#include<iostream>
#include<set>
#include<string>
using namespace std;

bool solve(string s) {
	if (s == "ABC")return true;
	bool flag = false;
	set<char> c; int l = s.length();
	for (int i = 0; i < l; ++i) {
		if (i > l - 3) {
			c.insert(s[i]);
			continue;
		}
		if (s.substr(i, 3) == "ABC") {
			s.replace(i, 3, "*"); l -= 2;
			flag = true;
		}
		else c.insert(s[i]);
	}
	if (c.size() != 2)return false;
	int buf = 0;
	for (auto x : c)buf += x;
	c.clear();
	char rc = 'A' + 'B' + 'C' - buf;
	for (auto& x : s)if (x == '*')x = rc;
	if (flag)return solve(s);
	else return false;
}

int main() {
	string s;
	cin >> s;
	if (solve(s))cout << "Yes" << endl;
	else cout << "No" << endl;
}
### Prompt

Generate a cpp solution to 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<iostream>
#include<set>
#include<string>
using namespace std;

bool solve(string s) {
	if (s == "ABC")return true;
	bool flag = false;
	set<char> c; int l = s.length();
	for (int i = 0; i < l; ++i) {
		if (i > l - 3) {
			c.insert(s[i]);
			continue;
		}
		if (s.substr(i, 3) == "ABC") {
			s.replace(i, 3, "*"); l -= 2;
			flag = true;
		}
		else c.insert(s[i]);
	}
	if (c.size() != 2)return false;
	int buf = 0;
	for (auto x : c)buf += x;
	c.clear();
	char rc = 'A' + 'B' + 'C' - buf;
	for (auto& x : s)if (x == '*')x = rc;
	if (flag)return solve(s);
	else return false;
}

int main() {
	string s;
	cin >> s;
	if (solve(s))cout << "Yes" << endl;
	else cout << "No" << endl;
}
```