Problem: Let's call an array a_1, a_2, ..., a_m of nonnegative integer numbers good if a_1 + a_2 + ... + a_m = 2⋅(a_1 ⊕ a_2 ⊕ ... ⊕ a_m), where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).

For example, array [1, 2, 3, 6] is good, as 1 + 2 + 3 + 6 = 12 = 2⋅ 6 = 2⋅ (1⊕ 2 ⊕ 3 ⊕ 6). At the same time, array [1, 2, 1, 3] isn't good, as 1 + 2 + 1 + 3 = 7 ≠ 2⋅ 1 = 2⋅(1⊕ 2 ⊕ 1 ⊕ 3).

You are given an array of length n: a_1, a_2, ..., a_n. Append at most 3 elements to it to make it good. Appended elements don't have to be different. It can be shown that the solution always exists under the given constraints. If there are different solutions, you are allowed to output any of them. Note that you don't have to minimize the number of added elements!. So, if an array is good already you are allowed to not append elements.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10 000). The description of the test cases follows.

The first line of each test case contains a single integer n (1≤ n ≤ 10^5) — the size of the array.

The second line of each test case contains n integers a_1, a_2, ..., a_n (0≤ a_i ≤ 10^9) — the elements of the array.

It is guaranteed that the sum of n over all test cases does not exceed 10^5.

Output

For each test case, output two lines.

In the first line, output a single integer s (0≤ s≤ 3) — the number of elements you want to append.

In the second line, output s integers b_1, ..., b_s (0≤ b_i ≤ 10^{18}) — the elements you want to append to the array.

If there are different solutions, you are allowed to output any of them.

Example

Input


3
4
1 2 3 6
1
8
2
1 1


Output


0

2
4 4
3
2 6 2

Note

In the first test case of the example, the sum of all numbers is 12, and their ⊕ is 6, so the condition is already satisfied.

In the second test case of the example, after adding 4, 4, the array becomes [8, 4, 4]. The sum of numbers in it is 16, ⊕ of numbers in it is 8.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.math.BigInteger;

 
public class Main implements Runnable {
  static Scanner in;
  // static FastReader in;
  static PrintWriter out;
  static Assert as;
  static int[][] dirs8 = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}, {1, 1}, {-1, -1}, {-1, 1}, {1, -1}};
  static int[][] dirs = {{0, -1}, {1, 0}, {0, +1}, {-1, 0}};
 
  static int[][] E;
  // static List<int[]>[] adj;
  static List<Integer>[] adj;
  static Set<Integer> vis;
 
  static long INFL = (long) 1e15 + 7;
  static int INF = (int) 1e9 + 7;
  static int mod = 998244353;
 
  static int T, n, m, k, count;
  static boolean flag;
  static int[] a, b;
  static int[][] map;

  

  static void solve() throws Exception {
    n = in.nextInt();
    a = new int[n];
    long sum = 0;
    long xorSum = 0;
    for (int i = 0; i < n; i++) {a[i] = in.nextInt(); sum += a[i]; xorSum = xorSum ^ a[i];}

    if (sum == 2 * xorSum) {out.println(0); out.println(); return;}

    long[] res = new long[3];
    int p = 0;
    
    res[p++] = Math.max(sum << 2, xorSum << 2) + (sum % 2);
    sum+= res[0];
    xorSum ^= res[0];

    // out.println(sum + " " + xorSum * 2);




    long cur = (2 * xorSum - sum) / 2;
    res[p++] = cur;
    res[p++] = cur;



    out.println(p);
    for (int i = 0; i < p; i++) {
      out.print(res[i] + " ");
    }
    out.println();


    
    
  }





  public static void main(String[] args) throws Exception {
 
    in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
    // in = new FastReader();
    out = new PrintWriter(System.out);
    as = new Assert();
 
    int T = in.nextInt();
    for (int tt = 1; tt <= T; tt++) {
      // Thread t = new Thread(null, new Main(), "Main", 1 << 28);
      // t.start();
      // t.join();
      solve();
    }
 
    // Thread t = new Thread(null, new Main(), "Main", 1 << 28);
    // t.start();
    // t.join();
    // solve();
 
    out.flush();
    out.close();
  }
 
  @Override
  public void run() {
    try {
      solve();
    } catch (Exception e) {
      e.printStackTrace(); 
    }
  }
 
  static class FastReader {
    public BufferedReader br; 
    StringTokenizer st; 
    public FastReader() {br = new BufferedReader(new InputStreamReader(System.in));} 
    String next() { 
      while (st == null || !st.hasMoreElements()) { 
          try {st = new StringTokenizer(br.readLine());} 
          catch (IOException e) {e.printStackTrace();} 
      } 
      return st.nextToken(); 
    } 
    int nextInt() {return Integer.parseInt(next());} 
    long nextLong() {return Long.parseLong(next());} 
    double nextDouble() {return Double.parseDouble(next());} 
    String nextLine() {
      String str = ""; 
        try {str = br.readLine();} 
        catch (IOException e) {e.printStackTrace();} 
        return str; 
    }
  }

  static class Assert {
    static <T> void eq(T a, T b) throws Exception {
      if (!a.equals(b)) {
        throw new Exception();
      }
    }

    static void test(boolean result) throws Exception {
      if (!result) {
        throw new Exception();
      }
    }
  }

  static int modInverse(int a, int m) { 
    int m0 = m; 
    int y = 0, x = 1; 
    if (m == 1) {return 0;} 
    while (a > 1) { 
        // q is quotient 
      int q = a / m; 
      int t = m; 
      // m is remainder now, process 
      // same as Euclid's algo 
      m = a % m; 
      a = t; 
      t = y; 
      // Update x and y 
      y = x - q * y; 
      x = t; 
    } 
    // Make x positive 
    if (x < 0) 
      x += m0; 
    return x; 
  } 
}