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:
# s = 'dic = {'
# c = 0
# for i in range(ord('A'),ord('X')):
# 	if chr(i) not in ['B','J','O','U']:
# 		s+= "'" + chr(i) + "':" + str(c) + ","
# 		c+=1
# s+="'" + 'Y' + "':" + str(c) + ","
# c+=1
# s+="'" + 'X' + "':" + str(c) + ","
# c = 0
# for i in range(ord('a'),ord('x')):
# 	if chr(i) not in ['b','j','o','u']:
# 		s+= "'" + chr(i) + "':" + str(c) + ","
# 		c+=1
# s+="'" + 'y' + "':" + str(c) + ","
# c+=1
# s+="'" + 'x' + "':" + str(c) + " }"
# print(s)
# n = int(input())
# b = list(map(int,input().split()))
# m = int(input())
# g = list(map(int,input().split()))
# c = 0
# b.sort()
# g.sort()
# t = [False]*m
# for i in range(n):
# 	for j in range(m):
# 		if abs(b[i]-g[j])<=1:
# 			c+=1
# 			g[j] = -500
# 			break
# print(c)
# a = list(input())
# b = list(input())
# a.sort()
# b.sort()
# print(a,b)
# x,y = 0,0
# if a>b:
# 	print(1)
# elif a<b:
# 	print(2)
# else:
# 	print(3)
# for i in range(len(a)):
# 	if ord(a[i])>ord(b[i]):
# 		x+=1
# 	elif ord(a[i])<ord(b[i]):
# 		y+=1
# 	else:
# 		x+=1
# 		y+=1
# 	print(x,y)
# if x>y:
# 	print('Wakanda')
# elif y>x:
# 	print('Kree')
# else:
# 	print('Tie')



# arr = [1]
# x = 1
# while x<=10**18:
# 	x*=2
# 	arr.append(x)
# print(arr)

# for _ in range(int(input())):
# 	p = list(map(int,input().split()))
# 	a = list(map(int,input().split()))
# 	diff = [a[0]-p[0],a[1]-p[1],a[2]-p[2]]
# 	mult = [-1]*3
# 	for i in range(3):
# 		if a[i]%p[i]==0:
# 			mult[i] = a[i]//p[i]
# 	if diff[0]==diff[1]==diff[2]:
# 		if diff[0]==0:
# 			print(0)
# 		else:
# 			print(1)
# 	elif mult[0]==mult[1]==mult[2]!=-1:
# 		print(1)
# 	elif diff[0]==diff[1]:
# 		if diff[0]==0 or diff[2]==0:
# 			print(1)
# 		else:
# 			print(2)
# 	elif diff[0]==diff[2]:
# 		if diff[0]==0 or diff[1]==0:
# 			print(1)
# 		else:
# 			print(2)
# 	elif diff[1]==diff[2]:
# 		if diff[1]==0 or diff[0]==0:
# 			print(1)
# 		else:
# 			print(2)
# 	elif mult[0]==mult[1]!=-1 or mult[0]==mult[2]!=-1 or mult[1]==mult[0]!=-1  or mult[1]==mult[2]!=-1  or mult[2]==mult[0]!=-1  or mult[2]==mult[1]!=-1 :
# 		print(2)
# 	elif (mult[0]*mult[1]==mult[2] and mult[0]!=-1 and mult[1]!=-1 and mult[2]!=-1) or (mult[1]*mult[2]==mult[0] and mult[0]!=-1 and mult[1]!=-1 and mult[2]!=-1) or (mult[0]*mult[2]==mult[1] and mult[0]!=-1 and mult[1]!=-1 and mult[2]!=-1):
# 		print(2)   
# 	elif a[0]%p[0]==a[1]%p[1] and a[0]%(a[0]%p[0]+p[0])==0 and a[1]%(a[1]%p[1]+p[1])==0 and a[2]%p[2]==0 and a[0]//(a[0]%p[0]+p[0])==a[1]%(a[1]%p[1]+p[1]):
# 		if a[2]==p[2] or a[2]//p[2]==a[0]//(a[0]%p[0]+p[0]):
# 			print(2)
# 	elif a[0]%p[0]==a[2]%p[2] and a[0]%(a[0]%p[0]+p[0])==0 and a[2]%(a[2]%p[2]+p[2])==0 and a[1]%p[1]==0 and a[0]//(a[0]%p[0]+p[0])==a[2]%(a[2]%p[2]+p[2]):
# 		if a[1]==p[1] or a[1]//p[1]==a[0]//(a[0]%p[0]+p[0]):
# 			print(2)
# 	elif a[2]%p[2]==a[1]%p[1] and a[2]%(a[2]%p[2]+p[2])==0 and a[1]%(a[1]%p[1]+p[1])==0 and a[0]%p[0]==0 and a[2]//(a[2]%p[2]+p[2])==a[1]%(a[1]%p[1]+p[1]):
# 		if a[0]==p[0] or a[0]//p[0]==a[2]//(a[2]%p[2]+p[2]):
# 			print(2)
# 	elif a[0]//p[0]==a[1]//p[1] and a[0]-(a[0]//p[0])*p[0] == a[1]-(a[1]//p[1])*p[1] == a[2]-p[2]:
# 		if a[2]==p[2]:
# 			print(1)
# 		else:
# 			print(2)
# 	elif a[0]//p[0]==a[2]//p[2] and a[0]-(a[0]//p[0])*p[0] == a[2]-(a[2]//p[2])*p[2] == a[1]-p[1]:
# 		if a[1]==p[1]:
# 			print(1)
# 		else:
# 			print(2)
# 	elif a[2]//p[2]==a[1]//p[1] and a[2]-(a[2]//p[2])*p[2] == a[1]-(a[1]//p[1])*p[1] == a[0]-p[0]:
# 		if a[0]==p[0]:
# 			print(1)
# 		else:
# 			print(2)
# 	elif a[0]==a[1]==a[2] and p[0]==p[1]!=p[2] or p[0]==p[2]!=p[1] or p[0]!=p[1]==p[2] or p[0]!=p[1]!=p[2]:
# 		print(2)
# 	else:
# 		print(3)

for _ in range(int(input())):
	n = int(input())
	arr = list(map(int,input().split()))
	ans = arr[:]
	if n==2:
		print(2)
		print(*arr)
	else:
		for i in range(1,n-1):
			if arr[i-1]<arr[i]>arr[i+1] or arr[i-1]>arr[i]<arr[i+1]:
				continue
			else:
				ans[i] = 0
				arr[i] = arr[i-1]
		t = []
		for i in ans:
			if i > 0:
				t.append(i)
		print(len(t))
		print(*t)