Problem: There is a game that involves three variables, denoted A, B, and C.

As the game progresses, there will be N events where you are asked to make a choice. Each of these choices is represented by a string s_i. If s_i is `AB`, you must add 1 to A or B then subtract 1 from the other; if s_i is `AC`, you must add 1 to A or C then subtract 1 from the other; if s_i is `BC`, you must add 1 to B or C then subtract 1 from the other.

After each choice, none of A, B, and C should be negative.

Determine whether it is possible to make N choices under this condition. If it is possible, also give one such way to make the choices.

Constraints

* 1 \leq N \leq 10^5
* 0 \leq A,B,C \leq 10^9
* N, A, B, C are integers.
* s_i is `AB`, `AC`, or `BC`.

Input

Input is given from Standard Input in the following format:


N A B C
s_1
s_2
:
s_N


Output

If it is possible to make N choices under the condition, print `Yes`; otherwise, print `No`.

Also, in the former case, show one such way to make the choices in the subsequent N lines. The (i+1)-th line should contain the name of the variable (`A`, `B`, or `C`) to which you add 1 in the i-th choice.

Examples

Input

2 1 3 0
AB
AC


Output

Yes
A
C


Input

3 1 0 0
AB
BC
AB


Output

No


Input

1 0 9 0
AC


Output

No


Input

8 6 9 1
AC
BC
AB
BC
AC
BC
AB
AB


Output

Yes
C
B
B
C
C
B
A
A

Solution (in CPP):

Solution:
#include <iostream>
#include<vector>
using namespace std;
int n,a[3],x,y;
string s,t;
vector<int> v;
int main(void){
    cin>>n>>a[0]>>a[1]>>a[2];
    cin>>s;
    for(int i=0;i<n;i++){
        if(i!=n-1)cin>>t;
        else t=s;
        x=s[0]-'A';
        y=s[1]-'A';
        if(a[x]==0&&a[y]==0){cout<<"No"<<endl;return 0;}
        else if(a[x]==0){a[x]++;a[y]--;v.push_back(x);}
        else if(a[y]==0){a[y]++;a[x]--;v.push_back(y);}
        else if(a[x]>a[y]){a[x]--;a[y]++;v.push_back(y);}
        else if(a[x]<a[y]){a[y]--;a[x]++;v.push_back(x);}
        else{
            if((t[0]-'A')==x||(t[1]-'A')==x){a[x]++;a[y]--;v.push_back(x);}
            else {a[x]--;a[y]++;v.push_back(y);}
        }
        s=t;
    }
    cout<<"Yes"<<endl;
    for(auto x:v){
        cout<<char(x+'A')<<endl;
    }
}