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:
for _ in range(int(input())):
    i_liczb = int(input())
    liczby = [int(x) for x in input().split()]
    if i_liczb == 2:
        print(i_liczb)
        print(*liczby)
        continue
    wyniki = []
    l1, l2, l3 = liczby[0] , liczby[1] , liczby[2]
    for x in range(3, i_liczb):
        if l1 <= l2 <= l3 or l1 >= l2 >= l3:
            l2 = l3
            l3 = liczby[x]
            #print("dupa")
        else:
            wyniki.append(l1)
            #print("dodajemy", l1)
            l1 = l2
            l2 = l3
            l3 = liczby[x]
    wyniki.append(l1)
    #print(l1, l2, l3)
    if not (l1 <= l2 <= l3 or l1 >= l2 >= l3):
        #print("duperele")
        wyniki.append(l2)
    wyniki.append(l3)
    print(len(wyniki))
    print(*wyniki)