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 java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStreamWriter;

import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Map.Entry;


import java.util.Random;
import java.util.TreeSet;

public final class CF_749_D2_A
{


	static boolean verb=true;
	static void log(Object X){if (verb) System.err.println(X);}
	static void log(Object[] X){if (verb) {for (Object U:X) System.err.print(U+" ");System.err.println("");}}
	static void log(int[] X){if (verb) {for (int U:X) System.err.print(U+" ");System.err.println("");}}
	static void logWln(int[] X){if (verb) {for (int U:X) System.err.print(U+" ");}}
	static void log(int[] X,int L){if (verb) {for (int i=0;i<L;i++) System.err.print(X[i]+" ");System.err.println("");}}
	static void log(long[] X){if (verb) {for (long U:X) System.err.print(U+" ");System.err.println("");}}

	static void logWln(Object X){if (verb) System.err.print(X);}
	static void info(Object o){	System.out.println(o);}
	static void output(Object o){outputWln(""+o+"\n");	}
	static void outputFlush(Object o){try {out.write(""+ o+"\n");out.flush();} catch (Exception e) {}}
	static void outputWln(Object o){try {out.write(""+ o);} catch (Exception e) {}}


	static void logBin(int[] tm) {for (int x:tm) logWln(bin(8,x)+" ");log("");}

	static String bin(int L,int x) {
		String s=Integer.toBinaryString(x);
		while (s.length()<L) s="0"+s;
		return s;
	}

	// Global vars
	static BufferedWriter out;
	static InputReader reader;


	static void test() {
		log("testing");

		Random r=new Random();
		int NTESTS=1000000;
		int NMAX=22;
		int VMAX=10;
		for (int t=0;t<NTESTS;t++) {

		}
		log("testing done");

	}



	static class Composite implements Comparable<Composite>{

		int a;
		int b;

		public int compareTo(Composite X) {
			int diff=b-a;
			int Xdiff=X.b-X.a;
			if (diff!=Xdiff)
				return diff-Xdiff;
			return a-X.a;
		}

		public Composite(int a, int b) {
			this.a = a;
			this.b = b;
		}



	}

	static int NX=1001;
	static int[] stack=new int[NX];
	
	static boolean isPrime(int x) {
		
		for (int u=2;u*u<=x;u++) {
			if (x%u==0)
				return true;
		}
		return false;
	}
	
	static ArrayList<Integer>[] friends;

	static void process() throws Exception {

		log("hello");

		out = new BufferedWriter(new OutputStreamWriter(System.out));
		reader = new InputReader(System.in);

		int T=reader.readInt();
		for (int t=0;t<T;t++) {
			int n=reader.readInt();
			//ArrayList<Integer> odd=new ArrayList<Integer>(n);
			//ArrayList<Integer> ev=new ArrayList<Integer>(n);
			int sum=0;
			int[] a=new int[n];
			for (int i=0;i<n;i++) {
				int x=reader.readInt();
				a[i]=x;
				sum+=x;
			}
			if (isPrime(sum)) {
				//log("case 1");
				output(n);
				for (int i=0;i<n;i++) {
					outputWln((i+1)+" ");
				}
				output("");
			} else {
				// even number of 1
				//log("case 2");
				output(n-1);
				
				boolean first=true;
				for (int i=0;i<n;i++) {
					
					if (a[i]%2==1) {
						if (first) {
							first=false;
						} else {
							outputWln((i+1)+" ");
						}
					} else {
						outputWln((i+1)+" ");
					}
				}
				output("");
			}
		}
	
		try {
			out.close();
		} catch (Exception Ex) {
		}

	}





	public static void main(String[] args) throws Exception {
		process();

	}

	static final class InputReader {
		private final InputStream stream;
		private final byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		private int read() throws IOException {
			if (curChar >= numChars) {
				curChar = 0;
				numChars = stream.read(buf);
				if (numChars <= 0) {
					return -1;
				}
			}
			return buf[curChar++];
		}

		public final String readString() throws IOException {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.append((char) c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public final String readString(int L) throws IOException {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			StringBuilder res = new StringBuilder(L);
			do {
				res.append((char) c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public final int readInt() throws IOException {
			int c = read();
			boolean neg = false;
			while (isSpaceChar(c)) {
				c = read();
			}
			char d = (char) c;
			// log("d:"+d);
			if (d == '-') {
				neg = true;
				c = read();
			}
			int res = 0;
			do {
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			// log("res:"+res);
			if (neg)
				return -res;
			return res;

		}

		public final long readLong() throws IOException {
			int c = read();
			boolean neg = false;
			while (isSpaceChar(c)) {
				c = read();
			}
			char d = (char) c;
			// log("d:"+d);
			if (d == '-') {
				neg = true;
				c = read();
			}
			long res = 0;
			do {
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			// log("res:"+res);
			if (neg)
				return -res;
			return res;

		}

		private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
	}

}
/*

1
10
1 0 0 0 0 1 0 0 1 1

1
12
1 0 0 1 0 0 1 0 0 0 0 1

1
12
1 0 0 1 0 0 1 0 0 0 0 1

3
12
1 0 0 1 0 0 1 0 0 0 0 1
10
1 0 0 0 0 1 0 0 1 1
12
1 0 0 1 0 0 1 0 0 0 0 1

1
11
1 0 0 0 0 0 0 0 1 1 1



19
1 1 0 1 1 1 1 1 1 0 1 0 0 0 0 1 0 1 1 


19
1 0 0 1 1 0 0 1 1 0 0 0 1 1 0 0 0 1 0 


19
1 0 0 0 1 1 0 0 1 1 0 0 0 1 1 0 0 1 0 


1
20
1 1 0 0 0 1 0 1 1 1 0 1 1 1 1 1 0 0 1 0 

 */