You are given n integers a_1, a_2, ..., a_n, such that for each 1≤ i ≤ n holds i-n≤ a_i≤ i-1.

Find some nonempty subset of these integers, whose sum is equal to 0. It can be shown that such a subset exists under given constraints. If there are several possible subsets with zero-sum, you can find any of them.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^6). The description of the test cases follows.

The first line of each test case contains a single integer n (1≤ n ≤ 10^6).

The second line of each test case contains n integers a_1, a_2, ..., a_n (i-n ≤ a_i ≤ i-1).

It is guaranteed that the sum of n over all test cases does not exceed 10^6.

Output

For each test case, output two lines.

In the first line, output s (1≤ s ≤ n) — the number of elements in your subset.

In the second line, output s integers i_1, i_2, ..., i_s (1≤ i_k ≤ n). All integers have to be pairwise different, and a_{i_1} + a_{i_2} + ... + a_{i_s} has to be equal to 0. If there are several possible subsets with zero-sum, you can find any of them.

Example

Input


2
5
0 1 2 3 4
4
-3 1 1 1


Output


1
1 
4
1 4 3 2 

Note

In the first example, we get sum is a_1 = 0.

In the second example, we get sum is a_1 + a_4 + a_3 + a_2 = 0.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.UncheckedIOException;
import java.nio.charset.Charset;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author mikit
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        LightScanner in = new LightScanner(inputStream);
        LightWriter out = new LightWriter(outputStream);
        GSubsetWithZeroSum solver = new GSubsetWithZeroSum();
        solver.solve(1, in, out);
        out.close();
    }

    static class GSubsetWithZeroSum {
        public void solve(int testNumber, LightScanner in, LightWriter out) {
            // out.setBoolLabel(LightWriter.BoolLabel.YES_NO_FIRST_UP);
            int testCases = in.ints();
            int[] ans = new int[1_000_000];
            int[] b = new int[1_000_000];
            boolean[] visited = new boolean[1_000_000];
            StringBuilder res = new StringBuilder();

            for (int testCase = 0; testCase < testCases; testCase++) {
                int n = in.ints();
                for (int i = 0; i < n; i++) {
                    b[i] = i - in.ints();
                }

                if (n == 1) {
                    res.append("1\n1\n");
                    continue;
                }

                int len = 0;
                for (int i = 0; i < n; i++) {
                    visited[i] = false;
                }

                int cur = 0, start = -1;
                while (len <= n) {
                    if (visited[cur]) {
                        start = cur;
                        break;
                    }
                    visited[cur] = true;
                    ans[len++] = cur;
                    cur = b[cur];
                }

                if (start == -1) throw new RuntimeException();

                int startIndex = 0;
                while (ans[startIndex] != start) startIndex++;
                res.append(len - startIndex);
                res.append('\n');
                for (int i = startIndex; i < len; i++) res.append(ans[i] + 1).append(' ');
                res.append('\n');
            }
            out.print(res.toString());
        }

    }

    static class LightWriter implements AutoCloseable {
        private final Writer out;
        private boolean breaked = true;

        public LightWriter(Writer out) {
            this.out = out;
        }

        public LightWriter(OutputStream out) {
            this(new BufferedWriter(new OutputStreamWriter(out, Charset.defaultCharset())));
        }

        public LightWriter print(String s) {
            try {
                out.write(s, 0, s.length());
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public void close() {
            try {
                out.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

    }

    static class LightScanner {
        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public LightScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        public String string() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new UncheckedIOException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int ints() {
            return Integer.parseInt(string());
        }

    }
}

