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 JAVA):

Solution:

import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Deque;
import java.util.List;
import java.util.Scanner;

public class Main {

	public static class State {
		int a;
		int b;
		int c;

		public State(int a, int b, int c) {
			super();
			this.a = a;
			this.b = b;
			this.c = c;
		}

	}

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		// 整数の入力
		int n = sc.nextInt();
		int a = sc.nextInt();
		int b = sc.nextInt();
		int c = sc.nextInt();

		State init = new State(a, b, c);
		
		String[] s = new String[n];
		for (int i = 0; i < n; i++) {
			s[i] = sc.next();
		}
		
		List<String> result = new ArrayList<>();  
		dfs( result, s, 0,n, init );
		
		if( result.size()== n ) {
			System.out.println("Yes");
			for (int i = result.size() -1; i >=0; i--) {
				System.out.println(result.get(i));
			}
		}else {
			System.out.println("No");
			
		}

	}

	private static boolean dfs(List<String> result, String[] s, int i, int n, State init) {
		if( i==n )return true;
		
		boolean noob = false;;
		switch (s[i]) {
		case "AB":
			noob = tryQueue(result,s, i, n, init,1,-1,0 , "A") ||
			tryQueue(result,s, i, n, init,-1,1,0 , "B");
			break;
		case "AC":
			noob = 
			tryQueue(result,s, i, n, init,1,0,-1 , "A") ||  
			tryQueue(result,s, i, n, init,-1,0,1 , "C");
			break;
		case "BC":
			noob = 
			tryQueue(result,s, i, n, init,0,1,-1 , "B") ||
			tryQueue(result,s, i, n, init,0,-1,1 , "C");
			break;
		default:
			break;
		}	
		return noob;
	}

	private static boolean tryQueue(List<String> result, String[] s, int level, int n,  State init, int i, int j, int k, String dir) {
		int a = init.a + i;
		int b = init.b + j;
		int c = init.c + k;

		if (a < 0 || b < 0 || c < 0)
			return false;
		State e = new State( a, b, c);
		if( dfs(result, s, level+1, n, e) ) {
			result.add(dir);
			return true;
		};
		
		return false;
	}

}