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:
t = int(input())
for _ in range(t):
    n1 = int(input())
    a= list(map(int,input().split()))
    g = []
    inc = -1
    c=0
    n=0
    # f = a[i-1]
    for i in range(1,n1):
        if a[i]>a[i-1]:
            if n>0:
                g.append(f)
                # g.append(a[i-1])
                n=0
                c=1
                inc=0
                f=a[i-1]
            elif inc==0:
                c+=1
            elif c==0:
                inc=0
                c=1
                f = a[i-1]
        else:
            if c>0:
                g.append(f)
                # g.append(a[i-1])
                inc=1
                c=0
                n=1
                inc=1
                f=a[i-1]
            elif inc==1:
                n+=1
            elif n==0:
                inc=1
                n=1
                f=a[i-1]

    if n==0 and c>=1:
        g.append(f)
        g.append(a[i])
    if c==0 and n>=1:
        g.append(f)
        g.append(a[i])
    print(len(g))
    print(*g, sep=" ")