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 math
# n,m=map(int,input().split())
# print(-n//a)
# print(m//a)
# print(math.ceil(m/a)*math.ceil(n/a))
# for _ in range(int(input())):
# 	n,m=map(int,input().split())
# 	a=abs(n-m)
# 	b=a//5
# 	c=(a%5)//2
# 	d=a%5%2
# 	print(b+c+d)
	# n=int(input())
	# print(((n**3)-n)//3)
# for _ in range(int(input())):
# 	n,m=map(int,input().split())
# 	a=list(map(int,input().split()))
# 	s=sum(a)
# 	if(s%m):
# 		print(n)
# 	else:
# 		l=-1
# 		r=0
# 		for i in range(0,n):
# 			if(a[i]%m):
# 				if(l==-1):
# 					l=i
# 				r=i
# 		if(l==-1):
# 			print(-1)
# 		else:
# 			print(n-min(l+1,n-r))
# for q in range(int(input())):
# 	a,b=input().split()
# 	a=int(a)
# 	b=int(b)
# 	ans=abs(a-b)
# 	if(a==b):
# 		print(0)
# 	else:
# 		print(ans//5+(ans%5)//2 +ans%5%2)
for q in range(int(input())):
	n=int(input())
	a=list(map(int,input().split()))
	b=[]
	
	for i in range(n):
		if(i==0 or i==n-1 or((a[i]>a[i-1])!=(a[i+1]>a[i]))):
			b.append(a[i])
	print(len(b))
	print(*b)