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:
import itertools
def brute(arr):
    n = len(arr)
    resultCmp = 0
    result = []
    for k in range(n, 1, -1):
        for combo in itertools.combinations(arr, k):
            subseq = list(combo)
            currCmp = 0
            for i in range(len(subseq) - 1):
                currCmp += abs(subseq[i] - subseq[i+1])
            # print(combo, currCmp)
            if currCmp >= resultCmp:
                resultCmp = currCmp
                result = subseq
    return result

def soln(arr):
    result = [arr[0]]
    currNum = arr[1]
    if arr[1] > arr[0]:
        goingUp = True
    else:
        goingUp = False
    for i in range(2, len(arr) - 1):
        num = arr[i]
        if goingUp:
            if num > currNum:
                currNum = num
            else:
                result.append(currNum)
                currNum = num
                goingUp = False
        else:
            if num < currNum:
                currNum = num
            else:
                result.append(currNum)
                currNum = num
                goingUp = True
    if currNum not in [0, float('inf')]:
        if goingUp and currNum > arr[-1]:
            result.append(currNum)
        elif not goingUp and currNum < arr[-1]:
            result.append(currNum)
    result.append(arr[-1])
    return result

def test():
    # arr = [3, 2, 1]
    # arr = [1, 3, 4, 2]
    # arr = [6, 3, 4, 2, 5, 1]
    arr = [4, 3, 1, 2, 5]
    b = brute(arr)
    f = soln(arr)
    print(b, f)

def randomTest():
    import random
    # t = 1000
    t = 2*10**4
    for i in range(1, t + 1):
        # n = random.randint(2, 15)
        # arr = list(range(1, n+1))
        # random.shuffle(arr)
        # print(i, arr)
        # b = brute(arr)
        # f = soln(arr)
        # # print(i, arr, b, f)
        # if b != f:
        #     print('Broken!')
        #     print(b, f)
        #     return
        
        n = random.randint(2, 10**5)
        arr = list(range(1, n+1))
        random.shuffle(arr)
        print(i)
        f = soln(arr)

def main():
    t = int(input())
    for _ in range(t):
        n = int(input())
        arr = [int(x) for x in input().split()]
        # result = brute(arr)
        result = soln(arr)
        print(len(result))
        print(' '.join(str(x) for x in result))

main()
# test()
# randomTest()