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 JAVA):

Solution:
import java.util.*;
 
public class Main {
    private static final Scanner sc = new Scanner(System.in);
 
    public static void solve() {
        int n = sc.nextInt();
        int[] arr = new int[n];
        for (int i = 0; i < n; i++)
            arr[i] = sc.nextInt();
 
        int i = 0, j = 0;
        List<Integer> vec = new ArrayList<>();
        vec.add(arr[0]);
        while (j < n) {
            while (j < n - 1 && arr[j] <= arr[j + 1]) {
                j++;
            }
 
            if (j != i) {
                vec.add(arr[j]);
                i = j;
            } else {
                while (j < n - 1 && arr[j] >= arr[j + 1]) {
                    j++;
                }
 
                if (j != i) {
                    vec.add(arr[j]);
                    i = j;
                }
            }
 
            if (j == n - 1)
                break;
        }
 
        int len = vec.size();
        System.out.println(len);
 
        for (int k = 0; k < len; k++) {
            System.out.print(vec.get(k));
            System.out.print(" ");
        }
        System.out.println("");
    }
 
    public static void main(String[] args) {
        int t = sc.nextInt();
        while (t-- > 0)
            solve();
    }
}