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 math


def process_test_case(i_t):
    n = int(input())
    p_vec = list(map(int, input().split()))

    first = p_vec[0]
    last = p_vec[-1]
    out_vec = [p_vec[0]]

    i = 0
    j = 1
    while i + j < n:
        i_diff = p_vec[i + 1] - p_vec[i]
        while i + j < n and i_diff * (p_vec[i + j] - p_vec[i + j - 1]) > 0:
            j += 1
        #while i + j < n and (p_vec[i] < p_vec[i + j - 1] <= p_vec[i + j] or p_vec[i] > p_vec[i + j - 1] >= p_vec[i + j]):
        #    j += 1
        if i + j < n:
            out_vec.append(p_vec[i + j - 1])
            i = i + j - 1
            j = 1
        else:
            out_vec.append(p_vec[-1])
            i = n

    print(len(out_vec))
    print(' '.join([str(x) for x in out_vec]))

    return None


n_tests = int(input())
for i_test in range(1, n_tests + 1):
    process_test_case(i_test)