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:
#!/usr/bin/python3

import getopt
import sys
import math

if __name__ == "__main__":
    onlyCase = -1
    verbose = False
    
    try:
         opts, args = getopt.getopt(sys.argv[1:], "vc:",
                                   ["case="])
    except getopt.GetoptError as err:
        print (str(err)) 
        sys.exit(2)

    for o, a in opts:
        if o in ("-c", "--case"):
            onlyCase = int(a)
        elif o  == "-v":
            verbose = True
        else: sys.exit()

    
    ncases = int(input())
    for c in range(1, ncases + 1):
        _ = input()

        A = [int(x) for x in input().split()]
        
        if onlyCase != -1 and onlyCase != c:
            continue

        N = []
        N.append(A[0])
        
        for i in range(1,len(A)-1):
            if N[-1] < A[i] and A[i] < A[i+1]:
                continue
            if N[-1] > A[i] and A[i] > A[i+1]:
                continue
            N.append(A[i])
            
        N.append(A[-1])

        print("%d\n%s" % (len(N), ' '.join(map(str,N))))