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 javax.swing.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.nio.file.attribute.FileAttribute;
import java.util.*;
import java.io.*;
//a+b = (a^b) + 2*(a&b)
//b^c = (a^b)^(a^c)
//gcd(x,y) = gcd(x-y,y)
// bit value at ith position changes in interval of 2^i
// Do not define variables by a weird name
// always use   (p*1LL >> q)
// prefer 'int' than 'long long'
// gcd(Fn,Fm) = Fgcd(n,m)  // Property of Fibonacci
// lets prime factorization of n=(p1^e1)*(p2^e2) //total factors will be (e1+1)*(e2+1)
// and some of factors would be (1+p1+p1^2 + .. p1^e1)*(1+p2+p2^2+...+p2^e2)
// nC(r) + nC(r+1) = (n+1)C(r+1) => pascal's formula
public class Main {

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

    static class TrieNode {
        TrieNode childern[] = new TrieNode[26];
        int count = 0;
        boolean isEnd = false;

        TrieNode() {
            for (int i = 0; i < childern.length; ++i) childern[i] = null;
        }
    }

    //----------------------


    static int max(int tree[], int index, int left, int right, int l, int r, int max) {

        if (left >= right) {
            return 0;
        }
        if (right < l || r < left) {
            return 0;
        }

        System.out.println(index + " " + left + " " + right);

        int mid = (left + right) / 2;
        int first = max(tree, 2 * index + 1, left, mid, l, r, max);
        int second = max(tree, 2 * index + 2, mid + 1, right, l, r, max);
        return Math.max(first, second);

    }

    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;
        }
    }

    static int mod = 1000000007;

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

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

    static long factorial(int n) {
        long ans = 1;
        for (int i = 1; i <= n; ++i) {
            ans = (ans % mod * i % mod) % mod;
        }
        return ans;
    }

    static long lcm(long a, long b) {
        return (a * b) / gcd(a, b);
    }

    static long power(long x, long y, int p) {
        long res = 1;
        x = x % p;

        while (y > 0) {


            if (y % 2 == 1)
                res = (res * x) % p;

            y = y >> 1;
            x = (x * x) % p;
        }

        return res;
    }


    static long modInverse(long n, int p) {
        return power(n, p - 2, p);
    }

    static long nCrModPFermat(int n, int r,
                              int p) {

        if (n < r) {
            return 0;
        } else if (r == 0) {
            return 1;
        }


        long[] fac = new long[n + 1];
        fac[0] = 1;

        for (int i = 1; i <= n; i++)
            fac[i] = fac[i - 1] * i % p;

        return (fac[n] * modInverse(fac[r], p)
                % p * modInverse(fac[n - r], p)
                % p)
                % p;
    }

    static void print(int arr[]) {
        for (int elements : arr) System.out.print(elements + " ");
    }

    static boolean union(int x, int y, int parent[]) {
        int root1 = find(x, parent);
        int root2 = find(y, parent);
        if (root1 == root2) {
            return false;
        }
        parent[root1] = root2;
        return true;
    }

    static int find(int x, int parent[]) {
        if (x == parent[x]) {
            return x;
        }
        return parent[x] = find(parent[x], parent);  //path compression
    }

    static int dp[] = new int[1000006];

    static void count() {
        int dp[] = new int[1000006];
        Arrays.fill(dp, -1);
        int count = 0;
        for (int i = 2; i < dp.length; ++i) {
            if (dp[i] == -1) {
                for (int j = i; j < dp.length; j += i) {
                    dp[j] = 1;
                    Main.dp[j]++;
                }
            }
        }

    }

    static class Pair implements Comparable<Pair> {
        int a;
        int b;
        int c;
        int d;


        Pair(int a, int b) {
            this.a = a;
            this.b = b;
            this.c = c;
            this.d = d;


        }

        @Override
        public int compareTo(Pair o) {
            if (this.a == o.a) {
                return this.b - o.b;
            } else {
                return this.a - o.a;
            }

        }
    }
     // Check for number prime or not
    static boolean isPrime(int n)
    {

        // Check if number is less than
        // equal to 1
        if (n <= 1)
            return false;

        // Check if number is 2
        else if (n == 2)
            return true;

        // Check if n is a multiple of 2
        else if (n % 2 == 0)
            return false;

        // If not, then just check the odds
        for (int i = 3; i <= Math.sqrt(n); i += 2)
        {
            if (n % i == 0)
                return false;
        }
        return true;
    }


    static int upperbound(int arr[], int element) {
        if (element < 0) {
            return -1;
        }
        int start = 0;
        int end = arr.length - 1;
        int answer = -1;
        while (start <= end) {
            int mid = ((start + end)) >> 1;
            //System.out.println(mid);
            if (arr[mid] < element) {
                start = mid + 1;
            } else {
                answer = mid;
                end = mid - 1;
            }

        }
        return answer;
    }

    static int lowerBound(int arr[], int element) {
        int start = 0;
        int end = arr.length - 1;
        int answer = -1;
        while (start <= end) {
            int mid = (start + end) >> 1;
            if (arr[mid] > element) {
                answer = mid;
                end = mid - 1;
            } else {
                start = mid + 1;
            }
        }
        return answer;
    }

    static long arr[] = new long[1000001];

    static void fill() {
        Arrays.fill(arr, -1);
        boolean bl[] = new boolean[1000001];
        for (int i = 2; i * i <= arr.length; ++i) {
            if (arr[i] == -1) {
                for (int j = i * i; j < arr.length; j += i) {
                    arr[j] = 1;

                }
            }
        }

    }

    static int search(int arr[], int element) {
        int start = 0;
        int end = arr.length - 1;
        int answer = arr.length;
        while (start <= end) {
            int mid = (start + end) / 2;
            if (arr[mid] > element) {
                answer = mid;
                end = mid - 1;
            } else {
                start = mid + 1;
            }

        }
        return answer;
    }

    static int count(int arr[], int element) {
        int count = 0;
        HashMap<Integer, Integer> H = new HashMap<>();

        for (int i = 0; i < arr.length; ++i) {
            H.put(arr[i], H.getOrDefault(arr[i], 0) + 1);
        }
        for (int i = 0; i < arr.length; ++i) {
            int required = element - arr[i];
            if (H.containsKey(required)) {
                if (arr[i] == required) {
                    count += H.get(required) - 1;
                } else {
                    count += H.get(required);
                }
            }
        }
        return count / 2;

    }

    static void reverse(int arr[]) {
        int left = 0;
        int right = arr.length - 1;
        while (left < right) {
            int temp = arr[left];
            arr[left] = arr[right];
            arr[right] = temp;
            ++left;
            --right;
        }
    }

    static int divs(int n) {
        if (n <= 1) {
            return 0;
        }
        int ans = 0;
        boolean check = false;
        for (int i = 3; i * i <= n; i += 2) {
            while (n % i == 0) {
                n = n / i;
                check = true;
                ++ans;
            }
            if (check == true) {
                break;
            }

        }
        if (check == false) {
            return 1;

        }
        return ans + divs(n);


    }

    public static void main(String[] args) {
        FastReader scan = new FastReader();
        int t = scan.nextInt();
        while (t-- > 0) {
            int n = scan.nextInt();
            ;
            ArrayList<Pair> A = new ArrayList<>();
            int sum=0;
            for (int i = 0; i < n; ++i) {
                int temp = scan.nextInt();
                sum+=temp;
                A.add(new Pair(i, temp));
            }
            if(isPrime(sum)==false){
                System.out.println(n);
                for(int i=1;i<=n;++i){
                    System.out.print(i+1+" ");
                }
            }
            else{
                for(int i=0;i<n;++i){
                    if(isPrime(sum-A.get(i).a)==false){
                        System.out.println(n-1);
                        for(int j=0;j<n;++j){
                            if(i==j){
                                continue;
                            }
                            else{
                                System.out.print(j+1+" ");
                            }
                        }
                    }
                }
                System.out.println();
            }


        }
    }

        }












