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;

const int N = 1e5 + 5;

int a, b, c, n;
string s[N];
char ans[N];

int main() {
	cin>>n>>a>>b>>c;
	for(int i = 1; i <= n; i++)
		cin>>s[i];
	for(int i = 1; i <= n; i++) {
		if(s[i] == "AB") {
			if(a == b) {
				if(s[i + 1] == "AC") a++, b--, ans[i] = 'A';
				else a--, b++, ans[i] = 'B'; 
			}
			else {
			    if(a > b) a--, b++, ans[i] = 'B';
			    else a++, b--, ans[i] = 'A';
			}
		}
		if(s[i] == "AC") {
			if(a == c) {
				if(s[i + 1] == "AB") a++, c--, ans[i] = 'A';
				else a--, c++, ans[i] = 'C'; 
			}
			else {
			    if(a > c) a--, c++, ans[i] = 'C';
			    else a++, c--, ans[i] = 'A';
			}
		}
		if(s[i] == "BC") {
			if(c == b) {
				if(s[i + 1] == "AC") c++, b--, ans[i] = 'C';
				else c--, b++, ans[i] = 'B'; 
			}
			else {
			    if(c > b) c--, b++, ans[i] = 'B';
			    else c++, b--, ans[i] = 'C';
			}
		}				
		if(min(a, min(b, c)) < 0) {
			cout<<"No"<<endl;
			return 0;
		}
	}
	cout<<"Yes"<<endl;
	for(int i = 1; i <= n; i++)
		cout<<ans[i]<<endl;
	return 0;
}