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:
# https://codeforces.com/problemset/problem/1364/B

import sys
import os
import heapq
import math

try:
    path = "./file/input.txt"
    if os.path.exists(path):
        sys.stdin = open(path, 'r')
    # sys.stdout = open(r"./file/output.txt", 'w')
except:
    pass

t = int(input())

def printd(value):
    # print(value)
    pass

def case():
    # The first line contains an integer 𝑡 (1≤𝑡≤2⋅104) — 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≤105) — the length of the permutation 𝑝.
    # The second line of each test case contains 𝑛 integers 𝑝1, 𝑝2, …, 𝑝𝑛 (1≤𝑝𝑖≤𝑛, 𝑝𝑖 are distinct) — the elements of the permutation 𝑝.
    # The sum of 𝑛 across the test cases doesn't exceed 105.

    n = int(input())
    p = list(map(int, input().split(" ")))
    #  𝑛, 𝑥 and 𝑚

    first = p[0]
    result = [first]
    for index in range(2, n):
        value = p[index]
        last = p[index - 1]
        if not ((first > last and last > value) or (first < last and last < value)):
            result.append(last)
            first = last

    result.append(p[n-1])
        
    print(len(result))
    print(" ".join(str(i) for i in result))
    
for _ in range(t):
    case()