A bow adorned with nameless flowers that bears the earnest hopes of an equally nameless person.

You have obtained the elegant bow known as the Windblume Ode. Inscribed in the weapon is an array of n (n ≥ 3) positive distinct integers (i.e. different, no duplicates are allowed).

Find the largest subset (i.e. having the maximum number of elements) of this array such that its sum is a composite number. A positive integer x is called composite if there exists a positive integer y such that 1 < y < x and x is divisible by y.

If there are multiple subsets with this largest size with the composite sum, you can output any of them. It can be proven that under the constraints of the problem such a non-empty subset always exists.

Input

Each test consists of multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 100). Description of the test cases follows.

The first line of each test case contains an integer n (3 ≤ n ≤ 100) — the length of the array.

The second line of each test case contains n distinct integers a_{1},a_{2},...,a_{n} (1 ≤ a_{i} ≤ 200) — the elements of the array.

Output

Each test case should have two lines of output.

The first line should contain a single integer x: the size of the largest subset with composite sum. The next line should contain x space separated integers representing the indices of the subset of the initial array.

Example

Input


4
3
8 1 2
4
6 9 4 2
9
1 2 3 4 5 6 7 8 9
3
200 199 198


Output


2
2 1
4
2 1 4 3
9
6 9 1 2 3 4 5 7 8
3
1 2 3 

Note

In the first test case, the subset \\{a_2, a_1\} has a sum of 9, which is a composite number. The only subset of size 3 has a prime sum equal to 11. Note that you could also have selected the subset \\{a_1, a_3\} with sum 8 + 2 = 10, which is composite as it's divisible by 2.

In the second test case, the sum of all elements equals to 21, which is a composite number. Here we simply take the whole array as our subset.
import static java.lang.Math.max;
import static java.lang.Math.min;
import static java.lang.Math.abs;
import java.util.*;
import java.io.*;
import java.math.*;

/**
 *
 * @Har_Har_Mahadev
 */

/**
 * Main , Solution , Remove Public
 */
public class A {

	public static void process() throws IOException {

		int n = sc.nextInt();
		int arr[] = sc.readArray(n);
		
		HashSet<Integer> set = new HashSet<Integer>();
		ArrayList<Integer> lis = new ArrayList<Integer>();
		int sum = 0;
		for(int i = 1; i<=n; i++) {
			set.add(i);
			sum+=arr[i-1];
		}
		if(!isPrime(sum)) {
			System.out.println(n);
			for(int e : set)System.out.print(e+" ");
			System.out.println();
			return;
		}
		for(int i = 0; i<n; i++) {
			sum-=arr[i];
			if(!isPrime(sum)) {
				set.remove(i+1);
				System.out.println(n-1);
				for(int e : set)System.out.print(e+" ");
				System.out.println();
				return;
			}
			sum+=arr[i];
		}
		
		
	}
	private static boolean isPrime(int n) {

        if(n == 1)
          return false;
        for(int i=2; i*i <= n; i++) {
          if(n%i == 0)
            return false;
        }
        return true;

      }
      

	//=============================================================================
	//--------------------------The End---------------------------------
	//=============================================================================
	private static long INF = 2000000000000000000L, M = 1000000007, MM = 998244353;
	private static int N = 0;

	private static void google(int tt) {
		System.out.print("Case #" + (tt) + ": ");
	}

	static FastScanner sc;
	static FastWriter out;

	public static void main(String[] args) throws IOException {
		boolean oj = true;
		if (oj) {
			sc = new FastScanner();
			out = new FastWriter(System.out);
		} else {
			sc = new FastScanner("input.txt");
			out = new FastWriter("output.txt");
		}
		long s = System.currentTimeMillis();
		int t = 1;
		t = sc.nextInt();
		int TTT = 1;
		while (t-- > 0) {
			//			google(TTT++);
			process();
		}
		out.flush();
		//		tr(System.currentTimeMillis()-s+"ms");
	}

	private static boolean oj = System.getProperty("ONLINE_JUDGE") != null;

	private static void tr(Object... o) {
		if (!oj)
			System.err.println(Arrays.deepToString(o));
	}

	static class Pair implements Comparable<Pair> {
		int x, y;

		Pair(int x, int y) {
			this.x = x;
			this.y = y;
		}

		@Override
		public int compareTo(Pair o) {
			return Integer.compare(this.x, o.x);
		}

		/*
		 	@Override
		    public boolean equals(Object o) {
		        if (this == o) return true;
		        if (!(o instanceof Pair)) return false;
		        Pair key = (Pair) o;
		        return x == key.x && y == key.y;
		    }
		 
		    @Override
		    public int hashCode() {
		        int result = x;
		        result = 31 * result + y;
		        return result;
		    }
		*/
	}

	/////////////////////////////////////////////////////////////////////////////////////////////////////////

	static int ceil(int x, int y) {
		return (x % y == 0 ? x / y : (x / y + 1));
	}

	static long ceil(long x, long y) {
		return (x % y == 0 ? x / y : (x / y + 1));
	}

	static long sqrt(long z) {
		long sqz = (long) Math.sqrt(z);
		while (sqz * 1L * sqz < z) {
			sqz++;
		}
		while (sqz * 1L * sqz > z) {
			sqz--;
		}
		return sqz;
	}

	static int log2(int N) {
		int result = (int) (Math.log(N) / Math.log(2));
		return result;
	}

	public static long gcd(long a, long b) {
		if (a > b)
			a = (a + b) - (b = a);
		if (a == 0L)
			return b;
		return gcd(b % a, a);
	}

	public static long lcm(long a, long b) {
		return (a * b) / gcd(a, b);
	}

	public static int lower_bound(int[] arr, int x) {
		int low = 0, high = arr.length - 1, mid = -1;
		int ans = -1;
		while (low <= high) {
			mid = (low + high) / 2;

			if (arr[mid] > x) {
				high = mid - 1;
			} else {
				ans = mid;
				low = mid + 1;
			}
		}

		return ans;
	}

	public static int upper_bound(int[] arr, int x) {
		int low = 0, high = arr.length - 1, mid = -1;
		int ans = arr.length;
		while (low < high) {
			mid = (low + high) / 2;

			if (arr[mid] >= x) {
				ans = mid;
				high = mid - 1;
			} else {
				low = mid + 1;
			}
		}

		return ans;
	}

	static void ruffleSort(int[] a) {
		Random get = new Random();
		for (int i = 0; i < a.length; i++) {
			int r = get.nextInt(a.length);
			int temp = a[i];
			a[i] = a[r];
			a[r] = temp;
		}
		Arrays.sort(a);
	}

	static void ruffleSort(long[] a) {
		Random get = new Random();
		for (int i = 0; i < a.length; i++) {
			int r = get.nextInt(a.length);
			long temp = a[i];
			a[i] = a[r];
			a[r] = temp;
		}
		Arrays.sort(a);
	}

	static void reverseArray(int[] a) {
		int n = a.length;
		int arr[] = new int[n];
		for (int i = 0; i < n; i++)
			arr[i] = a[n - i - 1];
		for (int i = 0; i < n; i++)
			a[i] = arr[i];
	}

	static void reverseArray(long[] a) {
		int n = a.length;
		long arr[] = new long[n];
		for (int i = 0; i < n; i++)
			arr[i] = a[n - i - 1];
		for (int i = 0; i < n; i++)
			a[i] = arr[i];
	}

	//custom multiset (replace with HashMap if needed)
	public static void push(TreeMap<Integer, Integer> map, int k, int v) {
		//map[k] += v;
		if (!map.containsKey(k))
			map.put(k, v);
		else
			map.put(k, map.get(k) + v);
	}

	public static void pull(TreeMap<Integer, Integer> map, int k, int v) {
		//assumes map[k] >= v
		//map[k] -= v
		int lol = map.get(k);
		if (lol == v)
			map.remove(k);
		else
			map.put(k, lol - v);
	}

	// compress Big value to Time Limit
	public static int[] compress(int[] arr) {
		ArrayList<Integer> ls = new ArrayList<Integer>();
		for (int x : arr)
			ls.add(x);
		Collections.sort(ls);
		HashMap<Integer, Integer> map = new HashMap<Integer, Integer>();
		int boof = 1; //min value
		for (int x : ls)
			if (!map.containsKey(x))
				map.put(x, boof++);
		int[] brr = new int[arr.length];
		for (int i = 0; i < arr.length; i++)
			brr[i] = map.get(arr[i]);
		return brr;
	}

	// Fast Writer 

	public static class FastWriter {
		private static final int BUF_SIZE = 1 << 13;
		private final byte[] buf = new byte[BUF_SIZE];
		private final OutputStream out;
		private int ptr = 0;

		private FastWriter() {
			out = null;
		}

		public FastWriter(OutputStream os) {
			this.out = os;
		}

		public FastWriter(String path) {
			try {
				this.out = new FileOutputStream(path);
			} catch (FileNotFoundException e) {
				throw new RuntimeException("FastWriter");
			}
		}

		public FastWriter write(byte b) {
			buf[ptr++] = b;
			if (ptr == BUF_SIZE)
				innerflush();
			return this;
		}

		public FastWriter write(char c) {
			return write((byte) c);
		}

		public FastWriter write(char[] s) {
			for (char c : s) {
				buf[ptr++] = (byte) c;
				if (ptr == BUF_SIZE)
					innerflush();
			}
			return this;
		}

		public FastWriter write(String s) {
			s.chars().forEach(c -> {
				buf[ptr++] = (byte) c;
				if (ptr == BUF_SIZE)
					innerflush();
			});
			return this;
		}

		private static int countDigits(int l) {
			if (l >= 1000000000)
				return 10;
			if (l >= 100000000)
				return 9;
			if (l >= 10000000)
				return 8;
			if (l >= 1000000)
				return 7;
			if (l >= 100000)
				return 6;
			if (l >= 10000)
				return 5;
			if (l >= 1000)
				return 4;
			if (l >= 100)
				return 3;
			if (l >= 10)
				return 2;
			return 1;
		}

		public FastWriter write(int x) {
			if (x == Integer.MIN_VALUE) {
				return write((long) x);
			}
			if (ptr + 12 >= BUF_SIZE)
				innerflush();
			if (x < 0) {
				write((byte) '-');
				x = -x;
			}
			int d = countDigits(x);
			for (int i = ptr + d - 1; i >= ptr; i--) {
				buf[i] = (byte) ('0' + x % 10);
				x /= 10;
			}
			ptr += d;
			return this;
		}

		private static int countDigits(long l) {
			if (l >= 1000000000000000000L)
				return 19;
			if (l >= 100000000000000000L)
				return 18;
			if (l >= 10000000000000000L)
				return 17;
			if (l >= 1000000000000000L)
				return 16;
			if (l >= 100000000000000L)
				return 15;
			if (l >= 10000000000000L)
				return 14;
			if (l >= 1000000000000L)
				return 13;
			if (l >= 100000000000L)
				return 12;
			if (l >= 10000000000L)
				return 11;
			if (l >= 1000000000L)
				return 10;
			if (l >= 100000000L)
				return 9;
			if (l >= 10000000L)
				return 8;
			if (l >= 1000000L)
				return 7;
			if (l >= 100000L)
				return 6;
			if (l >= 10000L)
				return 5;
			if (l >= 1000L)
				return 4;
			if (l >= 100L)
				return 3;
			if (l >= 10L)
				return 2;
			return 1;
		}

		public FastWriter write(long x) {
			if (x == Long.MIN_VALUE) {
				return write("" + x);
			}
			if (ptr + 21 >= BUF_SIZE)
				innerflush();
			if (x < 0) {
				write((byte) '-');
				x = -x;
			}
			int d = countDigits(x);
			for (int i = ptr + d - 1; i >= ptr; i--) {
				buf[i] = (byte) ('0' + x % 10);
				x /= 10;
			}
			ptr += d;
			return this;
		}

		public FastWriter write(double x, int precision) {
			if (x < 0) {
				write('-');
				x = -x;
			}
			x += Math.pow(10, -precision) / 2;
			//		if(x < 0){ x = 0; }
			write((long) x).write(".");
			x -= (long) x;
			for (int i = 0; i < precision; i++) {
				x *= 10;
				write((char) ('0' + (int) x));
				x -= (int) x;
			}
			return this;
		}

		public FastWriter writeln(char c) {
			return write(c).writeln();
		}

		public FastWriter writeln(int x) {
			return write(x).writeln();
		}

		public FastWriter writeln(long x) {
			return write(x).writeln();
		}

		public FastWriter writeln(double x, int precision) {
			return write(x, precision).writeln();
		}

		public FastWriter write(int... xs) {
			boolean first = true;
			for (int x : xs) {
				if (!first)
					write(' ');
				first = false;
				write(x);
			}
			return this;
		}

		public FastWriter write(long... xs) {
			boolean first = true;
			for (long x : xs) {
				if (!first)
					write(' ');
				first = false;
				write(x);
			}
			return this;
		}

		public FastWriter writeln() {
			return write((byte) '\n');
		}

		public FastWriter writeln(int... xs) {
			return write(xs).writeln();
		}

		public FastWriter writeln(long... xs) {
			return write(xs).writeln();
		}

		public FastWriter writeln(char[] line) {
			return write(line).writeln();
		}

		public FastWriter writeln(char[]... map) {
			for (char[] line : map)
				write(line).writeln();
			return this;
		}

		public FastWriter writeln(String s) {
			return write(s).writeln();
		}

		private void innerflush() {
			try {
				out.write(buf, 0, ptr);
				ptr = 0;
			} catch (IOException e) {
				throw new RuntimeException("innerflush");
			}
		}

		public void flush() {
			innerflush();
			try {
				out.flush();
			} catch (IOException e) {
				throw new RuntimeException("flush");
			}
		}

		public FastWriter print(byte b) {
			return write(b);
		}

		public FastWriter print(char c) {
			return write(c);
		}

		public FastWriter print(char[] s) {
			return write(s);
		}

		public FastWriter print(String s) {
			return write(s);
		}

		public FastWriter print(int x) {
			return write(x);
		}

		public FastWriter print(long x) {
			return write(x);
		}

		public FastWriter print(double x, int precision) {
			return write(x, precision);
		}

		public FastWriter println(char c) {
			return writeln(c);
		}

		public FastWriter println(int x) {
			return writeln(x);
		}

		public FastWriter println(long x) {
			return writeln(x);
		}

		public FastWriter println(double x, int precision) {
			return writeln(x, precision);
		}

		public FastWriter print(int... xs) {
			return write(xs);
		}

		public FastWriter print(long... xs) {
			return write(xs);
		}

		public FastWriter println(int... xs) {
			return writeln(xs);
		}

		public FastWriter println(long... xs) {
			return writeln(xs);
		}

		public FastWriter println(char[] line) {
			return writeln(line);
		}

		public FastWriter println(char[]... map) {
			return writeln(map);
		}

		public FastWriter println(String s) {
			return writeln(s);
		}

		public FastWriter println() {
			return writeln();
		}
	}

	// Fast Inputs
	static class FastScanner {
		//I don't understand how this works lmao
		private int BS = 1 << 16;
		private char NC = (char) 0;
		private byte[] buf = new byte[BS];
		private int bId = 0, size = 0;
		private char c = NC;
		private double cnt = 1;
		private BufferedInputStream in;

		public FastScanner() {
			in = new BufferedInputStream(System.in, BS);
		}

		public FastScanner(String s) {
			try {
				in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
			} catch (Exception e) {
				in = new BufferedInputStream(System.in, BS);
			}
		}

		private char getChar() {
			while (bId == size) {
				try {
					size = in.read(buf);
				} catch (Exception e) {
					return NC;
				}
				if (size == -1)
					return NC;
				bId = 0;
			}
			return (char) buf[bId++];
		}

		public int nextInt() {
			return (int) nextLong();
		}

		public int[] readArray(int N) {
			int[] res = new int[N];
			for (int i = 0; i < N; i++) {
				res[i] = (int) nextLong();
			}
			return res;
		}

		public long[] readArrayLong(int N) {
			long[] res = new long[N];
			for (int i = 0; i < N; i++) {
				res[i] = nextLong();
			}
			return res;
		}

		public int[][] readArrayMatrix(int N, int M, int Index) {
			if (Index == 0) {
				int[][] res = new int[N][M];
				for (int i = 0; i < N; i++) {
					for (int j = 0; j < M; j++)
						res[i][j] = (int) nextLong();
				}
				return res;
			}
			int[][] res = new int[N][M];
			for (int i = 1; i <= N; i++) {
				for (int j = 1; j <= M; j++)
					res[i][j] = (int) nextLong();
			}
			return res;

		}

		public long[][] readArrayMatrixLong(int N, int M, int Index) {
			if (Index == 0) {
				long[][] res = new long[N][M];
				for (int i = 0; i < N; i++) {
					for (int j = 0; j < M; j++)
						res[i][j] = nextLong();
				}
				return res;
			}
			long[][] res = new long[N][M];
			for (int i = 1; i <= N; i++) {
				for (int j = 1; j <= M; j++)
					res[i][j] = nextLong();
			}
			return res;

		}

		public long nextLong() {
			cnt = 1;
			boolean neg = false;
			if (c == NC)
				c = getChar();
			for (; (c < '0' || c > '9'); c = getChar()) {
				if (c == '-')
					neg = true;
			}
			long res = 0;
			for (; c >= '0' && c <= '9'; c = getChar()) {
				res = (res << 3) + (res << 1) + c - '0';
				cnt *= 10;
			}
			return neg ? -res : res;
		}

		public double nextDouble() {
			double cur = nextLong();
			return c != '.' ? cur : cur + nextLong() / cnt;
		}

		public double[] readArrayDouble(int N) {
			double[] res = new double[N];
			for (int i = 0; i < N; i++) {
				res[i] = nextDouble();
			}
			return res;
		}

		public String next() {
			StringBuilder res = new StringBuilder();
			while (c <= 32)
				c = getChar();
			while (c > 32) {
				res.append(c);
				c = getChar();
			}
			return res.toString();
		}

		public String nextLine() {
			StringBuilder res = new StringBuilder();
			while (c <= 32)
				c = getChar();
			while (c != '\n') {
				res.append(c);
				c = getChar();
			}
			return res.toString();
		}

		public boolean hasNext() {
			if (c > 32)
				return true;
			while (true) {
				c = getChar();
				if (c == NC)
					return false;
				else if (c > 32)
					return true;
			}
		}
	}

}
