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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const long long MOD = 1000000007;
int knigtx8[] = {2, 2, -2, -2, 1, 1, -1, -1};
int knigty8[] = {1, -1, 1, -1, 2, -2, 2, -2};
int dx8[] = {0, 0, 1, 1, 1, -1, -1, -1};
int dy8[] = {1, -1, 1, -1, 0, 0, -1, 1};
int dx4[] = {0, 0, 1, -1};
int dy4[] = {1, -1, 0, 0};
const int maxx = 100005;
bool sortinrev(const pair<int, int> &a, const pair<int, int> &b) {
  return a.first > b.first;
}
long long pw(long long a, long long b) {
  long long ans = 1;
  for (long long i = 1; i <= b; ++i) ans = (ans * a);
  return ans;
}
template <typename T>
inline T Bigmod(T base, T power, T MOD) {
  T ret = 1;
  while (power) {
    if (power & 1) ret = (ret * base) % MOD;
    base = (base * base) % MOD;
    power >>= 1;
  }
  return ret;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  ;
  int t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    int a[n + 2];
    for (int i = 1; i <= n; i++) {
      cin >> a[i];
    }
    vector<int> ans;
    int last = 1;
    ans.push_back(a[1]);
    for (int i = 2; i <= n; i++) {
      if (last == 1 and (a[i] - a[i - 1]) < 0) {
        last = 0;
        if (i != 2) {
          ans.push_back(a[i - 1]);
        }
      } else if (last == 0 and (a[i] - a[i - 1]) >= 0) {
        last = 1;
        ans.push_back(a[i - 1]);
      }
    }
    ans.push_back(a[n]);
    cout << ans.size() << endl;
    for (int i = 0; i < ans.size(); i++) cout << ans[i] << " ";
    cout << endl;
  }
  return 0;
}