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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Main implements Runnable {
    int n, m, k;
    static boolean use_n_tests = true;
    long[] res;

    void solve(FastScanner in, PrintWriter out, int testNumber) {
        n = in.nextInt();
        int[] p = in.nextArray(n);
        int l = 0;
        int r = n - 1;
        boolean[] skip = new boolean[n];
        for (int i = 1; i < n - 1; i++) {
            int wh = Math.abs(p[i - 1] - p[i]) + Math.abs(p[i] - p[i + 1]);
            int skipwh = Math.abs(p[i - 1] - p[i + 1]);
            if (skipwh >= wh) {
                skip[i] = true;
            }
        }
        List<Integer> answer = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            if (!skip[i]) {
                answer.add(p[i]);
            }
        }
        out.println(answer.size());
        for (int x : answer) {
            out.print(x + " ");
        }
        out.println();
    }

    // ****************************** template code ***********

    List<Integer> generatePrimes(int n) {
        List<Integer> res = new ArrayList<>();
        boolean[] sieve = new boolean[n + 1];
        for (int i = 2; i <= n; i++) {
            if (!sieve[i]) {
                res.add(i);
            }
            if ((long) i * i <= n) {
                for (int j = i * i; j <= n; j += i) {
                    sieve[j] = true;
                }
            }
        }
        return res;
    }

    int ask(int l, int r) {
        if (l >= r) {
            return -1;
        }
        System.out.printf("? %d %d\n", l + 1, r + 1);
        System.out.flush();
        return in.nextInt() - 1;
    }

    static int stack_size = 1 << 27;

    class Mod {
        long mod;

        Mod(long mod) {
            this.mod = mod;
        }

        long add(long a, long b) {
            a = mod(a);
            b = mod(b);
            return (a + b) % mod;
        }

        long sub(long a, long b) {
            a = mod(a);
            b = mod(b);
            return (a - b + mod) % mod;
        }

        long mul(long a, long b) {
            a = mod(a);
            b = mod(b);
            return a * b % mod;
        }

        long div(long a, long b) {
            a = mod(a);
            b = mod(b);
            return (a * inv(b)) % mod;
        }

        public long inv(long r) {
            if (r == 1)
                return 1;
            return ((mod - mod / r) * inv(mod % r)) % mod;
        }

        private long mod(long a) {
            return a % mod;
        }
    }

    class Coeff {
        long mod;
        long[][] C;
        long[] fact;
        boolean cycleWay = false;

        Coeff(int n, long mod) {
            this.mod = mod;
            fact = new long[n + 1];
            fact[0] = 1;
            for (int i = 1; i <= n; i++) {
                fact[i] = i;
                fact[i] %= mod;
                fact[i] *= fact[i - 1];
                fact[i] %= mod;
            }
        }

        Coeff(int n, int m, long mod) {
            // n > m
            cycleWay = true;
            this.mod = mod;
            C = new long[n + 1][m + 1];
            for (int i = 0; i <= n; i++) {
                for (int j = 0; j <= Math.min(i, m); j++) {
                    if (j == 0 || j == i) {
                        C[i][j] = 1;
                    } else {
                        C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
                        C[i][j] %= mod;
                    }
                }
            }
        }

        public long C(int n, int m) {
            if (cycleWay) {
                return C[n][m];
            }
            return fC(n, m);
        }

        private long fC(int n, int m) {
            return (fact[n] * inv(fact[n - m] * fact[m] % mod)) % mod;
        }

        private long inv(long r) {
            if (r == 1)
                return 1;
            return ((mod - mod / r) * inv(mod % r)) % mod;
        }
    }

    class Pair {
        int first;
        long second;

        Pair(int f, long s) {
            first = f;
            second = s;
        }

        public int getFirst() {
            return first;
        }

        public long getSecond() {
            return second;
        }
    }

    class MultisetTree<T> {
        int size = 0;

        TreeMap<T, Integer> mp = new TreeMap<>();

        void add(T x) {
            mp.merge(x, 1, Integer::sum);
            size++;
        }

        void remove(T x) {
            if (mp.containsKey(x)) {
                mp.merge(x, -1, Integer::sum);
                if (mp.get(x) == 0) {
                    mp.remove(x);
                }
                size--;
            }
        }

        boolean contains(T x) {
            return mp.containsKey(x);
        }

        T greatest() {
            return mp.lastKey();
        }

        T smallest() {
            return mp.firstKey();
        }

        int size() {
            return size;
        }

        int diffSize() {
            return mp.size();
        }
    }

    class Multiset<T> {
        int size = 0;

        Map<T, Integer> mp = new HashMap<>();

        void add(T x) {
            mp.merge(x, 1, Integer::sum);
            size++;
        }

        boolean contains(T x) {
            return mp.containsKey(x);
        }

        void remove(T x) {
            if (mp.containsKey(x)) {
                mp.merge(x, -1, Integer::sum);
                if (mp.get(x) == 0) {
                    mp.remove(x);
                }
                size--;
            }
        }

        int size() {
            return size;
        }

        int diffSize() {
            return mp.size();
        }
    }

    static class Range {
        int l, r;
        int id;

        public int getL() {
            return l;
        }

        public int getR() {
            return r;
        }

        public Range(int l, int r, int id) {
            this.l = l;
            this.r = r;
            this.id = id;
        }
    }

    static class Array {
        static Range[] readRanges(int n, FastScanner in) {
            Range[] result = new Range[n];
            for (int i = 0; i < n; i++) {
                result[i] = new Range(in.nextInt(), in.nextInt(), i);
            }
            return result;
        }

        static List<List<Integer>> intInit2D(int n) {
            List<List<Integer>> res = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                res.add(new ArrayList<>());
            }
            return res;
        }

        static boolean isSorted(Integer[] a) {
            for (int i = 0; i < a.length - 1; i++) {
                if (a[i] > a[i + 1]) {
                    return false;
                }
            }
            return true;
        }

        static public long sum(int[] a) {
            long sum = 0;
            for (int x : a) {
                sum += x;
            }
            return sum;
        }

        static public long sum(long[] a) {
            long sum = 0;
            for (long x : a) {
                sum += x;
            }
            return sum;
        }

        static public long sum(Integer[] a) {
            long sum = 0;
            for (int x : a) {
                sum += x;
            }
            return sum;
        }

        static public int min(Integer[] a) {
            int mn = Integer.MAX_VALUE;
            for (int x : a) {
                mn = Math.min(mn, x);
            }
            return mn;
        }

        static public int min(int[] a) {
            int mn = Integer.MAX_VALUE;
            for (int x : a) {
                mn = Math.min(mn, x);
            }
            return mn;
        }

        static public int max(Integer[] a) {
            int mx = Integer.MIN_VALUE;
            for (int x : a) {
                mx = Math.max(mx, x);
            }
            return mx;
        }

        static public int max(int[] a) {
            int mx = Integer.MIN_VALUE;
            for (int x : a) {
                mx = Math.max(mx, x);
            }
            return mx;
        }

        static public int[] readint(int n, FastScanner in) {
            int[] out = new int[n];
            for (int i = 0; i < out.length; i++) {
                out[i] = in.nextInt();
            }
            return out;
        }
    }

    class Graph {
        List<List<Integer>> graph;

        Graph(int n) {
            create(n);
        }

        void create(int n) {
            List<List<Integer>> graph = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                graph.add(new ArrayList<>());
            }
            this.graph = graph;
        }

        void readBi(int m, FastScanner in) {
            for (int i = 0; i < m; i++) {
                int v = in.nextInt() - 1;
                int u = in.nextInt() - 1;
                graph.get(v).add(u);
                graph.get(u).add(v);
            }
        }
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(InputStream io) {
            br = new BufferedReader(new InputStreamReader(io));
        }

        public String line() {
            String result = "";
            try {
                result = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return result;
        }

        public String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public int[] nextArray(int n) {
            int[] res = new int[n];
            for (int i = 0; i < n; i++) {
                res[i] = in.nextInt();
            }
            return res;
        }

        public long[] nextArrayL(int n) {
            long[] res = new long[n];
            for (int i = 0; i < n; i++) {
                res[i] = in.nextLong();
            }
            return res;
        }

        public Long[] nextArrayL2(int n) {
            Long[] res = new Long[n];
            for (int i = 0; i < n; i++) {
                res[i] = in.nextLong();
            }
            return res;
        }


        public Integer[] nextArray2(int n) {
            Integer[] res = new Integer[n];
            for (int i = 0; i < n; i++) {
                res[i] = in.nextInt();
            }
            return res;
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

    }

    void run_t_tests() {
        int t = in.nextInt();
        int i = 0;
        while (t-- > 0) {
            solve(in, out, i++);
        }
    }

    void run_one() {
        solve(in, out, -1);
    }

    @Override
    public void run() {
        in = new FastScanner(System.in);
        out = new PrintWriter(System.out);
        if (use_n_tests) {
            run_t_tests();
        } else {
            run_one();
        }
        out.close();
    }

    static FastScanner in;
    static PrintWriter out;

    public static void main(String[] args) throws InterruptedException {
        Thread thread = new Thread(null, new Main(), "", stack_size);
        thread.start();
        thread.join();
    }
}