Problem: This is an interactive problem.

There is an unknown integer x (1≤ x≤ n). You want to find x.

At first, you have a set of integers \{1, 2, …, n\}. You can perform the following operations no more than 10000 times:

  * A a: find how many numbers are multiples of a in the current set. 
  * B a: find how many numbers are multiples of a in this set, and then delete all multiples of a, but x will never be deleted (even if it is a multiple of a). In this operation, a must be greater than 1. 
  * C a: it means that you know that x=a. This operation can be only performed once. 



Remember that in the operation of type B a>1 must hold.

Write a program, that will find the value of x.

Input

The first line contains one integer n (1≤ n≤ 10^5). The remaining parts of the input will be given throughout the interaction process.

Interaction

In each round, your program needs to print a line containing one uppercase letter A, B or C and an integer a (1≤ a≤ n for operations A and C, 2≤ a≤ n for operation B). This line desribes operation you make.

If your operation has type C your program should terminate immediately.

Else your program should read one line containing a single integer, which is the answer to your operation.

After outputting each line, don't forget to flush the output. To do it use:

  * fflush(stdout) in C/C++; 
  * System.out.flush() in Java; 
  * sys.stdout.flush() in Python; 
  * flush(output) in Pascal; 
  * See the documentation for other languages. 



It is guaranteed, that the number x is fixed and won't change during the interaction process.

Hacks:

To make a hack, use such input format:

The only line should contain two integers n, x (1 ≤ x ≤ n ≤ 10^5).

Example

Input


10

2

4

0

Output



B 4

A 2

A 8

C 4

Note

Note that to make the sample more clear, we added extra empty lines. You shouldn't print any extra empty lines during the interaction process.

In the first test n=10 and x=4.

Initially the set is: \{1,2,3,4,5,6,7,8,9,10\}.

In the first operation, you ask how many numbers are multiples of 4 and delete them. The answer is 2 because there are two numbers divisible by 4: \{4,8\}. 8 will be deleted but 4 won't, because the number x will never be deleted. Now the set is \{1,2,3,4,5,6,7,9,10\}.

In the second operation, you ask how many numbers are multiples of 2. The answer is 4 because there are four numbers divisible by 2: \{2,4,6,10\}.

In the third operation, you ask how many numbers are multiples of 8. The answer is 0 because there isn't any number divisible by 8 in the current set.

In the fourth operation, you know that x=4, which is the right answer.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.StringTokenizer;

public class problemE {
    static final int MAXN = 1_000_00;
    static ArrayList<Integer> primes = new ArrayList<>();

    private static void getPrimes() {
        boolean[] dp = new boolean[MAXN];
        Arrays.fill(dp, true);
        for (int i = 2; i < MAXN; i ++ ) {
            if (dp[i]) {
                primes.add(i);
                for (long j = (long)i*i; j < MAXN; j += i ) {
                    dp[(int) j] = false;
                }
            }
        }
    }

    static HashSet<Integer> hs = new HashSet<>();
    private static void solve() throws Exception {
        getPrimes();
        int n = fs.nextInt();


        if (manual) {
            for (int i = 1; i <= n; i ++ ) hs.add(i);
        }

        long ans = 1;
        for (int p : primes) {
            if (p <= 317 && p <= n) {
                query('B', p);
                int curr = p;
                while (curr <= n) {
                    int res = query('A', curr);
                    if (res > 0) {
                        curr *= p;
                        ans *= p;
                    } else {
                        break ;
                    }
                }
            } else {
                break;
            }
        }

        int bucketSize = 100;
        int expectedSize = query('A', 1);

        ArrayList<Integer> lastQueries = new ArrayList<>(bucketSize);
        for (int p : primes) {
            if (p > 317 && p <= n) {
                int expectedDeletes = query('B', p);
                lastQueries.add(p);
                expectedSize -= expectedDeletes;

                if (lastQueries.size() == bucketSize) {
                    int gotSize = query('A', 1);
                    if (gotSize == expectedSize) {
                        lastQueries = new ArrayList<>(bucketSize);
                    } else {
                        break;
                    }
                }

            }
        }
        for (int p : lastQueries) {
            int res = query('A', p);
            if (res > 0) {
                ans *= p;
            }
        }

        System.out.println("C " + ans);
        System.out.flush();
    }

    static boolean manual = false;
    static int choosen = 99874;
    static int totalQueries = 0;
    private static int query(char type, int val) {
        System.out.println(type + " " + val);
        System.out.flush();
        totalQueries++;

        return manual ? answer(type, val) : fs.nextInt();
    }

    private static int answer(char type, int val) {
        if (type == 'A') {
            int count = 0 ;
            for (int x : hs) if (x % val == 0) count++;
            if (val == 49937) debug("answer", type, val, count);
            return count;
        } else if (type == 'B') {
            ArrayList<Integer> toRemove = new ArrayList<>();
            for (int x : hs) if (x % val == 0) toRemove.add(x);
            for (int x: toRemove) hs.remove(x);
            hs.add(choosen);
            if (val == 49937) debug("answer", type, val, toRemove);
            return toRemove.size();
        }
        return 0;
    }

    private static FastScanner fs = new FastScanner();
    private static PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) throws Exception {
        int T = 1;
        for (int t = 0; t < T; t++) {
            solve();
        }
        out.close();
    }

    static void debug(Object... O) {
        System.err.print("DEBUG ");
        System.err.println(Arrays.deepToString(O));
    }

    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

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

        long nextLong() {
            return Long.parseLong(next());
        }

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

        String nextString() {
            return next();
        }
    }
}