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.
/**
 * Created by Himanshu
 **/

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

public class A1586 {
    public static void main(String[] args) throws IOException {
        PrintWriter out = new PrintWriter(System.out);
        Reader s = new Reader();
        int t = s.i();
        while (t-- > 0) {
            int n = s.i();
            int [] arr = s.arr(n);
            int sum = 0;
            for (int x : arr) {
                sum += x;
            }
            if (sum == n && n == 3) {
                out.println(1);
                out.println(1);
                continue;
            }
            if (isPrime(sum)) {
                int in = -1;
               for (int i=0;i<n;i++) {
                   if (arr[i]%2 == 1) {
                       in = i+1;
                       break;
                   }
               }
               out.println(n-1);
                for (int i=1;i<=n;i++) {
                    if (i != in) out.print(i + " ");
                }
                out.println();
            } else {
                out.println(n);
                for (int i=1;i<=n;i++) {
                    out.print(i + " ");
                }
                out.println();
            }
        }
        out.flush();
    }
    private static boolean isPrime(int n) {
        for (int i=3;i*i<=n;i+=2) {
            if (n%i == 0) return false;
        }
        return true;
    }
    public static void shuffle(long[] arr) {
        int n = arr.length;
        Random rand = new Random();
        for (int i = 0; i < n; i++) {
            long temp = arr[i];
            int randomPos = i + rand.nextInt(n - i);
            arr[i] = arr[randomPos];
            arr[randomPos] = temp;
        }
    }

    private static long phi(long n) {
        long result = n;
        for (long i = 2; i * i <= n; i++) {
            if (n % i == 0) {
                while (n % i == 0)
                    n /= i;
                result -= result / i;
            }
        }
        if (n > 1)
            result -= result / n;
        return result;
    }

    private static int gcd(int a, int b) {
        if(b == 0) return a;
        return gcd(b,a%b);
    }

    public static long nCr(long[] fact, long[] inv, int n, int r, long mod) {
        if (n < r)
            return 0;
        return ((fact[n] * inv[n - r]) % mod * inv[r]) % mod;
    }

    private static void factorials(long[] fact, long[] inv, long mod, int n) {
        fact[0] = 1;
        inv[0] = 1;
        for (int i = 1; i <= n; ++i) {
            fact[i] = (fact[i - 1] * i) % mod;
            inv[i] = power(fact[i], mod - 2, mod);
        }
    }

    private static long power(long a, long n, long p) {
        long result = 1;
        while (n > 0) {
            if (n % 2 == 0) {
                a = (a * a) % p;
                n /= 2;
            } else {
                result = (result * a) % p;
                n--;
            }
        }
        return result;
    }

    private static long power(long a, long n) {
        long result = 1;
        while (n > 0) {
            if (n % 2 == 0) {
                a = (a * a);
                n /= 2;
            } else {
                result = (result * a);
                n--;
            }
        }
        return result;
    }

    private static long query(long[] tree, int in, int start, int end, int l, int r) {
        if (start >= l && r >= end) return tree[in];
        if (end < l || start > r) return 0;
        int mid = (start + end) / 2;
        long x = query(tree, 2 * in, start, mid, l, r);
        long y = query(tree, 2 * in + 1, mid + 1, end, l, r);
        return x + y;
    }

    private static void update(int[] arr, long[] tree, int in, int start, int end, int idx, int val) {
        if (start == end) {
            tree[in] = val;
            arr[idx] = val;
            return;
        }
        int mid = (start + end) / 2;
        if (idx > mid) update(arr, tree, 2 * in + 1, mid + 1, end, idx, val);
        else update(arr, tree, 2 * in, start, mid, idx, val);
        tree[in] = tree[2 * in] + tree[2 * in + 1];
    }

    private static void build(int[] arr, long[] tree, int in, int start, int end) {
        if (start == end) {
            tree[in] = arr[start];
            return;
        }
        int mid = (start + end) / 2;
        build(arr, tree, 2 * in, start, mid);
        build(arr, tree, 2 * in + 1, mid + 1, end);
        tree[in] = (tree[2 * in + 1] + tree[2 * in]);
    }

    static class Reader {
        private InputStream mIs;
        private byte[] buf = new byte[1024];
        private int curChar, numChars;

        public Reader() {
            this(System.in);
        }

        public Reader(InputStream is) {
            mIs = is;
        }

        public int read() {
            if (numChars == -1) throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = mIs.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public String s() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public long l() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int i() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public double d() throws IOException {
            return Double.parseDouble(s());
        }

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

        public boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

        public int[] arr(int n) {
            int[] ret = new int[n];
            for (int i = 0; i < n; i++) {
                ret[i] = i();
            }
            return ret;
        }

        public long[] arrLong(int n) {
            long[] ret = new long[n];
            for (int i = 0; i < n; i++) {
                ret[i] = l();
            }
            return ret;
        }
    }
//    static class pairLong implements Comparator<pairLong> {
//        long first, second;
//
//        pairLong() {
//        }
//
//        pairLong(long first, long second) {
//            this.first = first;
//            this.second = second;
//        }
//
//        @Override
//        public int compare(pairLong p1, pairLong p2) {
//            if (p1.first == p2.first) {
//                if(p1.second > p2.second) return 1;
//                else return -1;
//            }
//            if(p1.first > p2.first) return 1;
//            else return -1;
//        }
//    }
//    static class pair implements Comparator<pair> {
//        int first, second;
//
//        pair() {
//        }
//
//        pair(int first, int second) {
//            this.first = first;
//            this.second = second;
//        }
//
//        @Override
//        public int compare(pair p1, pair p2) {
//            if (p1.first == p2.first) return p1.second - p2.second;
//            return p1.first - p2.first;
//        }
//    }
}

