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;
long long t, n, p;
int main() {
  cin.sync_with_stdio(0);
  cin.tie();
  cin.exceptions(cin.failbit);
  cin >> t;
  for (int i = 1; i <= t; i++) {
    cin >> n;
    vector<int> arr;
    for (int j = 1; j <= n; j++) {
      cin >> p;
      arr.push_back(p);
    }
    if (arr.size() == 2) {
      cout << 2 << endl << arr[0] << " " << arr[1] << endl;
      continue;
    }
    long long sl = arr[0];
    long long l = arr[1];
    stack<long long> s;
    s.push(sl);
    s.push(l);
    for (int i = 2; i <= n - 1; i++) {
      int curr = arr[i];
      if ((curr - l) * (l - sl) >= 0) {
        s.pop();
      } else {
        sl = l;
      }
      s.push(curr);
      l = curr;
    }
    vector<int> sub;
    while (!s.empty()) {
      sub.push_back(s.top());
      s.pop();
    }
    reverse(begin(sub), end(sub));
    cout << sub.size() << endl;
    for (auto& k : sub) {
      cout << k << " ";
    }
    cout << endl;
  }
}