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>
#define ll long long
using namespace std;
int x[100005],y[100005],step[100005];
int main()
{
	int n,a[3];cin>>n>>a[0]>>a[1]>>a[2];
	for(int i=0;i<n;++i)
	{
		char s[3];
		cin>>s;
		x[i]=s[0]-'A';y[i]=s[1]-'A';
	} 
	for(int i=0;i<n;++i)
	{
		if(a[x[i]]>a[y[i]])
		swap(x[i],y[i]);
		else if(a[x[i]]==a[y[i]])
		{
		if(i+1<n&&(y[i]==x[i+1]||y[i]==y[i+1]))
		swap(x[i],y[i]);
		}
		if(a[y[i]]==0) 
		{
			cout<<"No";return 0;
		}
		a[x[i]]++;a[y[i]]--;step[i]=x[i];
	}
	cout<<"Yes"<<endl;
	for(int i=0;i<n;++i)
	cout<<char(step[i]+'A')<<endl;
 }