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.io.*;
import java.util.*;

public class B implements Runnable {
	boolean oj = false;
	Reader scn;
	PrintWriter out;
	String INPUT = "";

	void solve() {
		int t = scn.nextInt();
		while(t-- > 0) {
			int n = scn.nextInt();
			int[] arr = scn.nextIntArr(n);
			boolean[] take = new boolean[n];
			Arrays.fill(take, true);
			int ans = n, prev = 0;
			for(int i = 1; i + 1 < n; i++) {
				if(Math.abs(arr[i + 1] - arr[prev]) == Math.abs(arr[i] - arr[prev]) + Math.abs(arr[i] - arr[i + 1])) {
					take[i] = false;
					ans--;
				} else {
					prev = i;
				}
			}
			out.println(ans);
			for(int i = 0; i < n; i++) {
				if(take[i]) {
					out.print(arr[i] + " ");
				}
			}
			out.println();
		}
	}

	public void run() {
		long time = System.currentTimeMillis();
		boolean judge = System.getProperty("ONLINE_JUDGE") != null || oj;
		out = new PrintWriter(System.out);
		scn = new Reader(judge);
		solve();
		out.flush();
		if (!judge) {
			System.out.println(Arrays.deepToString(new Object[] { System.currentTimeMillis() - time + " ms" }));
		}
	}

	public static void main(String[] args) {
		new Thread(null, new B(), "Main", 1 << 28).start();
	}

	class Reader {
		InputStream is;

		public Reader(boolean oj) {
			is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		}

		byte[] inbuf = new byte[1024];
		public int lenbuf = 0, ptrbuf = 0;

		int readByte() {
			if (lenbuf == -1)
				throw new InputMismatchException();
			if (ptrbuf >= lenbuf) {
				ptrbuf = 0;
				try {
					lenbuf = is.read(inbuf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return -1;
			}
			return inbuf[ptrbuf++];
		}

		boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}

		int skip() {
			int b;
			while ((b = readByte()) != -1 && isSpaceChar(b))
				;
			return b;
		}

		String next() {
			int b = skip();
			StringBuilder stringB = new StringBuilder();
			while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
				stringB.appendCodePoint(b);
				b = readByte();
			}
			return stringB.toString();
		}

		String nextLine() {
			int b = skip();
			StringBuilder stringB = new StringBuilder();
			while ((!isSpaceChar(b) || b == ' ')) { // when nextLine, (isSpaceChar(b) && b != ' ')
				stringB.appendCodePoint(b);
				b = readByte();
			}
			return stringB.toString();
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		char nextChar() {
			return (char) skip();
		}

		char[] next(int n) {
			char[] buff = new char[n];
			int b = skip(), p = 0;
			while (p < n && !(isSpaceChar(b))) {
				buff[p++] = (char) b;
				b = readByte();
			}
			return n == p ? buff : Arrays.copyOf(buff, p);
		}

		int nextInt() {
			int num = 0, b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}

			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}

		long nextLong() {
			long num = 0;
			int b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}

			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}

		long[] nextLongArr(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		int[] nextIntArr(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		char[][] nextMat(int n, int m) {
			char[][] map = new char[n][];
			for (int i = 0; i < n; i++)
				map[i] = next(m);
			return map;
		}

		long[][] next2Long(int n, int m) {
			long[][] arr = new long[n][];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLongArr(m);
			}
			return arr;
		}

		int[][] next2Int(int n, int m) {
			int[][] arr = new int[n][];
			for (int i = 0; i < n; i++) {
				arr[i] = nextIntArr(m);
			}
			return arr;
		}

		long[] shuffle(long[] arr) {
			Random r = new Random();
			for (int i = 1, j; i < arr.length; i++) {
				j = r.nextInt(i);
				arr[i] = arr[i] ^ arr[j];
				arr[j] = arr[i] ^ arr[j];
				arr[i] = arr[i] ^ arr[j];
			}
			return arr;
		}

		int[] shuffle(int[] arr) {
			Random r = new Random();
			for (int i = 1, j; i < arr.length; i++) {
				j = r.nextInt(i);
				arr[i] = arr[i] ^ arr[j];
				arr[j] = arr[i] ^ arr[j];
				arr[i] = arr[i] ^ arr[j];
			}
			return arr;
		}

		long[] uniq(long[] arr) {
			arr = scn.shuffle(arr);
			Arrays.parallelSort(arr);
			long[] rv = new long[arr.length];
			int pos = 0;
			rv[pos++] = arr[0];
			for (int i = 1; i < arr.length; i++) {
				if (arr[i] != arr[i - 1]) {
					rv[pos++] = arr[i];
				}
			}
			return Arrays.copyOf(rv, pos);
		}

		int[] uniq(int[] arr) {
			arr = scn.shuffle(arr);
			Arrays.parallelSort(arr);
			int[] rv = new int[arr.length];
			int pos = 0;
			rv[pos++] = arr[0];
			for (int i = 1; i < arr.length; i++) {
				if (arr[i] != arr[i - 1]) {
					rv[pos++] = arr[i];
				}
			}
			return Arrays.copyOf(rv, pos);
		}

		long[] reverse(long[] arr) {
			int i = 0, j = arr.length - 1;
			while (i < j) {
				arr[i] = arr[i] ^ arr[j];
				arr[j] = arr[i] ^ arr[j];
				arr[i] = arr[i] ^ arr[j];
				i++;
				j--;
			}
			return arr;
		}

		int[] reverse(int[] arr) {
			int i = 0, j = arr.length - 1;
			while (i < j) {
				arr[i] = arr[i] ^ arr[j];
				arr[j] = arr[i] ^ arr[j];
				arr[i] = arr[i] ^ arr[j];
				i++;
				j--;
			}
			return arr;
		}

		long[] compres(long[] arr) {
			int n = arr.length;
			long[] rv = Arrays.copyOf(arr, n);
			rv = uniq(rv);
			for (int i = 0; i < n; i++) {
				arr[i] = Arrays.binarySearch(rv, arr[i]);
			}
			return arr;
		}

		int[] compres(int[] arr) {
			int n = arr.length;
			int[] rv = Arrays.copyOf(arr, n);
			rv = uniq(rv);
			for (int i = 0; i < n; i++) {
				arr[i] = Arrays.binarySearch(rv, arr[i]);
			}
			return arr;
		}

		void deepFillLong(Object array, long val) {
			if (!array.getClass().isArray()) {
				throw new IllegalArgumentException();
			}
			if (array instanceof long[]) {
				long[] intArray = (long[]) array;
				Arrays.fill(intArray, val);
			} else {
				Object[] objArray = (Object[]) array;
				for (Object obj : objArray) {
					deepFillLong(obj, val);
				}
			}
		}

		void deepFillInt(Object array, int val) {
			if (!array.getClass().isArray()) {
				throw new IllegalArgumentException();
			}
			if (array instanceof int[]) {
				int[] intArray = (int[]) array;
				Arrays.fill(intArray, val);
			} else {
				Object[] objArray = (Object[]) array;
				for (Object obj : objArray) {
					deepFillInt(obj, val);
				}
			}
		}

		void tr(Object... o) {
			if (!oj)
				System.out.println(Arrays.deepToString(o));
		}
	}
}