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.*;
import java.math.*;
import java.text.*;

import static java.lang.Math.*;
import static java.lang.System.*;

public class Solution {

    public static void main(String[] args) throws IOException {
        int T = cin.nextInt();
        for(int t = 0; t < T; t++) {
            int n = cin.nextInt();
            long[] nums = new long[n];
            StringBuilder sb = new StringBuilder();
            for(int i = 0; i < n; i++) {
                nums[i] = cin.nextInt();
            }
            int ct = 0;
            for(int i = 0; i < n; i++) {
                if((i - 1 < 0 || i + 1 == n) || (nums[i - 1] - nums[i]) * (nums[i + 1] - nums[i]) > 0) {
                    sb.append(nums[i] + " ");
                    ct++;
                }
            }
            sb.insert(0, "\n");
            sb.insert(0, ct);
            out.println(sb);
        }
    }

//    public static void main(String[] args) throws IOException {
//        int T = cin.nextInt();
//        for(int t = 0; t < T; t++) {
//            int n = cin.nextInt(), x = cin.nextInt();
//            long[] nums = new long[n];
//            long[] prefix = new long[n];
//            for(int i = 0; i < n; i++) {
//                nums[i] = cin.nextInt();
//                prefix[i] = nums[i];
//                prefix[i] += prefix[i - 1];
//            }
//
//            for(int i = 1; i < n; i++) {
//                // binary
//                kx ?
//            }
//
//            int ans = 0;
//            out.println(ans);
//        }
//    }

    private static void sort(double[] arr) {
        Double[] objArr = Arrays.stream(arr).boxed().toArray(Double[]::new);
        Arrays.sort(objArr);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = objArr[i];
        }
    }

    private static void sort(int[] arr) {
        Integer[] objArr = Arrays.stream(arr).boxed().toArray(Integer[]::new);
        Arrays.sort(objArr);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = objArr[i];
        }
    }

    private static void sort(long[] arr) {
        Long[] objArr = Arrays.stream(arr).boxed().toArray(Long[]::new);
        Arrays.sort(objArr);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = objArr[i];
        }
    }
    // Fast IO v2
    static class FastScanner{
        BufferedReader br;
        StringTokenizer st;
        public FastScanner(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in),16384);
            eat("");
        }
        public void eat(String s) {
            st = new StringTokenizer(s);
        }
        public String nextLine() {
            try {
                return br.readLine();
            } catch (IOException e) {
                return null;
            }
        }
        public boolean hasNext() {
            while(!st.hasMoreTokens()) {
                String s = nextLine();
                if(s==null) return false;
                eat(s);
            }
            return true;
        }
        public String next() {
            hasNext();
            return st.nextToken();
        }
        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }

    static FastScanner cin = new FastScanner(System.in);

    static class ModMath {
        private static final int DEFAULT_MOD = 1_000_000_007;
        private final long mod;

        public ModMath(long mod, boolean unsafe) {
        /*if (!unsafe && !IntMath.isPrime(mod)) {
            throw new RuntimeException("This class is designed for primes!");
        }*/
            this.mod = mod;
        }

        public ModMath(long mod) {
            this(mod, false);
        }

        public ModMath() {
            this(DEFAULT_MOD, true);
        }

        public long mod(long x) {
            x %= mod;
            return x < 0 ? x + mod : x;
        }

        public long inv(long x) {
            //return pow(x, mod - 2);
            return mod(LongEuclidSolver.solve(x, mod).x);
        }

        public Factorial getFactorial(int n) {
            return new Factorial(this, n);
        }

    }

    static class Factorial {
        private final ModMath mod;
        private final long[] natural;
        private final long[] reverse;

        public Factorial(ModMath mod, int max) {
            this.mod = mod;
            this.natural = new long[max];
            this.reverse = new long[max];
            natural[0] = 1;
            for (int i = 1; i < max; i++) {
                natural[i] = mod.mod(natural[i - 1] * i);
            }
            reverse[max - 1] = mod.inv(natural[max - 1]);
            for (int i = max - 1; i > 0; i--) {
                reverse[i - 1] = mod.mod(reverse[i] * i);
            }
        }

        public long fact(long x) {
            return natural[(int) x];
        }

        public long factinv(long x) {
            return reverse[(int) x];
        }

        public long npr(long n, long r) {
            return n < r ? 0 : mod.mod(fact(n) * factinv(n - r));
        }

        public long ncr(long n, long r) {
            return mod.mod(npr(n, r) * factinv(r));
        }

        public String toString() {
            return "Factorial{" +
                    "natural=" + Arrays.toString(natural) +
                    ", reverse=" + Arrays.toString(reverse) +
                    '}';
        }

    }

    static class LongEuclidSolver {
        private LongEuclidSolver() {
        }

        public static Vec3l solve(long a, long b) {
            LongEuclidSolver.ReferenceLong p = new LongEuclidSolver.ReferenceLong(), q = new LongEuclidSolver.ReferenceLong();
            long d = solve(a, b, p, q);
            return new Vec3l(p.val, q.val, d);
        }

        private static long solve(long a, long b, LongEuclidSolver.ReferenceLong p, LongEuclidSolver.ReferenceLong q) {
            if (b == 0) {
                p.val = 1;
                q.val = 0;
                return a;
            } else {
                long d = solve(b, a % b, q, p);
                q.val -= (a / b) * p.val;
                return d;
            }
        }

        private static class ReferenceLong {
            private long val;

        }

    }

    static class Vec3l implements Comparable<Vec3l> {
        public long x;
        public long y;
        public long z;

        public Vec3l(long x, long y, long z) {
            this.x = x;
            this.y = y;
            this.z = z;
        }

        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Vec3i vec3i = (Vec3i) o;
            return x == vec3i.x &&
                    y == vec3i.y &&
                    z == vec3i.z;
        }

        public int hashCode() {
            return Objects.hash(x, y, z);
        }

        public String toString() {
            return "(" + x + ", " + y + ", " + z + ")";
        }

        public int compareTo(Vec3l o) {
            if (x == o.x) {
                if (y == o.y) {
                    return Long.compare(z, o.z);
                }
                return Long.compare(y, o.z);
            }
            return Long.compare(x, o.x);
        }

    }

    static class Vec3i implements Comparable<Vec3i> {
        public int x;
        public int y;
        public int z;

        public Vec3i(int x, int y, int z) {
            this.x = x;
            this.y = y;
            this.z = z;
        }

        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Vec3i vec3i = (Vec3i) o;
            return x == vec3i.x &&
                    y == vec3i.y &&
                    z == vec3i.z;
        }

        public int hashCode() {
            return Objects.hash(x, y, z);
        }

        public String toString() {
            return "(" + x + ", " + y + ", " + z + ")";
        }

        public int compareTo(Vec3i o) {
            if (x == o.x) {
                if (y == o.y) {
                    return Integer.compare(z, o.z);
                }
                return Integer.compare(y, o.z);
            }
            return Integer.compare(x, o.x);
        }

    }
}