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;
using ll = long long;
const int NAX = 2e5 + 5, MOD = 1000000007;
struct Solution {
  Solution() {}
  void solveCase();
};
ll ask(char c, ll x) {
  cout << c << ' ' << x << endl;
  cin >> x;
  return x;
}
void Solution::solveCase() {
  int n;
  cin >> n;
  vector<bool> isPrime(n + 1, true);
  isPrime[0] = isPrime[1] = 0;
  vector<int> smol, large;
  for (ll i = 2; i <= n; i++)
    if (isPrime[i]) {
      if (i < 400)
        smol.push_back(i);
      else
        large.push_back(i);
      for (ll j = i * i; j <= n; j += i) isPrime[j] = false;
    }
  ll ans = 1;
  for (auto &x : smol) {
    ll cur = x;
    auto res = ask('B', x);
    while (true) {
      if (cur > n) break;
      res = ask('A', cur);
      if (res > 0) {
        ans *= x;
        cur *= x;
      } else
        break;
    }
  };
  const int BUCKET_SIZE = 100;
  int cnt = ask('A', 1);
  for (size_t b = 0; b < large.size(); b += BUCKET_SIZE) {
    int sum = 0;
    for (size_t i = b; i < min(b + BUCKET_SIZE, (large.size())); i++) {
      auto res = ask('B', large[i]);
      sum += res;
    }
    int cnt2 = ask('A', 1);
    if (cnt - sum != cnt2)
      for (size_t i = b; i < min(b + BUCKET_SIZE, (large.size())); i++) {
        auto res = ask('A', large[i]);
        if (res > 0) ans *= large[i];
      }
    cnt = cnt2;
  }
  cout << "C" << ' ' << ans << endl;
}
int32_t main() {
  int t = 1;
  Solution mySolver;
  for (int i = 1; i <= t; ++i) {
    mySolver.solveCase();
  }
  return 0;
}