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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Main {
    private static final FastReader fs = new FastReader();
    private static final PrintWriter out = new PrintWriter(System.out);
    private static long m = 1_000_000_009;
    private static long p = 31;
    private static long mod = 1_000_000_007;
    private static long ool = 1_000_000_000_000_000_009l;
    private static int ooi = 1_000_000_009;

    private static boolean composite(int num){
        for(int i = 1; i *i <= num; i++){
            if(num % i == 0 && i != 1 && i != num) return false;
        }
        return true;
    }

    private static void solve() {
        int n = fs.nextInt();
        int[] a = fs.readintarray(n);
        int sum = Arrays.stream(a).sum();
        if(composite(sum)){
            out.println(n-1);
            int idx = -1;
            for(int i = 0; i < n; i++){
                if(!composite(sum-a[i])){
                    idx = i;
                    break;
                }
            }
            assert idx != -1;
            for(int i = 0; i < n; i++) if(i != idx) out.print((i+1) + " ");
            out.println();
        }
        else{
            out.println(n);
            for(int i = 0; i < n; i++) out.print((i+1) + " ");
            out.println();
        }
    }

    public static void main(String[] args) {
        Thread t = new Thread(null, null, "", 1 << 28) {
            public void run() {
                int test_case = 1;
                test_case = fs.nextInt();
                for (int cs = 1; cs <= test_case; cs++)
                    solve();
                out.close();
            }
        };
        t.start();
        try {
            t.join();
        } catch (InterruptedException e) {
            e.printStackTrace();
        }
    }

    private static 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;
        }

        int[] readintarray(int n) {
            int res[] = new int[n];
            for (int i = 0; i < n; i++)
                res[i] = nextInt();
            return res;
        }

        long[] readlongarray(int n) {
            long res[] = new long[n];
            for (int i = 0; i < n; i++)
                res[i] = nextLong();
            return res;
        }
    }

    private static int max(int... arg) {
        int length = arg.length;
        if(length == 0)
            throw null;
        int maxVal = arg[0];
        for(int i = 1; i < length; i++)
            maxVal = Math.max(maxVal, arg[i]);
        return maxVal;
    }

    private static int min(int... arg) {
        int length = arg.length;
        if(length == 0)
            throw null;
        int maxVal = arg[0];
        for(int i = 1; i < length; i++)
            maxVal = Math.min(maxVal, arg[i]);
        return maxVal;
    }

    private static long max(long... arg) {
        int length = arg.length;
        if(length == 0)
            throw null;
        long maxVal = arg[0];
        for(int i = 1; i < length; i++)
            maxVal = Math.max(maxVal, arg[i]);
        return maxVal;
    }

    private static long min(long... arg) {
        int length = arg.length;
        if(length == 0)
            throw null;
        long maxVal = arg[0];
        for(int i = 1; i < length; i++)
            maxVal = Math.min(maxVal, arg[i]);
        return maxVal;
    }

    private static int abs(int a) {
        return a >= 0 ? a : -a;
    }

    private static int abs(int a, int b) {
        return a-b >= 0 ? a-b : b-a;
    }

    private static long abs(long a) {
        return a >= 0 ? a : -a;
    }

    private static long abs(long a, long b) {
        return a-b >= 0 ? a-b : b-a;
    }

    private static int power(int base, int exponent) {
        int res = 1;
        while(exponent > 0) {
            if((exponent & 1) != 0)
                res *= base;
            exponent >>= 1;
            base *= base;
        }
        return res;
    }

    private static long power(long base, long exponent) {
        long res = 1;
        while(exponent > 0) {
            if((exponent & 1) != 0)
                res *= base;
            exponent >>= 1;
            base *= base;
        }
        return res;
    }

    private static long mPower(long base, long exponent) throws Exception {
        long res = 1;
        base %= mod;
        while(exponent > 0) {
            if((exponent & 1) != 0)
                res = mul(res, base);
            exponent >>= 1;
            base = mul(base, base);
        }
        return res;
    }

    private static long mul(long a, long b) {
        return a*b % mod;
    }

    private static long add(long a, long b) {
        return (a+b) % mod;
    }

    private static long sub(long a, long b) {
        long res = (a - b) % mod;
        if(res < 0)
            res += mod;
        return res;
    }

    private static long xor(long n){
        long r = n % 4;
        if(r == 0)
            return n;
        else if(r == 1)
            return 1;
        else if(r == 2)
            return n+1;
        else
            return 0;
    }
}