …, p_{n} (1 ≤ p_i ≤ n, p_i are distinct) — the elements of the permutation p.

The sum of n across the test cases doesn't exceed 10^5.

Output

For each test case, the first line should contain the length of the found subsequence, k. The second line should contain s_1, s_2, …, s_k — its elements.

If multiple subsequences satisfy these conditions, you are allowed to find any of them.

Example

Input

2 3 3 2 1 4 1 3 4 2

Output

2 3 1 3 1 4 2

Note

In the first test case, there are 4 subsequences of length at least 2:

• [3,2] which gives us |3-2|=1.
• [3,1] which gives us |3-1|=2.
• [2,1] which gives us |2-1|=1.
• [3,2,1] which gives us |3-2|+|2-1|=2.

So the answer is either [3,1] or [3,2,1]. Since we want the subsequence to be as short as possible, the answer is [3,1].

inputFormat

Input

The first line contains an integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer n (2 ≤ n ≤ 10^5) — the length of the permutation p.

The second line of each test case contains n integers p_1, p_2, …, p_{n} (1 ≤ p_i ≤ n, p_i are distinct) — the elements of the permutation p.

The sum of n across the test cases doesn't exceed 10^5.

outputFormat

Output

For each test case, the first line should contain the length of the found subsequence, k. The second line should contain s_1, s_2, …, s_k — its elements.

If multiple subsequences satisfy these conditions, you are allowed to find any of them.

Example

Input

2 3 3 2 1 4 1 3 4 2

Output

2 3 1 3 1 4 2

Note

In the first test case, there are 4 subsequences of length at least 2:

• [3,2] which gives us |3-2|=1.
• [3,1] which gives us |3-1|=2.
• [2,1] which gives us |2-1|=1.
• [3,2,1] which gives us |3-2|+|2-1|=2.

So the answer is either [3,1] or [3,2,1]. Since we want the subsequence to be as short as possible, the answer is [3,1].

样例

2
3
3 2 1
4
1 3 4 2

2
3 1
3
1 4 2

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