Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

2 1 3 0
AB
AC

Sample Output 1

Yes
A
C

You can successfully make two choices, as follows:

In the first choice, add 1 to A and subtract 1 from B. A becomes 2, and B becomes 2.

In the second choice, add 1 to C and subtract 1 from A. C becomes 1, and A becomes 1.

Sample Input 2

3 1 0 0
AB
BC
AB

Sample Output 2

No

Sample Input 3

1 0 9 0
AC

Sample Output 3

No

Sample Input 4

8 6 9 1
AC
BC
AB
BC
AC
BC
AB
AB

Sample Output 4

Yes
C
B
B
C
C
B
A
A

Solution in Fortran (GNU Fortran 9.2.1) (judge verdict: Runtime Error)

program main
    implicit none
    INTEGER n,a(3),i,x(2),x2(2),ans(100000),flag
    CHARACTER s1*2,s2
    read(*,*) n,(a(i),i=1,3)
    i=0
    flag=1
!0が二つ含まれる場合
    if ( ((a(1)==0 .and. a(2)==0) .or. (a(2)==0 .and. a(3)==0) .or. (a(3)==0 .and. a(1)==0)) .and. a(1)+a(2)+a(3)/=2 ) then
        do i = 1,n
            call read_s(s1,x)
            if ( a(x(1))+a(x(2))==0 ) then
                write(*,*) "No"
                flag=0
                exit
            else
                call nomal(a,ans,x,i)
            end if
        end do
!1,1,0の場合
    else if ( a(1)+a(2)+a(3)==2 ) then
        call read_s(s1,x)
        do i = 1, n
            call read_s(s2,x2)
            call exceptional(a,ans,x,x2,i)
            x=x2
        end do
!それ以外
    else
        do i = 1, n
            call read_s(s1,x)
            call nomal(a,ans,x,i)
        end do
    end if

    if ( flag==1 ) then
        write(*,*) "Yes"
        do i = 1, n
            if(ans(i)==1) then
                write(*,*) "A"
            else if ( ans(i)==2 ) then
                write(*,*) "B"
            else
                write(*,*) "c"
            end if
        end do
    end if
contains
    subroutine read_s(sr, xr)
        implicit none
        INTEGER,INTENT(OUT):: xr(2)
        CHARACTER(*) sr
        read(*,*) sr
        if ( sr=="AB" ) then
            xr(1)=1
            xr(2)=2
        else if ( sr=="BC" ) then
            xr(1)=2
            xr(2)=3
        else 
            xr(1)=3
            xr(2)=1
        end if
    end subroutine read_s

    subroutine nomal(an, ansn, xn,in)
        implicit none
        INTEGER an(3),xn(2),ansn(100000),in
        if ( an(xn(1))>=an(xn(2)) ) then
            an(xn(1))=an(xn(1))-1
            an(xn(2))=an(xn(2))+1
            ansn(in)=xn(2)
        else
            an(xn(1))=an(xn(1))+1
            an(xn(2))=an(xn(2))-1
            ansn(in)=xn(1)
        end if
    end subroutine nomal

    subroutine exceptional(as, anss, xs, x2s,is)
        implicit none
        INTEGER as(3),xs(2),x2s(2),anss(100000),is
        if ( as(xs(1))>as(xs(2)) ) then
            as(xs(1))=as(xs(1))-1
            as(xs(2))=as(xs(2))+1
            anss(is)=xs(2)
        else if ( a(x(1))<a(x(2)) ) then
            as(xs(1))=as(xs(1))+1
            as(xs(2))=as(xs(2))-1
            anss(is)=xs(1)           
        else if ( xs(1)==x2s(1) .or. xs(1)==x2s(2) ) then
            as(xs(1))=as(xs(1))+1
            as(xs(2))=as(xs(2))-1
            anss(is)=xs(1) 
        else
            as(xs(1))=as(xs(1))-1
            as(xs(2))=as(xs(2))+1
            anss(is)=xs(2)
        end if
    end subroutine exceptional
end program main