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;
#define FOR(i,a,b) for(ll i=(a);i<(b);i++)
#define REP(i,a) FOR(i,0,a)
ll N;
const ll MAX_N=1e5;
string S[MAX_N];
ll ABC[3];
char ope[MAX_N+1];
ll ctoi(char c){
	return c-'A';
}
bool dfs(ll i){
	if(i==N){
		return true;
	}
	if(ABC[ctoi(S[i][0])]>0){
		
		ABC[ctoi(S[i][0])]--;
		ABC[ctoi(S[i][1])]++;
		ope[i]=S[i][1];
		if(dfs(i+1)){
			return true;
		}
		ABC[ctoi(S[i][0])]++;
		ABC[ctoi(S[i][1])]--;
		

	}
	if(ABC[ctoi(S[i][1])]>0){
		
		ABC[ctoi(S[i][1])]--;
		ABC[ctoi(S[i][0])]++;
		ope[i]=S[i][0];
		if(dfs(i+1)){
			return true;
		}
		ABC[ctoi(S[i][1])]++;
		ABC[ctoi(S[i][0])]--;
		
		
	}
	return false;
}

int main(){
	cin.tie(0);
	cin.sync_with_stdio(false);
	cin>>N;
	REP(i,3)cin>>ABC[i];
	REP(i,N)cin>>S[i];
	if(dfs(0)){
		cout<<"Yes"<<endl;
		REP(i,N){
			cout<<ope[i]<<endl;
		}
	}else{
		cout<<"No"<<endl;
	}
}