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:

#from collections import Counter,defaultdict,deque
#from heapq import *
#from itertools import *
#from operator import itemgetter
#from itertools import count, islice
#from functools import reduce
#alph = 'abcdefghijklmnopqrstuvwxyz'
#dirs = [[1,0],[0,1],[-1,0],[0,-1]]
#from math import factorial as fact
#a,b = [int(x) for x in input().split()]
#sarr = [x for x in input().strip().split()]
#import math
#from math import *

import sys
input=sys.stdin.readline
#sys.setrecursionlimit(2**30)
#MOD = 10**9+7

def solve():
    #n,x = [int(x) for x in input().split()]
    n = int(input())
    arr = [int(x) for x in input().split()]
    ans = [arr[0]]
    for i in range(1,n-1):
        if not (arr[i-1]<arr[i]<arr[i+1] or arr[i-1]>arr[i]>arr[i+1]):
            ans.append(arr[i])
    ans.append(arr[-1])
    print(len(ans))
    print(*ans)
    
    
tt = int(input())
for test in range(tt):
    solve()
 
 


 
 
 
 
 
 
 
 
 
 
 
 
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