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 queue 
import math

t = int(input())

while(t):

	n = int(input())
	a = list(map(int,input().split()))

	prev = a[0]
	start = a[0]
	seq1 = []
	for i in range(1,n):
		if (a[i] < prev):
			if (start != prev):
				seq1.append(start)
				seq1.append(prev)
			start = a[i]
		prev = a[i]

	if (start != prev):
		seq1.append(start)
	seq1.append(prev)

	ans1 = 0
	for i in range(len(seq1)-1):
		ans1 += abs(seq1[i]-seq1[i+1])
		
	prev = a[0]
	start = a[0]
	seq2 = []
	for i in range(1,n):
		if (a[i] > prev):
			if (start != prev):
				seq2.append(start)
				seq2.append(prev)
			start = a[i]
		prev = a[i]

	if (start != prev):
		seq2.append(start)
	seq2.append(prev)

	#print(seq2)
			
	ans2 = 0
	for i in range(len(seq2)-1):
		ans2 += abs(seq2[i]-seq2[i+1])	

	if (ans1 > ans2):
		seq = seq1
	elif (ans1 < ans2):
		seq = seq2
	else:
		if (len(seq1) < len(seq2)):
			seq = seq1
		else:
			seq = seq2

	print(len(seq))
	for x in seq:
		print(x,end=' ')
	print()


	t -= 1