You are given a sequence a of length n consisting of 0s and 1s.

You can perform the following operation on this sequence: 

  * Pick an index i from 1 to n-2 (inclusive). 
  * Change all of a_{i}, a_{i+1}, a_{i+2} to a_{i} ⊕ a_{i+1} ⊕ a_{i+2} simultaneously, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR)

Find a sequence of at most n operations that changes all elements of a to 0s or report that it's impossible.

We can prove that if there exists a sequence of operations of any length that changes all elements of a to 0s, then there is also such a sequence of length not greater than n.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^4).

The first line of each test case contains a single integer n (3 ≤ n ≤ 2⋅10^5) — the length of a.

The second line of each test case contains n integers a_1, a_2, …, a_n (a_i = 0 or a_i = 1) — elements of a.

It is guaranteed that the sum of n over all test cases does not exceed 2⋅10^5.

Output

For each test case, do the following: 

  * if there is no way of making all the elements of a equal to 0 after performing the above operation some number of times, print "NO". 
  * otherwise, in the first line print "YES", in the second line print k (0 ≤ k ≤ n) — the number of operations that you want to perform on a, and in the third line print a sequence b_1, b_2, ..., b_k (1 ≤ b_i ≤ n - 2) — the indices on which the operation should be applied. 



If there are multiple solutions, you may print any.

Example

Input


3
3
0 0 0
5
1 1 1 1 0
4
1 0 0 1


Output


YES
0
YES
2
3 1
NO

Note

In the first example, the sequence contains only 0s so we don't need to change anything.

In the second example, we can transform [1, 1, 1, 1, 0] to [1, 1, 0, 0, 0] and then to [0, 0, 0, 0, 0] by performing the operation on the third element of a and then on the first element of a.

In the third example, no matter whether we first perform the operation on the first or on the second element of a we will get [1, 1, 1, 1], which cannot be transformed to [0, 0, 0, 0].
import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.FileInputStream;
import java.io.FileOutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintStream;
import java.util.Locale;
import java.util.StringTokenizer;

public class Solution implements Runnable {
	
	private PrintStream out;
	private BufferedReader in;
	private StringTokenizer st;
	
	public void solve() throws IOException {
		long time0 = System.currentTimeMillis();
		
		int t = nextInt();
		for (int test = 1; test <= t; test++) {
			int n = nextInt();
			boolean[] a = new boolean[n];
			for (int i = 0; i < n; i++) {
				int aa = nextInt();
				if (aa == 1) {
					a[i] = true;
				}
			}
			int[] ans = solve(n, a);
			if (ans == null) {
				out.println("NO");
			} else {
				out.println("YES");
				out.println(ans.length);
				for (int i = 0; i < ans.length; i++) {
					out.print((ans[i] + 1) + " ");
				}
				out.println();
			}
		}
		
		System.err.println("time: " + (System.currentTimeMillis() - time0));
	}
	
	private int[] solve(int n, boolean[] a) {
		int[] ans = new int[n];
		int cnt = 0;
		int[] ones = new int[n + 1];
		int[] zeroes = new int[n + 1];
		for (int i = n - 1; i >= 0; i--) {
			if (a[i]) {
				ones[i] = ones[i + 1] + 1;
				zeroes[i] = 0;
			} else {
				ones[i] = ones[i + 1];
				zeroes[i] = zeroes[i + 1] + 1;
			}
		}
		if (ones[0] % 2 != 0) {
			return null;
		}
		int start = -1;
		int prestart = -1;
		for (int i = 0; i < n; i++) {
			if (!a[i] && (ones[i] % 2 == 0)) {
				start = i;
				break;
			}
			if (a[i] && (zeroes[i + 1] % 2 == 1) && (ones[i + 1] % 2 == 1)) {
				start = i + 1;
				prestart = i + zeroes[i + 1];
				break;
			}
		}
		if (start == -1) {
			return null;
		}
		if (prestart != -1) {
			for (int i = prestart; i > start; i -= 2) {
				ans[cnt++] = i - 1;
				a[i] = true;
				a[i - 1] = true;
			}
			ans[cnt++] = start - 1;
			a[start - 1] = false;
			a[start + 1] = false;
		}
		for (int i = start; i + 2 < n; i++) {
			if (!a[i + 1]) {
				continue;
			}
			if (a[i + 2]) {
				ans[cnt++] = i;
				a[i + 1] = false;
				a[i + 2] = false;
			} else {
				if (a[i + 3]) {
					ans[cnt++] = i + 1;
					a[i + 1] = false;
					a[i + 3] = false;
				} else {
					ans[cnt++] = i + 1;
					ans[cnt++] = i;
					a[i + 3] = true;
				}
			}
		}
		for (int i = start; i - 2 >= 0; i--) {
			if (!a[i - 1]) {
				continue;
			}
			if (a[i - 2]) {
				ans[cnt++] = i - 2;
				a[i - 1] = false;
				a[i - 2] = false;
			} else {
				if (a[i - 3]) {
					ans[cnt++] = i - 3;
					a[i - 1] = false;
					a[i - 3] = false;
				} else {
					ans[cnt++] = i - 3;
					ans[cnt++] = i - 2;
					a[i - 3] = true;
				}
			}
		}
		return copy(ans, cnt);
	}

	private int[] copy(int[] ans, int cnt) {
		int[] a = new int[cnt];
		for (int i = 0; i < cnt; i++) {
			a[i] = ans[i];
		}
		return a;
	}

	public double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}
	
	public long nextLong() throws IOException {
		return Long.parseLong(next());
	}
	
	public int nextInt() throws IOException {
		return Integer.parseInt(next());
	}
	
	public String next() throws IOException {
		while (!st.hasMoreTokens()) {
			String line = in.readLine();
			if (line == null) {
				return null;
			}
			st = new StringTokenizer(line);
		}
		return st.nextToken();
	}
	
	@Override
	public void run() {
		try {
			solve();
			out.close();
		} catch (Throwable e) {
			throw new RuntimeException(e);
		}
	}
	
	public Solution(String name) throws IOException {
		Locale.setDefault(Locale.US);
		if (name == null) {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintStream(new BufferedOutputStream(System.out));
		} else {
			in = new BufferedReader(new InputStreamReader(new FileInputStream(name + ".in")));
			out = new PrintStream(new BufferedOutputStream(new FileOutputStream(name + ".out")));
		}
		st = new StringTokenizer("");
	}
	
	public static void main(String[] args) throws IOException {
		new Thread(new Solution(null)).start();
	}
}
