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 sys
for _ in range(int(input())):
    n= int(input())
    p = list(map(int, input().split()))
    if(n==2):
        print(2)
        print(*p)
        continue
    v = [1]*n
    v1 = p[0]
    v1i = 0
    v2 = p[1]
    v2i = 1
    i=2
    while(i<n):
        if(((v1-v2) <= 0 and (v2-p[i])<=0) or ((v1-v2)>= 0 and (v2-p[i])>=0)):
            v[v2i] = 0
            v[v1i] = 1
            v2 = p[i]
            v2i = i
            i+=1
        else:
            v1 = v2
            v[v1i] = 1
            v[v2i] = 1
            v1i = v2i
            v2 = p[i]
            v2i = i
            i+=1
    su = sum(v)
    print(su)
    arr = [0]*su
    c = 0
    for i in range(0,n):
        if(v[i] == 1):
            arr[c] = p[i]
            c+=1
    print(*arr)