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 sys import stdin

A=int(stdin.readline())

for t in range(0,A):
    B=int(stdin.readline())
    C=stdin.readline().split()
    temp1=int(C[0])
    temp2=int(C[0])
    ans=1
    ANS=list()
    ANS.append(int(C[0]))
    hint=temp2-temp1

    for u in range(1,B):
        temp1=temp2
        temp2=int(C[u])

        if temp1==temp2:
            continue
        else:
            if hint==0:
                hint+=(temp2-temp1)
            elif hint>0:
                if temp2>temp1:
                    hint+=(temp2-temp1)
                if temp1>temp2:
                    ans+=1
                    ANS.append(temp1)
                    hint=(temp2-temp1)
            elif hint<0:
                if temp1>temp2:
                    hint+=(temp2-temp1)
                if temp1<temp2:
                    ANS.append(temp1)
                    ans+=1
                    hint=(temp2-temp1)


    if abs(hint)>0:
        print(ans+1)
        ANS.append(int(C[len(C)-1]))
        print(' '.join(map(str, ANS)))
    else:
        if ans==1:
            print(2)
            print([C[0],C[len(C)-1]])
        else:
            print(ans)
            print(' '.join(map(str, ANS)))