int sol(string s) {
  int rhs = 0, lhs = 0;
  for (int i = 0; i < s.size(); ++i) if (s[i] == 'A') ++rhs;
  // rhs equals number of A's after index i [inclusive]
  // lhs equals number of B's before index i [exclusive]
  int ans = rhs;
  for (int i = 0; i < s.size(); ++i) {
    if (s[i] == 'A') --rhs;
    else ++lhs;
    ans = min(ans, rhs + lhs);
  }
  return ans;
}