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 const nax = 3e5 + 10;
const int L = 1e5;
vector<int> primes;
bool is_prime[L + 5];
int expect[L + 5];
int n;
int main() {
  cin.tie(0)->sync_with_stdio(false);
  fill(is_prime + 2, is_prime + L + 1, true);
  for (int i = 2; i <= L; ++i) {
    if (!is_prime[i]) continue;
    for (int j = i + i; j <= L; j += i) is_prime[j] = false;
  }
  cin >> n;
  vector<int> small, large;
  for (int i = 2; i <= n; ++i) {
    if (!is_prime[i]) continue;
    if (int64_t(i) * i <= n)
      small.push_back(i);
    else
      large.push_back(i);
  }
  int64_t ans = 1;
  for (int x : small) {
    int64_t cur = x;
    cout << "B " << x << endl;
    int buf;
    cin >> buf;
    while (true) {
      cout << "A " << cur << endl;
      int res;
      cin >> res;
      if (res > 0) {
        ans *= x;
      } else
        break;
      cur *= x;
      if (cur > n) break;
    }
  }
  const int BS = 100;
  cout << "A 1" << endl;
  int alive;
  cin >> alive;
  for (int i = 0; i < int(large.size()); i += BS) {
    int out = 0;
    for (int j = i; j < min(int(large.size()), i + BS); ++j) {
      cout << "B " << large[j] << endl;
      int buf;
      cin >> buf;
      out += buf;
    }
    int many_left;
    cout << "A 1" << endl;
    cin >> many_left;
    if (alive - out != many_left) {
      for (int j = i; j < min(int(large.size()), i + BS); ++j) {
        cout << "A " << large[j] << endl;
        int has;
        cin >> has;
        if (has > 0) ans *= large[j];
      }
    }
    alive = many_left;
  }
  cout << "C " << ans << endl;
}