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.*;
import java.util.*;


import java.math.*;
import java.math.BigInteger;


public final class A
{    
	static PrintWriter out = new PrintWriter(System.out); 
	static StringBuilder ans=new StringBuilder();
	static FastReader in=new FastReader();
	static ArrayList<Integer> g[];
	static long mod=(long)1e9+7,INF=Long.MAX_VALUE;
	static boolean set[]; 
	static int par[],partial[];
	static int Days[],P[][];
	static int dp[][],sum=0,size[],D[];
	static int seg[],col[];
	static ArrayList<Long> A;
	//	static HashSet<Integer> visited,imposters;
	//	static HashSet<Integer> set;
	//	static node1 seg[];
	//static pair moves[]= {new pair(-1,0),new pair(1,0), new pair(0,-1), new pair(0,1)};
	public static void main(String args[])throws IOException
	{	


		int T=i();
		outer:while(T-->0)
		{
			int N=i();
			int A[]=input(N);
			long s=0;
			for(int a:A)s+=a;
			HashSet<Integer> set=new HashSet<>();
			long max=0;
			int index=-1;
			if(isPrime(s))
			{
				for(int i=0; i<N; i++)
				{
					if(isPrime(s-A[i])==false)
					{
						if(s-A[i]>max)
						{
							max=s-A[i];
							index=i+1;
						}
					}
				}
				ans.append(N-1+"\n");
				for(int i=1; i<=N; i++)
				{
					if(i==index)continue;
					ans.append(i+" ");
				}
				ans.append("\n");
				
			}
			else
			{
				ans.append(N+"\n");
				for(int i=1; i<=N; i++)
				{
//					if(i==index)continue;
					ans.append(i+" ");
				}
				ans.append("\n");
			}
		}
		out.println(ans);
		out.close();
	}
	static int ask(int a,int b)
	{
		System.out.println("? "+a+" "+b);
		return i();
	}
	

	
	static void update(char X[][],int min[][],int i,int j,int N,int M,int d)
	{
		int x=i,y=j;
		int t=d+1;
		while(t-->0 && i>=0 && j>=0 && X[i][j]=='*')
		{
			min[i][j]=Math.max(min[i][j],d);
			i--;
			j--;
		}
		i=x;
		j=y;
		t=d+1;
		while(t-->0 && i>=0 && j<M && X[i][j]=='*')
		{
			min[i][j]=Math.max(min[i][j],d);
			i--;
			j++;
		}	
	}

	static long and(int i,int j)
	{
		System.out.println("and "+i+" "+j);
		return l();
	}
	static long or(int i,int j)
	{
		System.out.println("or "+i+" "+j);
		return l();
	}
	static boolean is_Sorted(int A[])
	{
		int N=A.length;
		for(int i=1; i<=N; i++)if(A[i-1]!=i)return false;
		return true;
	}
	static boolean f(StringBuilder sb,String Y,String order)
	{
		StringBuilder res=new StringBuilder(sb.toString());
		HashSet<Character> set=new HashSet<>();
		for(char ch:order.toCharArray())
		{
			set.add(ch);
			for(int i=0; i<sb.length(); i++)
			{
				char x=sb.charAt(i);
				if(set.contains(x))continue;
				res.append(x);
			}
		}

		String str=res.toString();
		return str.equals(Y);
	}
	static boolean all_Zero(int f[])
	{
		for(int a:f)if(a!=0)return false;
		return true;
	}
	static long form(int a,int l)
	{
		long x=0;
		while(l-->0)
		{
			x*=10;
			x+=a;
		}
		return x;
	}
	static int count(String X)
	{
		HashSet<Integer> set=new HashSet<>();
		for(char x:X.toCharArray())set.add(x-'0');
		return set.size();
	}


	//	static void build(int v,int tl,int tr,long A[])
	//	{
	//		if(tl==tr)
	//		{
	//			seg[v]=A[tl];
	//		}
	//		else
	//		{
	//			int tm=(tl+tr)/2;
	//			build(v*2,tl,tm,A);
	//			build(v*2+1,tm+1,tr,A);
	//			seg[v]=Math.min(seg[v*2], seg[v*2+1]);
	//		}
	//	}
	static long ask(int v,int tl,int tr,int l,int r)
	{
		if(l>r)return (long)(1e10);
		if(tl==l && tr==r)
		{
			return seg[v];
		}
		int tm=(tl+tr)/2;
		return Math.min(ask(v*2,tl,tm,l,Math.min(tm, r)), ask(v*2+1,tm+1,tr,Math.max(l,tm+1),r));
	}
	static int [] sub(int A[],int B[])
	{
		int N=A.length;
		int f[]=new int[N];
		for(int i=N-1; i>=0; i--)
		{
			if(B[i]<A[i])
			{
				B[i]+=26;
				B[i-1]-=1;
			}
			f[i]=B[i]-A[i];
		}
		for(int i=0; i<N; i++)
		{
			if(f[i]%2!=0)f[i+1]+=26;
			f[i]/=2;
		}
		return f;
	}





	static int max(int a ,int b,int c,int d)
	{
		a=Math.max(a, b);
		c=Math.max(c,d);
		return Math.max(a, c);
	}
	static int min(int a ,int b,int c,int d)
	{
		a=Math.min(a, b);
		c=Math.min(c,d);
		return Math.min(a, c);
	}



	static HashMap<Integer,Integer> Hash(int A[])
	{
		HashMap<Integer,Integer> mp=new HashMap<>();
		for(int a:A)
		{
			int f=mp.getOrDefault(a,0)+1;
			mp.put(a, f);
		}
		return mp;
	}
	static long mul(long a, long b)
	{
		return ( a %mod * 1L * b%mod )%mod;
	}
	static void swap(int A[],int a,int b)
	{
		int t=A[a];
		A[a]=A[b];
		A[b]=t;
	}


	static int find(int a)
	{
		if(par[a]<0)return a;
		return par[a]=find(par[a]);
	}
	static void union(int a,int b)
	{
		a=find(a);
		b=find(b);
		if(a!=b)
		{
			par[a]+=par[b];
			par[b]=a;
		}
	}
	static boolean isSorted(int A[])
	{
		for(int i=1; i<A.length; i++)
		{
			if(A[i]<A[i-1])return false;
		}
		return true;
	}

	static boolean isDivisible(StringBuilder X,int i,long num)
	{
		long r=0;
		for(; i<X.length(); i++)
		{
			r=r*10+(X.charAt(i)-'0');
			r=r%num;
		}
		return r==0;
	}    



	static int lower_Bound(int A[],int low,int high, int x) 
	{ 
		if (low > high) 
			if (x >= A[high]) 
				return A[high]; 

		int mid = (low + high) / 2; 

		if (A[mid] == x) 
			return A[mid]; 

		if (mid > 0 && A[mid - 1] <= x && x < A[mid]) 
			return A[mid - 1]; 

		if (x < A[mid]) 
			return lower_Bound( A, low, mid - 1, x); 

		return lower_Bound(A, mid + 1, high, x); 
	} 

	static String f(String A)
	{
		String X="";
		for(int i=A.length()-1; i>=0; i--)
		{
			int c=A.charAt(i)-'0';
			X+=(c+1)%2;
		}
		return X;
	}

	static void sort(long[] a) //check for long
	{
		ArrayList<Long> l=new ArrayList<>();
		for (long i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}

	static String swap(String X,int i,int j)
	{
		char ch[]=X.toCharArray();
		char a=ch[i];
		ch[i]=ch[j];
		ch[j]=a;
		return new String(ch);
	}

	static int sD(long n)  
	{  

		if (n % 2 == 0 )  
			return 2;  

		for (int i = 3; i * i <= n; i += 2) {  
			if (n % i == 0 )  
				return i;  
		}  

		return (int)n;  
	}  

	static void setGraph(int N)
	{
		//		tot=new int[N+1];
		partial=new int[N+1];
		Days=new int[N+1];
		P=new int[N+1][(int)(Math.log(N)+10)];
		set=new boolean[N+1];
		g=new ArrayList[N+1];
		D=new int[N+1];
		for(int i=0; i<=N; i++)
		{

			g[i]=new ArrayList<>();		
			Days[i]=-1;
			D[i]=Integer.MAX_VALUE;
			//D2[i]=INF;
		}
	}



	static  long pow(long a,long b)
	{
		//long mod=1000000007;
		long pow=1;
		long x=a;
		while(b!=0)
		{
			if((b&1)!=0)pow=(pow*x)%mod;
			x=(x*x)%mod;
			b/=2;
		}
		return pow;
	}

	static long toggleBits(long x)//one's complement || Toggle bits
	{
		int n=(int)(Math.floor(Math.log(x)/Math.log(2)))+1;

		return ((1<<n)-1)^x;
	}

	static int countBits(long a)
	{
		return (int)(Math.log(a)/Math.log(2)+1);
	}

	static long fact(long N)
	{ 
		long n=2; 
		if(N<=1)return 1;
		else
		{
			for(int i=3; i<=N; i++)n=(n*i)%mod;
		}
		return n;
	}

	static int kadane(int A[])
	{
		int lsum=A[0],gsum=A[0];
		for(int i=1; i<A.length; i++)
		{
			lsum=Math.max(lsum+A[i],A[i]);
			gsum=Math.max(gsum,lsum);
		}
		return gsum;
	}

	static void sort(int[] a) {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}

	static boolean isPrime(long N)
	{
		if (N<=1)  return false; 
		if (N<=3)  return true; 
		if (N%2 == 0 || N%3 == 0) return false; 
		for (int i=5; i*i<=N; i=i+6) 
			if (N%i == 0 || N%(i+2) == 0) 
				return false; 
		return true; 
	}
	static void print(char A[])
	{
		for(char c:A)System.out.print(c+" ");
		System.out.println();
	}
	static void print(boolean A[])
	{
		for(boolean c:A)System.out.print(c+" ");
		System.out.println();
	}
	static void print(int A[])
	{
		for(int a:A)System.out.print(a+" ");
		System.out.println();	
	}
	static void print(long A[])
	{
		for(long i:A)System.out.print(i+ " ");
		System.out.println();

	}
	static void print(boolean A[][])
	{
		for(boolean a[]:A)print(a);
	}
	static void print(long A[][])
	{
		for(long a[]:A)print(a);
	}
	static void print(int A[][])
	{
		for(int a[]:A)print(a);
	}
	static void print(ArrayList<Integer> A)
	{
		for(int a:A)System.out.print(a+" ");
		System.out.println();
	}

	static int i()
	{
		return in.nextInt();
	}

	static long l()
	{
		return in.nextLong();
	}

	static int[] input(int N){
		int A[]=new int[N];
		for(int i=0; i<N; i++)
		{
			A[i]=in.nextInt();
		}
		return A;
	}

	static long[] inputLong(int N)     {
		long A[]=new long[N];
		for(int i=0; i<A.length; i++)A[i]=in.nextLong();
		return A;
	}

	static long GCD(long a,long b) 
	{
		if(b==0)
		{
			return a;
		}
		else return GCD(b,a%b );
	}

}
class Edge
{
	int a,cnt;
	//	boolean said;
	Edge(int a,int cnt)
	{
		this.a=a;
		//		this.said=said;
		this.cnt=cnt;
	}

}


//Code For FastReader
//Code For FastReader
//Code For FastReader
//Code For FastReader
class FastReader
{
	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;
	}

}