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 queue import LifoQueue


def print_sol(c, sol):
    print('Case #{}: {}'.format(c, sol))


def rd_int():
    return int(input())


def rd_str():
    return input()


def rd_str_lst():
    return input().split(' ')


def sp_str_lst():
    return list(input())


def rd_int_lst():
    return [int(i) for i in rd_str_lst()]


def sp_int_lst():
    return [int(i) for i in sp_str_lst()]


def dfs(g, i, v):
    """
    recursive post order dfs
    Args:
        g: array of graph nodes
        i: node to traverse
        v: visited array

    Returns: a post order dfs of graph g
    """
    v[i] = True
    for j in g[i]:
        if not v[j]:
            dfs(g, j, v)

    print(i)


def dfs_iter(g, i, n):
    v = [False] * n
    stack = LifoQueue()
    stack.put(i)
    while stack.not_empty:
        u = stack.get()
        v[u] = True
        print(u)
        for i in g[u]:
            if not v[i]:
                stack.put(i)


def main():
    t = rd_int()

    for c in range(1, t + 1):
        n = rd_int()
        p = rd_int_lst()

        inc = True if p[1] > p[0] else False
        s = [0] * n
        s[0] = p[0]
        k = 1
        for i in range(2, n):
            if inc:
                if p[i] > p[i - 1]:
                    continue
                else:
                    inc = False
                    s[k] = p[i - 1]
                    k += 1
            else:
                if p[i] < p[i - 1]:
                    continue
                else:
                    inc = True
                    s[k] = p[i - 1]
                    k += 1
        s[k] = p[n - 1]
        k += 1
        print(k)
        print(*s[:k])


if __name__ == '__main__':
    main()