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:
#import <bits/stdc++.h>
using namespace std;typedef int l;
#define rp(i,n) for(l i=0;i<n;++i)
l main(){l n;cin>>n;l v[99];for(char c='A';c<='C';++c)cin>>v[c];string s[220000];rp(i,n)cin>>s[i];char a[220000];rp(i,n){char x=s[i][0],y=s[i][1],M=(v[x]>=v[y]?x:y),m=x^y^M;if(v[x]==v[y]&&i+1<n&&(s[i+1][0]==x||s[i+1][1]==x))swap(M,m);if(v[M]==0){puts("No");return 0;}v[M]--,v[m]++;a[i]=m;}puts("Yes");rp(i,n)cout<<a[i]<<'\n';}