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.math.*;
import java.util.*;
import java.io.*;
 
 
 
public class main
{
  static Map<String,Integer> map=new HashMap<>();
             static int[] parent;
         static  int[] size;
    public static void main(String[] args)
    {
        InputReader in = new InputReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        
//         FileReader fr=new FileReader("/sagar.txt");
//        InputStreamReader isr=new InputStreamReader(fr);
        
//         BufferedReader isr=new BufferedReader(fr);
        
//         FileWriter fw=new FileWriter("ProblemA1_ans.txt");
//         BufferedWriter bw=new BufferedWriter(fw);
         final int mod=1000000007;
       // int test_case =Integer.parseInt(isr.read());
          int test_case=in.nextInt();
       // int test_case=1;
                    StringBuilder sb=new StringBuilder();
      //  long mod=998244353;
        long[] fact=new long[100001];
        fact[0]=1;
        fact[1]=1;
        fact[2]=1;
        for(int i=3;i<fact.length;i++)
        {
            fact[i]=((fact[i-1])%mod*(i%mod))%mod;
            //System.out.println(fact[i]);
        }
        
      for(int t1=0;t1<test_case;t1++)
      {

          int n=in.nextInt();
          int[] a=in.nextIntArray(n);
          int sum=0;
          for(int i:a)
          {
              sum+=i;
          }
          
          boolean[] f=new boolean[100000];
          sieve(f,f.length);
          if(f[sum])
          {
              int temp=0;
              for(int i=0;i<n;i++)
              {
                  if(!f[sum-a[i]])
                  {
                      temp=i;
                      break;
                  }
              }
              System.out.println(n-1);
              for(int i=1;i<=n;i++)
              {
                  if(i!=temp)
                  {
                      System.out.print(i+" ");
                  }
                      
              }
              
              
          }else{
              System.out.println(n);
              for(int i=1;i<=n;i++)
              {
                  System.out.print(i+" ");
              }
          }
          System.out.println();
      }
 
    
        pw.flush();
        pw.close();
    }
    
   static  void solve(int[] a,List<Integer>  ls,int n,boolean[] f,int ans,int c,int r,int k)
    {
        if(k==n)
        {
            ls.add(ans);
            max=Math.max(ans,max);
            return  ;
        }
      
        for(int i=0;i<n;i++)
        {
            
            if(f[i])
            {
              continue;
            }
            f[i]=true;
            for(int j=0;j<n;j++)
            {
                
                if(f[j])
                {
                    continue;
                }
                 int ans1=(GCD(a[i],a[j])*r);
                ans+=ans1;
                f[j]=true;
                solve(a,ls,n,f,ans,0,r+1,k+2);
                ans-=ans1;
                f[j]=false;
                
            }
            f[i]=false;
            
        }
        
    }
        static int lower(long[] ages, long target) {
        if (ages == null || ages.length == 0) {
            return 0;
        }
        int l = 0;
        int r = ages.length - 1;
        if (target <= ages[0]) {
            return 0;
        }
        if (target > ages[r]) {
            return -1;
        }
        while (l  <  r) {
            int m = l + (r - l ) / 2 ;

            if (ages[m] >= target) {
                r = m;
            }else {
                l = m + 1;
            }
        }
        return r;
    }
    
    static int upper(long[] ages, long target) {
        if (ages == null || ages.length == 0) {
            return 0;
        }
        int l = 0;
        int r = ages.length - 1;
        if (target < ages[0]) {
            return -1;
        }
        if (target >= ages[r]) {
            return r;
        }
        while (l  <  r - 1) {
            int m = l + (r - l ) / 2 ;
            if (ages[m] <= target) {
                l = m;
            }else {
                r = m - 1;
            }
        }
        return ages[r] <= target ? r : l;
    }

    
    static int LowerBound(long a[], long x) { // x is the target value or key
  int l=0,r=a.length;
  while(l<r) {
    int m=(l+r)>>>1;
    if(a[m]>=x) r=m;
    else l=m+1;
  }
        if(l<a.length&&a[l]<x)
        {
            l++;
        }
  return l;
}
    
    static int UpperBound(long a[], long x) {// x is the key or target value
    int l=0,r=a.length;
    while(l<r) {
       int m=(l+r)>>>1;
       if(a[m]<=x) l=m+1;
       else r=m;
    }
        if(l<a.length&&a[l]<=x)
        {
            l++;
        }
    return l;
 }
    
    static   int max=0;
    
    static void ProblemA2(boolean f,int c,int min,char key,Map<Character,List<Character>> map,char target,char temp,A2 a2,Set<Character>  set)
    {
                      // System.out.println(temp);
        
        
        if(map.containsKey(key))
        {
            
            set.add(key);
            
            for(Character value:map.get(key))
            {
                
                c++;
                
                if(set.contains(value))
                {
                    return;
                }
                
                
               // System.out.println(value+" "+target);
                if(value==target)
                {
                    f=f||true;
                    min=Math.min(c,min);
                 //           System.out.println(f+" "+min);
                    a2.f=f||a2.f;
                    a2.min=Math.min(min,a2.min);
                }else if(value==temp){
                    f=f||false;
                    a2.f=f||a2.f;
                    a2.min=Math.min(min,a2.min);
                    break;
                    
                }else{
                    
 
                    ProblemA2(f,c,min,value,map,target,temp,a2,set);
                    
                   // return a2;
                     
                }
               // set.remove(value);
               c--;
            }
            
            set.remove(key);
        }
     //   System.out.println(a2.f+" "+a2.min);
 
        
    }
    
    static class A2{
 
        boolean f;
        int min=0;
        A2(boolean f,int min)
        {
            this.f=f;
            this.min=min;
        }
        
    }
    
   static boolean backtrack(int i,int j,int[][] a,int[][] gol,int n,Set<String> set,int parentx,int parenty)
    {
       System.out.println(i+" "+j);
       
        if(Arrays.equals(a,gol))
        {
            return true;
        }
        
        boolean f=false;
        
        int[] dx={-1,0,0,1};
        int[] dy={0,-1,1,0};
         set.add(i+"root"+j);
        for(int k=0;k<dx.length;k++)
        {
           
            
            
            if((i+dx[k])>=0&&(i+dx[k])<n&&(j+dy[k])>=0&&(j+dy[k])<n)
            {
                if(i+dx[k]==parentx&&j+dy[k]==parenty||set.contains((i+dx[k])+"root"+(j+dy[k])))
                {
                  continue;
                }
                
               //  System.out.println((i+dx[k])+" "+(j+dy[k]));
                int temp=a[i][j];
                a[i][j]=a[i+dx[k]][j+dy[k]];
                a[i+dx[k]][j+dy[k]]=temp;
                f=backtrack(i+dx[k],j+dy[k],a,gol,n,set,i,j);
                if(f)
                {
                    System.out.println(temp+" "+a[i][j]);
                    return f;
                }
                temp=a[i][j];
                a[i][j]=a[i+dx[k]][j+dy[k]];
                a[i+dx[k]][j+dy[k]]=temp;
            }
        }
       // visited[i][j]=false;
        return f;
        
        
        
    }
    
    static int find_parent(int p)
    {
 
        if(p==parent[p])
        {
            return p;
        }
        return parent[p]=find_parent(parent[p]);
    }
    
    static void set_union(int x,int y)
    {
        if(size[x]<size[y])
        {
            swap(x,y);
        }
        
        parent[y]=x;
        size[x]+=size[y];
    }
    
    static boolean bipartite(int i,List<List<Integer>> ls,boolean[] visited,int[] color, int x)
    {
        
        color[i]=x;
        visited[i]=true;
        
        for(int x1:ls.get(i))
        {
            
           // System.out.println(visited[x1]+" "+color[x1]==x);
            
            if(visited[x1]&&color[x1]==x)
            {
                return false;
            }
            
            if(!visited[x1])
            {
              return  bipartite(x1,ls,visited,color,(x==-1?1:-1));
            }
        }
        
        return true;
        
    }
    
    
    static boolean isDirectedCycle(List<Integer> stack,boolean[] visited,List<List<Integer>>  ls)
    {
        int i=stack.get(stack.size()-1);
        visited[i]=true;
        for(int x:ls.get(i))
        {
             stack.add(x);
            if(!visited[x]&&isDirectedCycle(stack,visited,ls))
            {
                return true;
            }
            
            if(stack.contains(x))
            {
                return true;
            }
            stack.remove(stack.size()-1);
           
            
        }
        
        return false;
    }
    
    static boolean isCyclic(int i,List<List<Integer>> ls,boolean[] visited,int parent)
    {
        visited[i]=true;
        for(int x:ls.get(i))
        {
            if(x!=parent){
                
                if(visited[x])
                {
                    return true;
                }
                
                if(!visited[x]&&isCyclic(x,ls,visited,i))
                {
                    return true;
                }
                
            }
            
            
        }
        
        return false;
    }
    
    static void dfs(List<List<Integer>> ls,boolean[] f,List<Integer> stack)
    {
        int x=stack.remove(stack.size()-1);
        System.out.print(x+"->");
        f[x]=true;
        for(int x1:ls.get(x))
        {
            if(!f[x1])
            {
                stack.add(x1);
                dfs(ls,f,stack);
            }
            
        }
        
    }
    
    static int factorial(int n,int mod)
    {
        long res = 1;
        for (int i=2; i<=n; i++)
            res=((res%mod)*(i%mod))%mod;
        return (int)res;
    }
    
 
 
    
    static int length(long l)
    {
        int c=0;
        while(l>0)
        {
            c++;
            l/=2;
        }
        
        return c;
    }
 
    
    static int CeilIndex(int A[], int l, int r, int key) 
    { 
        while (r - l > 1) { 
            int m = l + (r - l) / 2; 
            if (A[m] <= key) 
                r = m; 
            else
                l = m; 
        } 
  
        return r; 
    } 
    static int LongestIncreasingSubsequenceLength(int A[], int size) 
    { 
        // Add boundary case, when array size is one 
  
        int[] tailTable = new int[size]; 
        int len; // always points empty slot 
  
        tailTable[0] = A[0]; 
        len = 1; 
        for (int i = 1; i < size; i++) { 
            if (A[i] > tailTable[0]) 
 
                tailTable[0] = A[i]; 
  
            else if (A[i] <= tailTable[len - 1]) 
 
                tailTable[len++] = A[i]; 
  
            else
 
                tailTable[CeilIndex(tailTable, -1, len - 1, A[i])] = A[i]; 
        } 
  
        return len; 
    }
    
 
    
    static int[] next(int arr[], int n) { 
 
        Stack<Integer> S = new Stack<>(); 
  
        int[] next=new int[n];
 
        for (int i = n-1; i >= 0; i--) { 
 
            while (!S.empty() && arr[S.peek()] <= arr[i]) { 
                S.pop(); 
 
            } 
            if (S.empty()) { 
                next[i]=-1;
            } 
            else 
            { 
 
                next[i]=S.peek(); 
            } 
            S.push(i); 
        } 
        return next;
    }
    static int[] back(int arr[], int n) { 
 
        Stack<Integer> S = new Stack<>(); 
  
        int[] back=new int[n];
 
        for (int i = 0; i < n; i++) { 
 
            while (!S.empty() && arr[S.peek()] < arr[i]) { 
                S.pop(); 
            } 
            if (S.empty()) { 
                back[i]=-1;
            } 
            else 
            { 
                back[i]=S.peek(); 
            } 
            S.push(i); 
        } 
        
        return back;
    }
 
    
    
 
    static class InputReader
    {
 
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream)
        {
            this.stream = stream;
        }
 
        public int snext()
        {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars)
            {
                curChar = 0;
                try
                {
                    snumChars = stream.read(buf);
                }
                catch (IOException e)
                {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
 
        public int nextInt()
        {
            int c = snext();
            while (isSpaceChar(c))
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public long nextLong()
        {
            int c = snext();
            while (isSpaceChar(c))
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public int[] nextIntArray(int n)
        {
            int a[] = new int[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = nextInt();
            }
            return a;
        }
        public long[] nextlongArray(int n)
        {
            long a[] = new long[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = nextLong();
            }
            return a;
        }
 
        public String readString()
        {
            int c = snext();
            while (isSpaceChar(c))
            {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }
 
        public String nextLine()
        {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(c));
            return res.toString();
        }
 
        public boolean isSpaceChar(int c)
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        private boolean isEndOfLine(int c)
        {
            return c == '\n' || c == '\r' || c == -1;
        }
 
        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }
 
    public static long mod = 1000000007;
    public static int d;
    public static int p;
    public static int q;
 
    public static int[] suffle(int[] a,Random gen)
    {
        int n = a.length;
        for(int i=0;i<n;i++)
        {
            int ind = gen.nextInt(n-i)+i;
            int temp = a[ind];
            a[ind] = a[i];
            a[i] = temp;
        }
        return a;
    }
 
    public static void swap(int a, int b){
        int temp = a;
        a = b;
        b = temp;
    }
 
    public static HashSet<Integer> primeFactorization(int n)
    {
        HashSet<Integer> a =new HashSet<Integer>();
        for(int i=2;i*i<=n;i++)
        {
            while(n%i==0)
            {
                a.add(i);
                n/=i;
            }
        }
        if(n!=1)
            a.add(n);
        return a;
    }
 
    public static void sieve(boolean[] isPrime,int n)
    {
        for(int i=1;i<n;i++)
            isPrime[i] = true;
 
        isPrime[0] = false;
        isPrime[1] = false;
 
        for(int i=2;i*i<n;i++)
        {
            if(isPrime[i] == true)
            {
                for(int j=(2*i);j<n;j+=i)
                    isPrime[j] = false;
            }
        }
    }
 
    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 void extendedEuclid(int A,int B)
    {
        if(B==0)
        {
            d = A;
            p = 1 ;
            q = 0;
        }
        else
        {
            extendedEuclid(B, A%B);
            int temp = p;
            p = q;
            q = temp - (A/B)*q;
        }
    }
 
    public static long LCM(long a,long b)
    {
        return (a*b)/GCD(a,b);
    }
 
    public static int LCM(int a,int b)
    {
        return (a*b)/GCD(a,b);
    }
 
    public static int binaryExponentiation(int x,int n)
    {
        int result=1;
        while(n>0)
        {
            if(n % 2 ==1)
                result=result * x;
            x=x*x;
            n=n/2;
        }
        return result;
    }
    int binarySearch(int arr[], int l, int r, int x) 
    { 
        if (r >= l) { 
            int mid = l + (r - l) / 2; 
  
 
            if (arr[mid] == x) 
                return mid; 
  
 
            if (arr[mid] > x) 
                return binarySearch(arr, l, mid - 1, x); 
  
 
            return binarySearch(arr, mid + 1, r, x); 
        } 
  
 
        return -1; 
    } 
  
 
    public static long binaryExponentiation(long x,long n)
    {
        long result=1;
        while(n>0)
        {
            if(n % 2 ==1)
                result=result * x;
            x=x*x;
            n=n/2;
        }
        return result;
    }
 
    public static int modularExponentiation(int x,int n,int M)
    {
        int result=1;
        while(n>0)
        {
            if(n % 2 ==1)
                result=(result * x)%M;
            x=(x*x)%M;
            n=n/2;
        }
        return result;
    }
 
    public static long modularExponentiation(long x,long n,long M)
    {
        long result=1;
        while(n>0)
        {
            if(n % 2 ==1)
                result=(result * x)%M;
            x=(x*x)%M;
            n=n/2;
        }
        return result;
    }
 
    public static int modInverse(int A,int M)
    {
        return modularExponentiation(A,M-2,M);
    }
 
    public static long modInverse(long A,long M)
    {
        return modularExponentiation(A,M-2,M);
    }
 
    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;
 
        for (int i=5; i*i<=n; i=i+6)
        {
            if (n%i == 0 || n%(i+2) == 0)
                return false;
        }
 
        return true;
    }
    static class Pair
    {
        int  x;
        int  y;
    }
 
    static class pair implements Comparable<pair>
    {
        Integer x, y;
        pair(int x,int y)
        {
            this.x=x;
            this.y=y;
        }
 
        public int compareTo(pair o) {
            int result = x.compareTo(o.x);
            if(result==0)
                result = y.compareTo(o.y);
 
            return result;
        }
 
        public String toString()
        {
            return x+" "+y;
        }
 
        public boolean equals(Object o)
        {
            if (o instanceof pair)
            {
                pair p = (pair)o;
                return (Math.abs(p.x-x)==0 && Math.abs(p.y-y)==0);
            }
            return false;
        }
 
        public int hashCode()
        {
            return new Long(x).hashCode()*31 + new Long(y).hashCode();
        }
    }
}