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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int A(int x) {
  int s;
  return cout << "A " << x << endl, cin >> s, s;
}
int B(int x) {
  int s;
  return cout << "B " << x << endl, cin >> s, s;
}
const int N = 1e5 + 3;
bool b[N];
int p[9999];
int main() {
  int n, i, j, k, t = 0, s = 1;
  cin >> n;
  for (i = 2; i <= n; ++i)
    if (!b[i]) {
      if (i > 330) p[++t] = i;
      for (j = i * 2; j <= n; j += i) b[j] = 1;
    }
  for (i = 2; i <= min(n, 330); ++i)
    if (!b[i]) {
      B(i);
      for (j = 1; j * i <= n && A(j * i); j *= i)
        ;
      s *= j;
    }
  if (s > 1) {
    for (i = t; i; --i)
      if (A(p[i]) > 1) {
        s *= p[i];
        goto gg;
      }
  } else
    for (i = t; i > 0; i -= 100) {
      j = max(1, i - 99);
      for (k = j; k <= i; ++k) B(p[k]);
      if (A(1) > j)
        for (k = j; k <= i; ++k)
          if (A(p[k])) {
            s *= p[k];
            goto gg;
          }
    }
gg:
  cout << "C " << s << endl;
  return 0;
}