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.util.*;
import java.io.*;
// import java.lang.*;
// import java.math.*;

public class Codeforces {
    static FastReader sc=new FastReader();
	static PrintWriter out=new PrintWriter(System.out);
	static long mod=1000000007;
	// static long mod=998244353;
	static int MAX=Integer.MAX_VALUE;
	static int MIN=Integer.MIN_VALUE;
	static long MAXL=Long.MAX_VALUE;
	static long MINL=Long.MIN_VALUE;
	static ArrayList<Integer> graph[];
	static long fact[];
	static StringBuffer sb;
	public static void main (String[] args) throws java.lang.Exception
	{
		// code goes here
		int t=I();
		outer:while(t-->0)
		{
			int n=I();
			int a[]=new int[n];
			int sum=0;
			for(int i=0;i<n;i++){
				a[i]=I();
				sum+=a[i];
			}
			if(!isPrime(sum)){
				out.println(n);
				for(int i=1;i<=n;i++){
					out.print(i+" ");
				}out.println();
			}else{
				int q=-1;
				for(int i=0;i<n;i++){
					if(!isPrime(sum-a[i])){
						q=i;
						break;
					}
				}
				out.println(n-1);
				for(int i=1;i<=n;i++){
					if(i==q+1)continue;
					out.print(i+" ");
				}out.println();
			}
		}
		out.close();
	}
	public static class pair
    {
    	int a;
    	int b;
    	public pair(int val,int index)
    	{
    	    a=val;
    	    b=index;
    	}
    }
	public static class myComp implements Comparator<pair>
	{
		//sort in ascending order.
		public int compare(pair p1,pair p2)
		{
			if(p1.a==p2.a)
    	    return 0;
    	    else if(p1.a<p2.a)
    	    return -1;
    	    else
    	    return 1;
		}
		//sort in descending order.
		// public int compare(pair p1,pair p2)
    	// {
    	//     if(p1.a==p2.a)
    	//     return 0;
    	//     else if(p1.a<p2.a)
    	//     return 1;
    	//     else
    	//     return -1;
    	// }
	}
	public static long nPr(int n,int r)
	{
		long ans=divide(fact(n),fact(n-r),mod);
		return ans;
	}
	public static long nCr(int n,int r)
	{
		long ans=divide(fact[n],mul(fact[n-r],fact[r]),mod);
		return ans;
	}
	public static long kadane(long a[],int n)  //largest sum subarray
	{
		long max_sum=Long.MIN_VALUE,max_end=0;
		for(int i=0;i<n;i++){
			max_end+=a[i];
			if(max_sum<max_end){max_sum=max_end;}
			if(max_end<0){max_end=0;}
		}
		return max_sum;
	}
	public static void DFS(int s,boolean visited[])
	{
		visited[s]=true;
		for(int i:graph[s]){
			if(!visited[i]){
				DFS(i,visited);
			}
		}
	}
	public static void setGraph(int n,int m)
	{
		graph=new ArrayList[n+1];
		for(int i=0;i<=n;i++){
			graph[i]=new ArrayList<>();
		}
		for(int i=0;i<m;i++){
			int u=I(),v=I();
			graph[u].add(v);
			graph[v].add(u);
		}
	}
	public static int BS(long a[],long x,int ii,int jj)
	{
		// int n=a.length;
		int mid=0;
		int i=ii,j=jj;
		while(i<=j)
		{
			mid=(i+j)/2;
			if(a[mid]<x){
				i=mid+1;
			}else if(a[mid]>x){
				j=mid-1;
			}else{
				return mid;
			}
		}
		return -1;
	}

	//LOWER_BOUND and UPPER_BOUND functions

	public static int lower_bound(long arr[],int start, int end, long X)   //start=0,end=n-1
	{
		if(arr[arr.length-1]<X)return end;
		if(arr[0]>X)return -1;
		int left=start,right=end;
		while(left<right){
			int mid=(left+right)/2;
			if(arr[mid]==X){                                      //Returns last index of lower bound value.
				if(mid<end && arr[mid+1]==X){
					left=mid+1;
				}else{
					return mid;
				}
			}
			// if(arr[mid]==X){                                   //Returns first index of lower bound value.
			// 	if(mid>start && arr[mid-1]==X){
			// 		right=mid-1;
			// 	}else{
			// 		return mid;
			// 	}
			// }
			else if(arr[mid]>X){
				if(mid>start && arr[mid-1]<X){
					return mid-1;
				}else{
					right=mid-1;
				}
			}else{
				if(mid<end && arr[mid+1]>X){
					return mid;
				}else{
					left=mid+1;
				}
			}
		}
		return left;
	}
	public static int upper_bound(long arr[],int start,int end,long X)			//start=0,end=n-1
	{
		if(arr[0]>=X)return start;
		if(arr[arr.length-1]<X)return -1;
		int left=start,right=end;
		while(left<right){
			int mid=(left+right)/2;
			if(arr[mid]==X){                                   //returns first index of upper bound value.
				if(mid>start && arr[mid-1]==X){
					right=mid-1;
				}else{
					return mid;
				}
			}
			// if(arr[mid]==X){									//returns last index of upper bound value.
			// 	if(mid<end && arr[mid+1]==X){
			// 		left=mid+1;
			// 	}else{
			// 		return mid;
			// 	}
			// }
			else if(arr[mid]>X){
				if(mid>start && arr[mid-1]<X){
					return mid;
				}else{
					right=mid-1;
				}
			}else{
				if(mid<end && arr[mid+1]>X){
					return mid+1;
				}else{
					left=mid+1;
				}
			}
		}
		return left;
	}

	//END

	public static boolean isSorted(int a[])
	{
		int n=a.length;
		for(int i=0;i<n-1;i++){
			if(a[i]>a[i+1])return false;
		}
		return true;
	}
	public static boolean isSorted(long a[])
	{
		int n=a.length;
		for(int i=0;i<n-1;i++){
			if(a[i]>a[i+1])return false;
		}
		return true;
	}
	public static int computeXOR(int n) //compute XOR of all numbers between 1 to n.
    {
        if (n % 4 == 0)
            return n;
        if (n % 4 == 1)
            return 1;
        if (n % 4 == 2)
            return n + 1;
        return 0;
    }
	public static ArrayList<Integer> primeSieve(int n)
	{
	    ArrayList<Integer> arr=new ArrayList<>();
	    boolean prime[] = new boolean[n + 1];
        for (int i = 0; i <= n; i++)
        prime[i] = true;
        for (int p = 2; p * p <= n; p++)
        {
            if (prime[p] == true)
            {
                for (int i = p * p; i <= n; i += p)
                prime[i] = false;
            }
        }
        for (int i = 2; i <= n; i++)
        {
            if (prime[i] == true)
            arr.add(i);
        }
        return arr;
	}

	// Fenwick / BinaryIndexed  Tree  USE IT - FenwickTree ft1=new FenwickTree(n);
	public static class FenwickTree
	{
		int farr[];
		int n;
		public FenwickTree(int c)
		{
			n=c+1;
			farr=new int[n];
		}
		// public void update_range(int l,int r,long p)
		// {
		// 	update(l,p);
		// 	update(r+1,(-1)*p);
		// }
		public void update(int x,int p)
		{
			for(;x<n;x+=x&(-x))
			{
				farr[x]+=p;
			}
		}
		public long get(int x)
		{
			long ans=0;
			for(;x>0;x-=x&(-x))
			{
				ans=ans+farr[x];
			}
			return ans;
		}
	}

	//Disjoint Set Union
	public static class DSU
	{
	    int par[],rank[];
	    public DSU(int c)
	    {
	        par=new int[c+1];
	        rank=new int[c+1];
	        for(int i=0;i<=c;i++)
	        {
	            par[i]=i;
	            rank[i]=0;
	        }
	    }
	    public int find(int a)
	    {
	        if(a==par[a])
	        return a;
	        return par[a]=find(par[a]);
	    }
	    public void union(int a,int b)
	    {
	        int a_rep=find(a),b_rep=find(b);
	        if(a_rep==b_rep)
	        return;
	        if(rank[a_rep]<rank[b_rep])
	        par[a_rep]=b_rep;
	        else if(rank[a_rep]>rank[b_rep])
	        par[b_rep]=a_rep;
	        else
	        {
	            par[b_rep]=a_rep;
	            rank[a_rep]++;
	        }
	    }
	}
    public static class myComp1 implements Comparator<pair1>
    {
		//sort in ascending order.
    	public int compare(pair1 p1,pair1 p2)
    	{
    	    if(p1.a==p2.a)
    	    return 0;
    	    else if(p1.a<p2.a)
    	    return -1;
    	    else
    	    return 1;
    	}
		//sort in descending order.
		// public int compare(pair p1,pair p2)
    	// {
    	//     if(p1.a==p2.a)
    	//     return 0;
    	//     else if(p1.a<p2.a)
    	//     return 1;
    	//     else
    	//     return -1;
    	// }
    }
	public static class pair1
    {
    	long a;
    	long b;
    	public pair1(long val,long index)
    	{
    	    a=val;
    	    b=index;
    	}
    }
    public static ArrayList<pair1> mergeIntervals(ArrayList<pair1> arr)
	{
	    //****************use this in main function-Collections.sort(arr,new myComp1());
	    ArrayList<pair1> a1=new ArrayList<>();
	    if(arr.size()<=1)
	    return arr;
	    a1.add(arr.get(0));
	    int i=1,j=0;
	    while(i<arr.size())
	    {
	        if(a1.get(j).b<arr.get(i).a)
	        {
	           a1.add(arr.get(i));
	           i++;
	           j++;
	        }
	        else if(a1.get(j).b>arr.get(i).a && a1.get(j).b>=arr.get(i).b)
	        {
	            i++;
	        }
	        else if(a1.get(j).b>=arr.get(i).a)
	        {
	            long a=a1.get(j).a;
	            long b=arr.get(i).b;
	            a1.remove(j);
	            a1.add(new pair1(a,b));
	            i++;
	        }
	    }
	    return a1;
	}
	public static ArrayList<Long> primeFact(long a)
	{
	    ArrayList<Long> arr=new ArrayList<>();
	    while(a%2==0){
	        arr.add(2L);
	        a=a/2;
	    }
	    for(long i=3;i*i<=a;i+=2){
	        while(a%i==0){
	            arr.add(i);
	            a=a/i;
	        }
	    }
	    if(a>2)arr.add(a);
	    return arr;
	}
	public static boolean isInteger(double N)
	{
		int X = (int)N;
		double temp2 = N - X;
		if (temp2 > 0)
		{
			return false;
		}
		return true;
	}
	public static boolean isPalindrome(String s,int n)
	{
		for(int i=0;i<=n/2;i++){
			if(s.charAt(i)!=s.charAt(n-i-1)){
				return false;
			}
		}
		return true;
	}
	public static int gcd(int a,int b)
	{
	    if(b==0)
	    return a;
	    else
	    return gcd(b,a%b);
	}
	public static long gcd(long a,long b)
	{
	    if(b==0)
	    return a;
	    else
	    return gcd(b,a%b);
	}
	public static long fact(long n)
	{
		long fact=1;
		for(long i=2;i<=n;i++){
			fact=((fact%mod)*(i%mod))%mod;
		}
		return fact;
	}
	public static long fact(int n)
	{
		long fact=1;
		for(int i=2;i<=n;i++){
			fact=((fact%mod)*(i%mod))%mod;
		}
		return fact;
	} 
	public static boolean isPrime(int n) 
	{ 
	    if (n <= 1) 
	        return false; 
	    if (n <= 3) 
	        return true; 
	    if (n % 2 == 0 || n % 3 == 0) 
	        return false; 
	    double sq=Math.sqrt(n);
	  
	    for (int i = 5; i <= sq; i = i + 6) 
	        if (n % i == 0 || n % (i + 2) == 0) 
	            return false; 
	    return true; 
	} 
    public static boolean isPrime(long n) 
	{ 
	    if (n <= 1) 
	        return false; 
	    if (n <= 3) 
	        return true; 
	    if (n % 2 == 0 || n % 3 == 0) 
	        return false; 
	    double sq=Math.sqrt(n);
	
	    for (int i = 5; i <= sq; i = i + 6) 
	        if (n % i == 0 || n % (i + 2) == 0) 
	            return false; 
	    return true; 
	}
	public static void printArray(long a[])
	{
		for(int i=0;i<a.length;i++){
			out.print(a[i]+" ");
		}
		out.println();
	}
	public static void printArray(int a[])
	{
		for(int i=0;i<a.length;i++){
			out.print(a[i]+" ");
		}
		out.println();
	}
	public static void printArray(char a[])
	{
		for(int i=0;i<a.length;i++){
			out.print(a[i]);
		}
		out.println();
	}
	public static void printArray(String a[])
	{
		for(int i=0;i<a.length;i++){
			out.print(a[i]+" ");
		}
		out.println();
	}
	public static void printArray(boolean a[])
	{
		for(int i=0;i<a.length;i++){
			out.print(a[i]+" ");
		}
		out.println();
	}
	public static void printArray(pair a[])
	{
		for(pair p:a){
			out.println(p.a+"->"+p.b);
		}
	}
	public static void printArray(int a[][])
	{
		for(int i=0;i<a.length;i++){
			for(int j=0;j<a[i].length;j++){
				out.print(a[i][j]+" ");
			}out.println();
		}
	}
	public static void printArray(long a[][])
	{
		for(int i=0;i<a.length;i++){
			for(int j=0;j<a[i].length;j++){
				out.print(a[i][j]+" ");
			}out.println();
		}
	}
	public static void printArray(char a[][])
	{
		for(int i=0;i<a.length;i++){
			for(int j=0;j<a[i].length;j++){
				out.print(a[i][j]+" ");
			}out.println();
		}
	}
	public static void printArrayL(ArrayList<Long> arr)
	{
		for(int i=0;i<arr.size();i++){
			out.print(arr.get(i)+" ");
		}
		out.println();
	}
	public static void printArrayI(ArrayList<Integer> arr)
	{
		for(int i=0;i<arr.size();i++){
			out.print(arr.get(i)+" ");
		}
		out.println();
	}
	public static void printArrayS(ArrayList<String> arr)
	{
		for(int i=0;i<arr.size();i++){
			out.print(arr.get(i)+" ");
		}
		out.println();
	}
	public static void printMapInt(HashMap<Integer,Integer> hm){
		for(Map.Entry<Integer,Integer> e:hm.entrySet()){
			out.println(e.getKey()+"->"+e.getValue());
		}out.println();
	}
	public static void printMapLong(HashMap<Long,Long> hm){
		for(Map.Entry<Long,Long> e:hm.entrySet()){
			out.println(e.getKey()+"->"+e.getValue());
		}out.println();
	}

	//Modular Arithmetic

	public static long add(long a,long b)
	{
		a+=b;
		if(a>=mod)a-=mod;
		return a;
	}
	public static long sub(long a,long b)
	{
		a-=b;
		if(a<0)a+=mod;
		return a;
	}
	public static long mul(long a,long b)
	{
		return ((a%mod)*(b%mod))%mod;
	}
	public static long divide(long a,long b,long m)
	{
		a=mul(a,modInverse(b,m));
		return a;
	}
	public static long modInverse(long a,long m)
	{
		int x=0,y=0;
		own p=new own(x,y);
		long g=gcdExt(a,m,p);
		if(g!=1){
			out.println("inverse does not exists");
			return -1;
		}else{
			long res=((p.a%m)+m)%m;
			return res;
		}
	}
	public static long gcdExt(long a,long b,own p)
	{
		if(b==0){
			p.a=1;
			p.b=0;
			return a;
		}
		int x1=0,y1=0;
		own p1=new own(x1,y1);
		long gcd=gcdExt(b,a%b,p1);
		p.b=p1.a - (a/b) * p1.b;
		p.a=p1.b;
		return gcd;
	}
	public static long pwr(long m,long n)
	{
		long res=1;
		m=m%mod;
		if(m==0)
		return 0;
		while(n>0)
		{
			if((n&1)!=0)
			{
				res=(res*m)%mod;
			}
			n=n>>1;
			m=(m*m)%mod;
		}
		return res;
	}
	public static class own
    {
    	long a;
    	long b;
    	public own(long val,long index)
    	{
    	    a=val;
    	    b=index;
    	}
    }

	//Modular Airthmetic

	public static void sort(int[] A)
	{
        int n = A.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i)
		{
            int tmp = A[i];
            int randomPos = i + rnd.nextInt(n-i);
            A[i] = A[randomPos];
            A[randomPos] = tmp;
        }
        Arrays.sort(A);
    }
	public static void sort(char[] A)
	{
        int n = A.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i)
		{
            char tmp = A[i];
            int randomPos = i + rnd.nextInt(n-i);
            A[i] = A[randomPos];
            A[randomPos] = tmp;
        }
        Arrays.sort(A);
    }
    public static void sort(long[] A)
	{
	    int n = A.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i)
		{
            long tmp = A[i];
            int randomPos = i + rnd.nextInt(n-i);
            A[i] = A[randomPos];
            A[randomPos] = tmp;
        }
	    Arrays.sort(A);
	}
	public static int I(){return sc.I();}
    public static long L(){return sc.L();}
    public static String S(){return sc.S();}
    public static double D(){return sc.D();}
}
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 I(){ 
        return Integer.parseInt(next());
    }
    long L(){ 
        return Long.parseLong(next());
    }
    double D(){
         return Double.parseDouble(next());
    }
    String S(){
        String str = "";
        try 
        {
            str = br.readLine();
        }
        catch (IOException e)
        {
            e.printStackTrace();
        }
        return str;
    }
}
