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.*;

public class Main {
    private static final Scanner sc = new Scanner(System.in);

    private void exec(int[] x, int i, int j) {
        ++x[i];
        --x[j];
    }

    private void run() {
        int N = sc.nextInt();
        int[] x = new int[3];
        x[0] = sc.nextInt();
        x[1] = sc.nextInt();
        x[2] = sc.nextInt();

        for (int i = 0; i < 3; i++) {
            x[i] = Math.min(2, x[i]);
        }

        boolean[][][][] dp = new boolean[N + 1][3][3][3];
        dp[0][x[0]][x[1]][x[2]] = true;
        int[][][][][] prev = new int[N + 1][3][3][3][4];

        for (int i = 0; i < N; i++) {
            String s = sc.next();

            for (int l1 = 0; l1 < 3; ++l1) {
                for (int l2 = 0; l2 < 3; l2++) {
                    for (int l3 = 0; l3 < 3; l3++) {
                        if (!dp[i][l1][l2][l3]) {
                            continue;
                        }

                        int t1 = l1, t2 = l2, t3 = l3;
                        if (s.equals("AB")) {
                            if (t1 - 1 >= 0) {
                                t1 = t1 - 1;
                                t2 = Math.min(2, t2 + 1);
                                dp[i + 1][t1][t2][t3] = true;
                                prev[i + 1][t1][t2][t3][0] = l1;
                                prev[i + 1][t1][t2][t3][1] = l2;
                                prev[i + 1][t1][t2][t3][2] = l3;
                                prev[i + 1][t1][t2][t3][3] = 1;
                            }

                            t1 = l1; t2 = l2; t3 = l3;
                            if (t2 - 1 >= 0){
                                t1 = Math.min(2, t1 + 1);
                                t2 = t2 - 1;
                                dp[i + 1][t1][t2][t3] = true;
                                prev[i + 1][t1][t2][t3][0] = l1;
                                prev[i + 1][t1][t2][t3][1] = l2;
                                prev[i + 1][t1][t2][t3][2] = l3;
                                prev[i + 1][t1][t2][t3][3] = 0;
                            }
                        } else if (s.equals("BC")) {
                            if (t2 - 1 >= 0) {
                                t2 = t2 - 1;
                                t3 = Math.min(2, t3 + 1);
                                dp[i + 1][t1][t2][t3] = true;
                                prev[i + 1][t1][t2][t3][0] = l1;
                                prev[i + 1][t1][t2][t3][1] = l2;
                                prev[i + 1][t1][t2][t3][2] = l3;
                                prev[i + 1][t1][t2][t3][3] = 2;
                            }

                            t1 = l1; t2 = l2; t3 = l3;
                            if (t3 - 1 >= 0) {
                                t2 = Math.min(2, t2 + 1);
                                t3 = t3 - 1;
                                dp[i + 1][t1][t2][t3] = true;
                                prev[i + 1][t1][t2][t3][0] = l1;
                                prev[i + 1][t1][t2][t3][1] = l2;
                                prev[i + 1][t1][t2][t3][2] = l3;
                                prev[i + 1][t1][t2][t3][3] = 1;
                            }
                        } else {
                            if (t1 - 1 >= 0) {
                                t1 = t1 - 1;
                                t3 = Math.min(2, t3 + 1);
                                dp[i + 1][t1][t2][t3] = true;
                                prev[i + 1][t1][t2][t3][0] = l1;
                                prev[i + 1][t1][t2][t3][1] = l2;
                                prev[i + 1][t1][t2][t3][2] = l3;
                                prev[i + 1][t1][t2][t3][3] = 2;
                            }

                            t1 = l1; t2 = l2; t3 = l3;
                            if (t3 - 1 >= 0) {
                                t1 = Math.min(2, t1 + 1);
                                t3 = t3 - 1;
                                dp[i + 1][t1][t2][t3] = true;
                                prev[i + 1][t1][t2][t3][0] = l1;
                                prev[i + 1][t1][t2][t3][1] = l2;
                                prev[i + 1][t1][t2][t3][2] = l3;
                                prev[i + 1][t1][t2][t3][3] = 0;
                            }
                        }
                    }
                }
            }
        }

        for (int l1 = 0; l1 < 3; l1++) {
            for (int l2 = 0; l2 < 3; l2++) {
                for (int l3 = 0; l3 < 3; l3++) {
                    if (dp[N][l1][l2][l3]) {
                        System.out.println("Yes");

                        List<Integer> ans = new ArrayList<>();
                        int t1 = l1, t2 = l2, t3 = l3;
                        for (int t = N; t > 0; --t) {
                            ans.add(prev[t][t1][t2][t3][3]);
                            int a1 = prev[t][t1][t2][t3][0];
                            int a2 = prev[t][t1][t2][t3][1];
                            int a3 = prev[t][t1][t2][t3][2];

                            t1 = a1;
                            t2 = a2;
                            t3 = a3;
                        }

                        for (int t = N - 1; t >= 0; --t) {
                            int v = ans.get(t);
                            if (v == 0) {
                                System.out.println("A");
                            } else if (v == 1) {
                                System.out.println("B");
                            } else {
                                System.out.println("C");
                            }
                        }

                        return;
                    }
                }
            }
        }
        System.out.println("No");
    }

    public static void main(String[] args) {
        new Main().run();
    }
}