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>
#define MAX_N 1e5
using namespace std;
int n, a,b,c;
char aAns[(int)MAX_N] = {};
string aInp[(int)MAX_N];
 
bool checkAllPos(int* cArr){
    for(int i =0 ; i < 3 ; ++i){
        if(cArr[i] < 0) return false;
    }
    return true;
}

void incArr(int* cArr, int lhs, int rhs, int incLhs){
    cArr[lhs] += incLhs;
    cArr[rhs] -= incLhs;
}
 
bool sol(int ptr,int* cArr){
    if(ptr == n){
        return true;
    }
    int lhs = aInp[ptr][0]-'A';
    int rhs = aInp[ptr][1]-'A';
 
    incArr(cArr, lhs, rhs, 1);
    aAns[ptr]=aInp[ptr][0];
    if(checkAllPos(cArr) && sol(ptr+1,cArr)) return true;
 
    incArr(cArr, lhs, rhs, -2);
    aAns[ptr]=aInp[ptr][1];
    if(checkAllPos(cArr) && sol(ptr+1,cArr)) return true;
    incArr(cArr, lhs, rhs, 1);
    aAns[ptr]='-';
    return false;
}
 
int main(){
    cin >> n >> a >> b >> c;
    for(int i = 0 ; i < n ; ++i){
        cin >> aInp[i];
    }
    int arr[3] = {a,b,c};
    if(sol(0,arr)){
        cout << "Yes\n";
        for(int i = 0; i < n ; ++i){
            cout << aAns[i] << "\n";
        }
    }
    else{
        cout << "No\n";
    }
 
    return 0;
}