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:
def check(l):
    if(len(l)==2):
        print(2)
        for i in range(2):
            if(i==1):
                print(l[i])
            else:
                print(l[i],end=" ")
    else:

        to_send=[l[0]]
        curr=l[0]
        for i in range(1,len(l)-1):
            if(curr<l[i] and l[i]<=l[i+1]):
                if(i+1==len(l)-1):
                    to_send.append(l[i+1])
                curr=l[i]
                continue
            elif(curr>l[i] and l[i]>=l[i+1]):
                if(i+1==len(l)-1):
                    to_send.append(l[i+1])
                curr=l[i]
                continue
            elif(curr>l[i] and l[i]<l[i+1]):
                if(i+1==len(l)-1):
                    to_send.append(l[i])
                    to_send.append(l[i+1])
                else:
                    to_send.append(l[i])
            elif(curr<l[i] and l[i]>l[i+1]):
                if(i+1==len(l)-1):
                    to_send.append(l[i])
                    to_send.append(l[i+1])
                else:
                    to_send.append(l[i])
            curr=l[i]
        k=len(to_send)
        print(k)
        for i in range(len(to_send)):
            if(i==k-1):
                print(to_send[i])
            else:
                print(to_send[i],end=" ")
t=int(input())
for i in range(t):
    n=int(input())
    l=list(map(int,input().strip().split()))
    check(l)