//#include <bits/stdc++.h>

#include <iostream>
#include <algorithm>

#include <bitset>
#include <vector>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <stack>
#include <queue>
#include <deque>
#include <cstring>
#include <string>
#include <utility>
#include <array>
#include <complex>
#include <valarray>

#include <cassert>
#include <cmath>
#include <functional>
#include <iomanip>
#include <chrono>
#include <random>
#include <numeric>

#include<memory>


using namespace std;
//#define int long long

typedef long long ll;
typedef unsigned long long ull;
//typedef unsigned __int128 HASH;
typedef pair<int,int> pii;
typedef pair<ll, ll> pll;
typedef pair<ull, ull> pullull;
typedef pair<ll,int> plli;
typedef pair<double,int> pdi;
typedef pair<long double, int> pdbi;
typedef pair<int,pii> pipii;
typedef pair<ll,pll> plpll;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<pii> vpii;
typedef vector<vector<int>> mat;

#define rep(i,n) for (int i=0;i<(n);i++)
#define rep2(i,a,b) for (int i=(a);i<(b);i++)
#define rrep(i,n) for (int i=(n);i>0;i--)
#define rrep2(i,a,b) for (int i=(a);i>b;i--)
#define pb push_back
#define fi first
#define se second
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()

const ll hmod1 = 999999937;
const ll hmod2 = 1000000000 + 9;
const int INF = 1<<30;
const ll INFLL = 1LL<<62;
const long double EPS = 1e-12;
const ll mod = 1000000000 + 7;
//const ll mod = 998244353;
const int dx4[4] = {1, 0, -1, 0};
const int dy4[4] = {0, 1, 0, -1};
const int dx8[8] = {1, 1, 1, 0, 0, -1, -1, -1};
const int dy8[8] = {0, 1, -1, 1, -1, 0, 1, -1};
const long double pi = 3.141592653589793;

#define addm(X, Y) (X) = ((X) + ((Y) % mod) + mod) % mod
#define inside(y, x, h, w) (0 <= (y) && (y) < (h) && 0 <= (x) && (x) < (w)) ? true : false

//debug
#define DEBUG

#define DUMPOUT cout

#ifdef DEBUG
#define dump(...) DUMPOUT<<#__VA_ARGS__<<" :["<<__FUNCTION__<<":"<<__LINE__<<"]"<<endl; DUMPOUT<<"    "; dump_func(__VA_ARGS__)
#else
#define dump(...)
#endif

void dump_func() {DUMPOUT << endl;};

template <class Head, class... Tail> void dump_func(Head&& head, Tail&&... tail) {
    DUMPOUT << head;
    if (sizeof...(Tail) == 0) DUMPOUT << " ";
    else DUMPOUT << ", ";
    dump_func(std::move(tail)...);
}

//ostream
template<typename T> ostream& operator << (ostream& os, vector<T>& vec) {
    os << "["; for (int i = 0; i<vec.size(); i++) os << vec[i] << (i + 1 == vec.size() ? "" : ", "); os << "]";
    return os;
}

template<typename T, typename U> ostream& operator << (ostream& os, pair<T, U>& pair_var) {
    os << "(" << pair_var.first << ", " << pair_var.second << ")";
    return os;
}

template<typename T, typename U> ostream& operator << (ostream& os, map<T, U>& map_var) {
    os << "[";
    for (auto itr = map_var.begin(); itr != map_var.end(); itr++) {
        os << "(" << itr->first << ", " << itr->second << ")"; itr++;  if(itr != map_var.end()) os << ", "; itr--;
    }
    os << "]";
    return os;
}

template<typename T> ostream& operator << (ostream& os, set<T>& set_var) {
    os << "[";
    for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
        os << *itr; ++itr; if(itr != set_var.end()) os << ", "; itr--;
    }
    os << "]";
    return os;
}

string s;

signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cin >> s;
  //int loop = 0;
  while (true) {
    //loop++;
    int n = s.size();
    if (n == 3) {
      if (s == "ABC") {
        cout << "Yes" << endl;
      }
      else {
        cout << "No" << endl;
      }
      return 0;
    }
    string nxs = "";
    int cnt_ABC = 0;
    rep(i, n) {
      if (s[i] != 'A') continue;
      string tmp = "";
      rep(j, 3) {
        if (i + j >= n) break;
        tmp += s[i + j];
      }
      if (tmp == "ABC") {
        cnt_ABC++;
        i += 2;
      }
    }
    if (cnt_ABC == 0) {
      cout << "No" << endl;
      return 0;
    }
    bool exist_c[3] = {};
    rep(i, n) {
      string tmp = "";
      rep(j, 3) {
        if (i + j >= n) break;
        tmp += s[i + j];
      }
      if (tmp != "ABC") {
        exist_c[s[i] - 'A'] = true;
      }
      else {
        i += 2;
      }
    }
    char erase_c;
    int cnt = 0;
    rep(i, 3) {
      if (exist_c[i]) cnt++;
      else erase_c = i + 'A';
    }
    if (cnt != 2) {
      cout << "No" << endl;
      return 0;
    }
    rep(i, n) {
      if (s[i] != 'A') {
        nxs += s[i];
        continue;
      }
      string tmp = "";
      rep(j, 3) {
        if (i + j >= n) break;
        tmp += s[i + j];
      }
      if (tmp == "ABC") {
        nxs += erase_c;
        i += 2;
      }
      else {
        nxs += s[i];
      }
    }
    s = nxs;
  }
}


### Prompt

Your challenge is to write 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 <bits/stdc++.h>

#include <iostream>
#include <algorithm>

#include <bitset>
#include <vector>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <stack>
#include <queue>
#include <deque>
#include <cstring>
#include <string>
#include <utility>
#include <array>
#include <complex>
#include <valarray>

#include <cassert>
#include <cmath>
#include <functional>
#include <iomanip>
#include <chrono>
#include <random>
#include <numeric>

#include<memory>


using namespace std;
//#define int long long

typedef long long ll;
typedef unsigned long long ull;
//typedef unsigned __int128 HASH;
typedef pair<int,int> pii;
typedef pair<ll, ll> pll;
typedef pair<ull, ull> pullull;
typedef pair<ll,int> plli;
typedef pair<double,int> pdi;
typedef pair<long double, int> pdbi;
typedef pair<int,pii> pipii;
typedef pair<ll,pll> plpll;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<pii> vpii;
typedef vector<vector<int>> mat;

#define rep(i,n) for (int i=0;i<(n);i++)
#define rep2(i,a,b) for (int i=(a);i<(b);i++)
#define rrep(i,n) for (int i=(n);i>0;i--)
#define rrep2(i,a,b) for (int i=(a);i>b;i--)
#define pb push_back
#define fi first
#define se second
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()

const ll hmod1 = 999999937;
const ll hmod2 = 1000000000 + 9;
const int INF = 1<<30;
const ll INFLL = 1LL<<62;
const long double EPS = 1e-12;
const ll mod = 1000000000 + 7;
//const ll mod = 998244353;
const int dx4[4] = {1, 0, -1, 0};
const int dy4[4] = {0, 1, 0, -1};
const int dx8[8] = {1, 1, 1, 0, 0, -1, -1, -1};
const int dy8[8] = {0, 1, -1, 1, -1, 0, 1, -1};
const long double pi = 3.141592653589793;

#define addm(X, Y) (X) = ((X) + ((Y) % mod) + mod) % mod
#define inside(y, x, h, w) (0 <= (y) && (y) < (h) && 0 <= (x) && (x) < (w)) ? true : false

//debug
#define DEBUG

#define DUMPOUT cout

#ifdef DEBUG
#define dump(...) DUMPOUT<<#__VA_ARGS__<<" :["<<__FUNCTION__<<":"<<__LINE__<<"]"<<endl; DUMPOUT<<"    "; dump_func(__VA_ARGS__)
#else
#define dump(...)
#endif

void dump_func() {DUMPOUT << endl;};

template <class Head, class... Tail> void dump_func(Head&& head, Tail&&... tail) {
    DUMPOUT << head;
    if (sizeof...(Tail) == 0) DUMPOUT << " ";
    else DUMPOUT << ", ";
    dump_func(std::move(tail)...);
}

//ostream
template<typename T> ostream& operator << (ostream& os, vector<T>& vec) {
    os << "["; for (int i = 0; i<vec.size(); i++) os << vec[i] << (i + 1 == vec.size() ? "" : ", "); os << "]";
    return os;
}

template<typename T, typename U> ostream& operator << (ostream& os, pair<T, U>& pair_var) {
    os << "(" << pair_var.first << ", " << pair_var.second << ")";
    return os;
}

template<typename T, typename U> ostream& operator << (ostream& os, map<T, U>& map_var) {
    os << "[";
    for (auto itr = map_var.begin(); itr != map_var.end(); itr++) {
        os << "(" << itr->first << ", " << itr->second << ")"; itr++;  if(itr != map_var.end()) os << ", "; itr--;
    }
    os << "]";
    return os;
}

template<typename T> ostream& operator << (ostream& os, set<T>& set_var) {
    os << "[";
    for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
        os << *itr; ++itr; if(itr != set_var.end()) os << ", "; itr--;
    }
    os << "]";
    return os;
}

string s;

signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cin >> s;
  //int loop = 0;
  while (true) {
    //loop++;
    int n = s.size();
    if (n == 3) {
      if (s == "ABC") {
        cout << "Yes" << endl;
      }
      else {
        cout << "No" << endl;
      }
      return 0;
    }
    string nxs = "";
    int cnt_ABC = 0;
    rep(i, n) {
      if (s[i] != 'A') continue;
      string tmp = "";
      rep(j, 3) {
        if (i + j >= n) break;
        tmp += s[i + j];
      }
      if (tmp == "ABC") {
        cnt_ABC++;
        i += 2;
      }
    }
    if (cnt_ABC == 0) {
      cout << "No" << endl;
      return 0;
    }
    bool exist_c[3] = {};
    rep(i, n) {
      string tmp = "";
      rep(j, 3) {
        if (i + j >= n) break;
        tmp += s[i + j];
      }
      if (tmp != "ABC") {
        exist_c[s[i] - 'A'] = true;
      }
      else {
        i += 2;
      }
    }
    char erase_c;
    int cnt = 0;
    rep(i, 3) {
      if (exist_c[i]) cnt++;
      else erase_c = i + 'A';
    }
    if (cnt != 2) {
      cout << "No" << endl;
      return 0;
    }
    rep(i, n) {
      if (s[i] != 'A') {
        nxs += s[i];
        continue;
      }
      string tmp = "";
      rep(j, 3) {
        if (i + j >= n) break;
        tmp += s[i + j];
      }
      if (tmp == "ABC") {
        nxs += erase_c;
        i += 2;
      }
      else {
        nxs += s[i];
      }
    }
    s = nxs;
  }
}


```