Given a permutation $p$ of length $n$, find its subsequence $s_1$, $s_2$, $\ldots$, $s_k$ of length at least $2$ such that:  $|s_1-s_2|+|s_2-s_3|+\ldots+|s_{k-1}-s_k|$ 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 $t$ ($1 \le t \le 2 \cdot 10^4$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer $n$ ($2 \le n \le 10^5$) — the length of the permutation $p$.

The second line of each test case contains $n$ integers $p_1$, $p_2$, $\ldots$, $p_{n}$ ($1 \le p_i \le n$, $p_i$ 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 $s_1$, $s_2$, $\ldots$, $s_k$ — 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 $[3,1]$.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'for t in range(int(input())):\n    n = int(input())\n    a = list(map(int, input().split()))\n    b = [a[0]] + [a[i] for i in range(1, n - 1) if not(a[i - 1] < a[i] < a[i + 1] or \n                                                   a[i - 1] > a[i] > a[i + 1])] + [a[-1]]\n    print(len(b))\n    print(*b)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13073