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, stdout

int_in = lambda: int(stdin.readline())
arr_in = lambda: [int(x) for x in stdin.readline().split()]
mat_in = lambda rows: [arr_in() for y in range(rows)]
str_in = lambda: stdin.readline().strip()
out = lambda o: stdout.write("{}\n".format(o))
arr_out = lambda o: out(" ".join(map(str, o)))
bool_out = lambda o: out("YES" if o else "NO")
tests = lambda: range(1, int_in() + 1)
case_out = lambda i, o: out("Case #{}: {}".format(i, o))


def solve(n, p):
    result = [p[0]]
    going_down = p[0] - p[1] > 0
    for i in range(1, n):
        if going_down and p[i-1] - p[i] < 0:
            going_down = False
            result.append(p[i - 1])
        elif not going_down and p[i - 1] - p[i] > 0:
            going_down = True
            result.append(p[i - 1])
    result.append(p[-1])
    return result

if __name__ == "__main__":
    for i in tests():
        n = int_in()
        p = arr_in()
        result = solve(n, p)
        out(len(result))
        arr_out(result)