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  
import collections
import heapq
import itertools
import functools
import math
import operator
import string

ALPHABET = string.ascii_lowercase
DIGITS = string.digits

def read_line():
    return stdin.readline().strip()
def read_int():
    return int(read_line())
def read_arr():
    return read_line().split(' ')
def read_int_arr():
    return [int(x) for x in read_arr()]
def query_interactive(s):
    print(s)
    stdout.flush()

def solve():
    n = read_int()
    p = read_int_arr()
    res = []
    for i in range(n):
        if i == 0 or i == n - 1:
            res.append(p[i])
        else:
            if p[i] > p[i - 1] and p[i] > p[i + 1]:
                res.append(p[i])
            elif p[i] < p[i - 1] and p[i] < p[i + 1]:
                res.append(p[i])
    print(len(res))
    print(*res, sep= ' ')

def main():
    T = 1
    T = read_int()
    for _ in range(T):
        solve()

if __name__ == "__main__":
    main()