#include <string>
#include <vector>
#include <iostream>

typedef unsigned long mask;

struct Rule {
  mask i1, i2, o;
 
  Rule(char i1, char i2, char o)
    : i1(1ul<<(i1-'A')),
      i2(1ul<<(i2-'A')),
      o(1ul<<(o-'A')) {
  }
};

std::vector<Rule> rules = {
  Rule{'A','A','A'},
  Rule{'A','A','C'},
  Rule{'C','A','B'},
  Rule{'A','B','B'}
};

void parse(std::string s) {
  int n = s.length();
  mask conversions[n+1][n+1];
 
  for (int i=0; i<n; ++i)
    conversions[i][i+1] = 1ul << (s[i]-'A');
 
 
  for (int l=2; l<=n; ++l) {
    for (int i=0; i<=n-l; ++i) {
      int j = i+l;
      conversions[i][j] = 0ul;
      for (int k = i+1; k < j; ++k) {
        for (Rule rule : rules) {
          if ((rule.i1 & conversions[i][k])
              && (rule.i2 & conversions[k][j]))
            conversions[i][j] |= rule.o;
        }
      }
    }
  }
 
  for (mask m = conversions[0][n], i=0; m; i++, m >>= 1){
    if (m & 1ul)
      std::cout << char('A'+i) << ' ';
  }
  std::cout << '\n';
}

int main() {
  parse("AAAB");
}