Problem: 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].

Solution (in PYTHON3):

Solution:
cases = int(input())

for i in range(cases):
    l1 = int(input())
    l2 = input().split(' ')
    arr = []
    for j in l2:
        arr.append(int(j))
    ans = []
    index = []
    start = 0
    transition = 0
    inc = False
    dec = False
    while start < len(arr)-1:
        ele1 = arr[start]
        ele2 = arr[start+1]
        if transition == 0:
            if ele1 > ele2:
                dec = True
                transition += 1
                index.append(start)
            elif ele2 > ele1:
                inc = True
                transition += 1
                index.append(start)
        elif transition == 1:
            if inc:
                if ele2 < ele1:
                    index.append(start)
                    dec = True
                    inc = False
            elif dec:
                if ele2>ele1:
                    index.append(start)
                    inc = True
                    dec = False
        start += 1
    if transition == 1:
        if index[-1]!= len(arr)-1:
            index.append(len(arr)-1)
    for ind in index:
        ans.append(str(arr[ind]))
    print (len(ans))
    print (' '.join(ans))