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<bits/stdc++.h>
using namespace std;
typedef long long ll;
string od[100050];
char ans[100050];
int n;
void dfs(int i,int a,int b,int c){
    if(i==n){
        printf("Yes\n");
        for(int j=0;j<n;j++)
            printf("%c\n",ans[j]);
        exit(0);
    }
    if(od[i]=="AB"){
        if(a>0) {
                ans[i]='B';
                dfs(i+1,a-1,b+1,c);
        }
        if(b>0) {
            ans[i]='A';
            dfs(i+1,a+1,b-1,c);
        }
    }
    if(od[i]=="BC"){
        if(b>0) {
            ans[i]='C';
            dfs(i+1,a,b-1,c+1);
        }
        if(c>0) {
            ans[i]='B';
            dfs(i+1,a,b+1,c-1);
        }
    }
    if(od[i]=="AC"){
        if(a>0) {
            ans[i]='C';
            dfs(i+1,a-1,b,c+1);
        }
        if(c>0) {
            ans[i]='A';
            dfs(i+1,a+1,b,c-1);
        }
    }
}
int main(){
    int a,b,c;
    scanf("%d%d%d%d",&n,&a,&b,&c);
    for(int i=0;i<n;i++){
        cin>>od[i];
    }
    dfs(0,a,b,c);
    printf("No");
}