Three Variables Game

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

inputFormat

Input

Input is given from Standard Input in the following format:

N A B C s_1 s_2 : s_N

outputFormat

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

样例

2 1 3 0
AB
AC

Yes
A
C

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