#include <bits/stdc++.h>
using namespace std;

string S;
string table = "ABC";

bool solve(){
    while(S.size() > 3){
        set<char> s;
        int n = S.size();
        string t = "";
        vector<string> vt;
        for(int i=0; i<n; i++){
            bool ok = true;
            for(int j=0; j<3; j++){
                if(i+j >= n || S[i+j] != table[j])
                    ok = false;
            }
            
            if(ok){
                i += 2;
                vt.push_back(t);
                t = "";
            }else{
                t += S[i];
                s.insert(S[i]);
            }
        }
        vt.push_back(t);
        
        if(s.size() != 2)
            return false;
        if(vt.size() == 1)
            return false;
        
        char c = '\0';
        for(int i=0; i<3; i++)
            if(s.find(table[i]) == s.end())
                c = table[i];
            
        S = "";
        for(int i=0; i<vt.size(); i++){
            S += vt[i];
            if(i != vt.size()-1)
                S += c;
        }
    }
    return "ABC" == S;
}

int main(){
    cin >> S;
    cout << (solve()? "Yes": "No") << endl;
    return 0;
}
### Prompt

Create a solution in CPP for the following problem:

ABC Gene

There is a gene sequence represented by the string `ABC`. You can rewrite this gene sequence by performing the following operations several times.

* Choose one of the letters `A`,` B`, `C`. Let this be x. Replace all x in the gene sequence with `ABC` at the same time.



Given a string S consisting only of `A`,` B`, and `C`. Determine if the gene sequence can be matched to S.

Constraints

* 1 ≤ | S | ≤ 5,000
* S consists only of `A`,` B`, and `C`.



Input Format

Input is given from standard input in the following format.


S


Output Format

Output `Yes` if the gene sequence can be matched to S, and` No` if it cannot be matched.

Sample Input 1


ABC


Sample Output 1


Yes


The gene sequence is `ABC` from the beginning.

Sample Input 2


AABCC


Sample Output 2


Yes


If you select `B` and perform the operation, it becomes` ABC` → `AABCC`.

Sample Input 3


AABCABC


Sample Output 3


No


For example, even if you select `C` and perform an operation, it does not change from` AABCC` to `AABCABC`. Since all `C`s are replaced with` ABC` at the same time, the actual result is `AABCC` →` AABABCABC`.





Example

Input

ABC


Output

Yes

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;

string S;
string table = "ABC";

bool solve(){
    while(S.size() > 3){
        set<char> s;
        int n = S.size();
        string t = "";
        vector<string> vt;
        for(int i=0; i<n; i++){
            bool ok = true;
            for(int j=0; j<3; j++){
                if(i+j >= n || S[i+j] != table[j])
                    ok = false;
            }
            
            if(ok){
                i += 2;
                vt.push_back(t);
                t = "";
            }else{
                t += S[i];
                s.insert(S[i]);
            }
        }
        vt.push_back(t);
        
        if(s.size() != 2)
            return false;
        if(vt.size() == 1)
            return false;
        
        char c = '\0';
        for(int i=0; i<3; i++)
            if(s.find(table[i]) == s.end())
                c = table[i];
            
        S = "";
        for(int i=0; i<vt.size(); i++){
            S += vt[i];
            if(i != vt.size()-1)
                S += c;
        }
    }
    return "ABC" == S;
}

int main(){
    cin >> S;
    cout << (solve()? "Yes": "No") << endl;
    return 0;
}
```