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 os,io
input=io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
t=int(input())
for _ in range(t):
    n=int(input())
    p=list(map(int,input().split()))
    sum1=0
    ans1=[]
    ans1.append(p[0])
    increasing=1
    for i in range(1,n):
        if increasing==1 and p[i]>ans1[-1]:
            ans1[-1]=p[i]
            continue
        if increasing==0 and p[i]<ans1[-1]:
            ans1[-1]=p[i]
            continue
        increasing=1-increasing
        ans1.append(p[i])
    for i in range(len(ans1)-1):
        sum1+=abs(ans1[i+1]-ans1[i])
    sum2=0
    ans2=[]
    ans2.append(p[0])
    increasing=0
    for i in range(1,n):
        if increasing==1 and p[i]>ans2[-1]:
            ans2[-1]=p[i]
            continue
        if increasing==0 and p[i]<ans2[-1]:
            ans2[-1]=p[i]
            continue
        increasing=1-increasing
        ans2.append(p[i])
    for i in range(len(ans2)-1):
        sum2+=abs(ans2[i+1]-ans2[i])
    if sum1>sum2 or ((sum1==sum2) and len(ans1)<len(ans2)):
        a=[]
        for i in range(len(ans1)):
            a.append(str(ans1[i]))
        print(len(ans1))
        print(' '.join(a))
    else:
        a=[]
        for i in range(len(ans2)):
            a.append(str(ans2[i]))
        print(len(ans2))
        print(' '.join(a))