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.Arrays;
import java.util.Comparator;
import java.util.Scanner;

import javax.lang.model.util.ElementScanner6;

public class Solution {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int t = in.nextInt();
        in.nextLine();
        for (int z = 0; z < t; z++) {
            int n = in.nextInt();
            int[] a = new int[n];
            int size = 1;
            if (n == 2) {
                System.out.println(2);
                System.out.println(in.nextInt() + " " + in.nextInt());
            } else {
                int n1 = in.nextInt();
                a[0] = n1;
                int n2 = in.nextInt();
                int n3 = 0;
                for (int i = 2; i < n; i++) {
                    n3 = in.nextInt();
                    if ((n2 > n1 && n2 > n3) || (n2 < n1 && n2 < n3)) {
                        a[size] = n2;
                        size++;
                    }
                    n1 = n2;
                    n2 = n3;
                }
                a[size] = n3;
                size++;
                System.out.println(size);
                for (int i = 0; i < size; i++) {
                    System.out.print(a[i] + " ");
                }
                System.out.println("");
            }
        }

        in.close();
    }

}