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.IOException;
import java.io.InputStream;
import java.io.PrintWriter; // System.out is a PrintStream
import java.util.InputMismatchException;


public class A {
    private static int MOD = (int)1e9 + 7, mod = 99_82_44_353;
    private static double PI = 3.14159265358979323846;

    public static void main(String[] args) throws IOException {
        FasterScanner scn = new FasterScanner();
        PrintWriter out = new PrintWriter(System.out);
        boolean[] notPrimes = seive(101 * 201);
        for (int tc = scn.nextInt(); tc > 0; tc--) {
            int N = scn.nextInt(), sm = 0;
            int[] arr = new int[N];
            for (int i = 0; i < N; i++) {
                sm += arr[i] = scn.nextInt();
            }
            if (notPrimes[sm]) {
                out.println(N);
                for (int i = 1; i <= N; i++) {
                    out.print(i + " ");
                }
                out.println();
            } else {
                for (int i = 0; i < N; i++) {
                    if (notPrimes[sm - arr[i]]) {
                        out.println(N - 1);
                        for (int j = 0; j < N; j++) {
                            if (i == j) continue;
                            out.print(j + 1 + " ");
                        }
                        out.println();
                        break;
                    }
                }
            }
        }
        out.close();
    }

    /* ------------------- Sorting ------------------- */
    private static void ruffleSort(int[] arr) {
        // int N = arr.length;
        // Random rand = new Random();
        // for (int i = 0; i < N; i++) {
        //     int oi = rand.nextInt(N), temp = arr[i];
        //     arr[i] = arr[oi];
        //     arr[oi] = temp;
        // }
        // Arrays.sort(arr);
    }
        
    /* ------------------- Sorting ------------------- */
    
    private static boolean isPalindrome(String str) {
        for (int i = 0, j = str.length() - 1; i < j; i++, j--) {
            if (str.charAt(i) != str.charAt(j)) {
                return false;
            }
        }
        return true;
    }
    
    private static boolean isPalindrome(char[] str) {
        for (int i = 0, j = str.length - 1; i < j; i++, j--) {
            if (str[i] != str[j]) {
                return false;
            }
        }
        return true;
    }
    
    /* ------------------- Pair class ------------------- */
    private static class Pair implements Comparable<Pair> {
		int x, y;
		Pair(int x, int y) {
			this.x = x;
			this.y = y;
		}
		public int compareTo(Pair o) {
			return this.x == o.x ? this.y - o.y : this.x - o.x;
		}
	}

    /* ------------------- HCF and LCM ------------------- */
    private static int gcd(int num1, int num2) {
        int temp = 0;
        while (num2 != 0) {
            temp = num1;
            num1 = num2;
            num2 = temp % num2;
        }
        return num1;
    }
    
    private static int lcm(int num1, int num2) {
        return (int)((1L * num1 * num2) / gcd(num1, num2));
    }
    
    /* ------------------- primes and prime factorization ------------------- */
    private static boolean[] seive(int N) {
        // true means not prime, false means is a prime number :)
        boolean[] notPrimes = new boolean[N + 1];
        notPrimes[0] = notPrimes[1] = true;
        for (int i = 2; i * i <= N; i++) {
            if (notPrimes[i]) continue;
            for (int j = i * i; j <= N; j += i) {
                notPrimes[j] = true;
            }
        }
        return notPrimes;
    }

	/*
    private static TreeMap<Integer, Integer> primeFactors(long N) {
		TreeMap<Integer, Integer> primeFact = new TreeMap<>();
		for (int i = 2; i <= Math.sqrt(N); i++) {
            int count = 0;
            while (N % i == 0) {
                N /= i;
                count++;
            }
            if (count != 0) {
                primeFact.put(i, count);
            }
		}
		if (N != 1) {
            primeFact.put((int)N, 1);
        }
		return primeFact;
	}
    */

    /* ------------------- Binary Search ------------------- */
    private static long factorial(int N) {
        long ans = 1L;
        for (int i = 2; i <= N; i++) {
            ans *= i;
        }
        return ans;
    }

    private static long[] factorialDP(int N) {
        long[] factDP = new long[N + 1];
        factDP[0] = factDP[1] = 1;
        for (int i = 2; i <= N; i++) {
            factDP[i] = factDP[i - 1] * i;
        }
        return factDP;
    }

    private static long factorialMod(int N, int mod) {
        long ans = 1L;
        for (int i = 2; i <= N; i++) {
            ans = ((ans % mod) * (i % mod)) % mod;
        }
        return ans;
    }

    /* ------------------- Binary Search ------------------- */
    private static int floorSearch(int[] arr, int st, int ed, int tar) {
        int ans = -1;
        while (st <= ed) {
            int mid = ((ed - st) >> 1) + st;
            if (arr[mid] <= tar) {
                ans = mid;
                st = mid + 1;
            } else {
                ed = mid - 1;
            }
        }
        return ans;
    }
    
    private static int ceilingSearch(int[] arr, int st, int ed, int tar) {
        int ans = -1;
        while (st <= ed) {
            int mid = ((ed - st) >> 1) + st;
            if (arr[mid] < tar) {
                st = mid + 1;
            } else {
                ans = mid;
                ed = mid - 1;
            }
        }
        return ans;
    }
    
    /* ------------------- Power Function ------------------- */
    public static long pow(long x, long y) {
        long res = 1;
		while (y > 0) {
            if ((y & 1) != 0) {
                res = (res * x);
				y--;
			}
			x = (x * x);
			y >>= 1;
		}
		return res;
	}
    
	public static long powMod(long x, long y, int mod) {
        long res = 1;
		while (y > 0) {
            if ((y & 1) != 0) {
                res = (res * x) % mod;
				y--;
			}
			x = (x * x) % mod;
			y >>= 1;
		}
		return res % mod;
	}

    /* ------------------- Disjoint Set(Union and Find) ------------------- */
    private static class DSU {
		public int[] parent, rank;
		DSU(int N) {
			parent = new int[N];
			rank = new int[N];
			for (int i = 0; i < N; i++) {
				parent[i] = i;
                rank[i] = 1;
            }
		}
		public int find(int a) {
			if (parent[a] == a) {
				return a;
            }
            return parent[a] = find(parent[a]);
		}
		public boolean union(int a, int b) {
			int parA = find(a), parB = find(b);
			if (parA == parB) return false;
			if (rank[parA] > rank[parB]) {
                parent[parB] = parA;
            } else if (rank[parA] < rank[parB]) {
                parent[parA] = parB;
            } else {
                parent[parA] = parB;
                rank[parB]++;
            }
            return true;
		}
	}
    
    /* ------------------- Scanner class for input ------------------- */
    
    private static class FasterScanner {
		private InputStream stream;
		private byte[] buffer = new byte[1024];
		private int curChar, numChars;
		private SpaceCharFilter filter;

		public FasterScanner() {
            // default
			this.stream = System.in;
		}

		public FasterScanner(InputStream stream) {
			this.stream = stream;
		}

		private int readChar() {
			if (numChars == -1) {
				throw new InputMismatchException();
            }
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException(e.getMessage());
				}
				if (numChars <= 0) {
					return -1;
                }
			}
			return buffer[curChar++];
		}

		private boolean isWhiteSpace(int c) {
			if (filter != null) {
				return filter.isWhiteSpace(c);
            }
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isNewLine(int ch) {
			if (filter != null) {
				return filter.isNewLine(ch);
            }
			return ch == '\r' || ch == '\n' || ch == -1;
		}

        public char nextChar() {
            int ch = readChar();
            char res = '\0';
            while (isWhiteSpace(ch)) {
                ch = readChar();
            }
            do {
                res = (char)ch;
                ch = readChar();
            } while (!isWhiteSpace(ch));
            return res;
        }

		public String next() {
			int ch = readChar();
            StringBuilder res = new StringBuilder();
			while (isWhiteSpace(ch)) {
				ch = readChar();
            }
			do {
				res.appendCodePoint(ch);
				ch = readChar();
			} while (!isWhiteSpace(ch));
			return res.toString();
		}

		public String nextLine() {
			int ch = readChar();
            StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(ch);
				ch = readChar();
			} while (!isNewLine(ch));
			return res.toString();
		}

		public int nextInt() {
			int ch = -1, sgn = 1, res = 0;
            do {
                ch = readChar();
            } while (isWhiteSpace(ch));
			if (ch == '-') {
				sgn = -1;
				ch = readChar();
			}
			do {
				if (ch < '0' || ch > '9') {
					throw new InputMismatchException("not a number");
                }
				res = (res * 10) + (ch - '0');
				ch = readChar();
			} while (!isWhiteSpace(ch));
            
			return res * sgn;
		}

		public long nextLong() {
			int ch = -1, sgn = 1;
            long res = 0L;
            do {
                ch = readChar();
            } while (isWhiteSpace(ch));
			if (ch == '-') {
				sgn = -1;
				ch = readChar();
			}
			do {
				if (ch < '0' || ch > '9') {
					throw new InputMismatchException("not a number");
                }
				res = (10L * res) + (ch - '0');
				ch = readChar();
			} while (!isWhiteSpace(ch));

			return 1L * res * sgn;
		}

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        /* for custom delimiters */
		public interface SpaceCharFilter {
			public boolean isWhiteSpace(int ch);
			public boolean isNewLine(int ch);
		}
	}
}
