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:
// package name;
import java.io.*;
import java.util.*;

public class Main {
	static final long mod = 1000000007;
	static final long lmx = 9223372036854775807l, lmn = -9223372036854775808l;
	static final int imx = 2147483647, imn = -2147483648;
	static final String Y = "YES", NO = "NO", LN = "\n", SPC = " ";
	static Scanner s = new Scanner(System.in);
	//static Reader s = new Reader();
	static PrintWriter out = new PrintWriter(System.out);
	static StringBuffer sb = new StringBuffer();

	public static void main(String[] args) throws IOException {
		int t = 1;
		t = s.nextInt();
		//slinp();
		while (t > 0) {
			t--;
			int n = iinp();
			int a[] = iinp(n, 0, n);
			int c = 0;
			ArrayList<Integer> arr = new ArrayList<>();
			arr.add(a[0]);
			c++;
			for(int i = 1; i < n; i++) {
				if(a[i] > a[i - 1]) {
					while(i < n && a[i] > a[i - 1]) i++;
					i--;
					arr.add(a[i]);
					c++;
				}
				else {
					while(i < n && a[i] < a[i - 1]) i++;
					i--;
					arr.add(a[i]);
					c++;
				}
			}
			app(c + LN);
			for(int i = 0; i < arr.size(); i++) app(arr.get(i) + " ");
			ln();
		}
		out.print(sb);
		out.flush();
	}

	static void app(String x) throws IOException {
		sb.append(x);
	}

	static void spc() throws IOException {
		sb.append(SPC);
	}

	static void ln() throws IOException {
		sb.append(LN);
	}

	static int iinp() throws IOException {
		return s.nextInt();
	}

	static long linp() throws IOException {
		return s.nextLong();
	}

	static double dinp() throws IOException {
		return s.nextDouble();
	}

	static String sinp() throws IOException {
		return s.next();
	}

	static String slinp() throws IOException {
		return s.nextLine();
	}

	static int[] iarr(int n) {
		return new int[n];
	}

	static long[] larr(int n) {
		return new long[n];
	}

	static double[] darr(int n) {
		return new double[n];
	}

	static boolean[] barr(int n) {
		return new boolean[n];
	}

	static String[] sarr(int n) {
		return new String[n];
	}

	static int[][] iarr(int n, int m) {
		return new int[n][m];
	}

	static long[][] larr(int n, int m) {
		return new long[n][m];
	}

	static int[] iinp(int n, int st, int size) throws IOException {
		int a[] = iarr(n);
		for (int i = st; i < st + size; i++)
			a[i] = iinp();
		return a;
	}

	static long[] linp(int n, int st, int size) throws IOException {
		long a[] = larr(n);
		for (int i = st; i < st + size; i++)
			a[i] = linp();
		return a;
	}

	static String[] sinp(int n, int st, int size, String str) throws IOException {
		String a[] = sarr(n);
		for (int i = st; i < st + size; i++)
			if (str.equalsIgnoreCase(SPC))
				a[i] = sinp();
			else
				a[i] = slinp();
		return a;
	}

	static int[][] iinp(int n, int m, int row, int rows, int col, int cols) throws IOException {
		int a[][] = iarr(n, m);
		for (int i = row; i < row + rows; i++)
			for (int j = col; j < col + cols; j++)
				a[i][j] = iinp();
		return a;
	}

	static long[][] linp(int n, int m, int row, int rows, int col, int cols) throws IOException {
		long a[][] = larr(n, m);
		for (int i = row; i < row + rows; i++)
			for (int j = col; j < col + cols; j++)
				a[i][j] = linp();
		return a;
	}

	static void ginp(ArrayList<Integer> g[], int m) throws IOException {
		for (int i = 0; i < m; i++) {
			int u = iinp(), v = iinp();
			g[u].add(u);
			g[v].add(u);
		}
	}

	static long min(long... a) {
		long min = lmx;//Long.MAX_VALUE;
		for (long i : a)
			if (i < min)
				min = i;
		return min;
	}

	static int min(int... a) {
		int min = imx;//Long.MAX_VALUE;
		for (int i : a)
			if (i < min)
				min = i;
		return min;
	}

	static long max(long... a) {
		long max = lmn;//Long.MIN_VALUE;
		for (long i : a)
			if (i > max)
				max = i;
		return max;
	}

	static int max(int... a) {
		int max = imn;//Long.MIN_VALUE;
		for (int i : a)
			if (i > max)
				max = i;
		return max;
	}

	static long gcd(long a, long b) {
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}

	static int gcd(int a, int b) {
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}

	static void sort(int a[]) {
		Arrays.sort(a);
	};

	static void sort(long a[]) {
		Arrays.sort(a);
	};

	static void sort(String a[]) {
		Arrays.sort(a);
	};

	static void sort(int a[], int st, int e) {
		Arrays.sort(a, st, e);
	};

	static void sort(long a[], int st, int e) {
		Arrays.sort(a, st, e);
	};

	static void sort(String a[], int st, int e) {
		Arrays.sort(a, st, e);
	};

	static void sortbycol(int arr[][]) {
		Arrays.sort(arr, new Comparator<int[]>() {
			public int compare(int[] x, int[] y) {
				if (x[1] == y[1])
					return x[2] - y[2];
				return x[1] - y[1]; // sort in increasing order on the basis of first column
			}
		});
	}

	static StringBuffer printarr(long a[], String str) {
		StringBuffer ans = new StringBuffer();
		for (long i : a)
			ans.append(i + str);
		return ans;
	}

}

class Pair implements Comparator<Pair> {
	long a, b;

	Pair(long x, long y) {
		a = x;
		b = y;
	}

	public int compare(Pair p1, Pair p2) {
		if (p1.a != p2.a)
			return (p1.a - p2.a > 0) ? 1 : -1;
		return (p1.b - p2.b > 0) ? 1 : -1;
	}
}