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 C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;

int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    int n,a,b,c;
    cin >> n >> a >> b >> c;
    int cnt=0;
    for(int x:{a,b,c}) cnt+=(x==0);
    int m=1;
    if(cnt==1) m=3;
    if(cnt==2) m=6;
    a=min(a,m);
    b=min(b,m);
    c=min(c,m);
    vector<vector<vector<vector<bool>>>> dp(n+1,vector<vector<vector<bool>>>(7,vector<vector<bool>>(7,vector<bool>(7,0))));
    vector<vector<vector<vector<char>>>> p(n+1,vector<vector<vector<char>>>(7,vector<vector<char>>(7,vector<char>(7,0))));
    dp[0][a][b][c]=1;
    string s;
    vector<string> t(n+1);
    for(int i=0;i<n;i++)
    {
        cin >> s;
        t[i+1]=s;
        for(int x=0;x<=6;x++)
        {
            for(int y=0;y<=6;y++)
            {
                for(int z=0;z<=6;z++)
                {
                    if(dp[i][x][y][z]==0) continue;
                    if(s=="AB")
                    {
                        if(y>0)
                        {
                            dp[i+1][x+1][y-1][z]=1;
                            p[i+1][x+1][y-1][z]='A';
                        }
                        if(x>0)
                        {
                            dp[i+1][x-1][y+1][z]=1;
                            p[i+1][x-1][y+1][z]='B';
                        }
                    }
                    if(s=="AC")
                    {
                        if(z>0)
                        {
                            dp[i+1][x+1][y][z-1]=1;
                            p[i+1][x+1][y][z-1]='A';
                        }
                        if(x>0)
                        {
                            dp[i+1][x-1][y][z+1]=1;
                            p[i+1][x-1][y][z+1]='C';
                        }
                    }
                    if(s=="BC")
                    {
                        if(z>0)
                        {
                            dp[i+1][x][y+1][z-1]=1;
                            p[i+1][x][y+1][z-1]='B';
                        }
                        if(y>0)
                        {
                            dp[i+1][x][y-1][z+1]=1;
                            p[i+1][x][y-1][z+1]='C';
                        }
                    }
                }
            }
        }
    }
    bool ok=0;
    array<int,3> now;
    for(int x=0;x<=6;x++)
    {
        for(int y=0;y<=6;y++)
        {
            for(int z=0;z<=6;z++)
            {
                if(dp[n][x][y][z]==1)
                {
                    now={x,y,z};
                    ok=1;
                }
            }
        }
    }
    if(ok)
    {
        cout << "Yes\n";
        string res;
        for(int i=n;i>=1;i--)
        {
            auto [x,y,z]=now;
            //cout << x << " " << y << " " << z << endl;
            char e=p[i][x][y][z];
            res+=e;
            if(t[i]=="AB")
            {
                if(e=='A') {x--; y++;}
                else {x++; y--;}
            }
            if(t[i]=="AC")
            {
                if(e=='A') {x--; z++;}
                else {x++; z--;}
            }
            if(t[i]=="BC")
            {
                if(e=='B') {y--; z++;}
                else {y++; z--;}
            }
            now={x,y,z};
        }
        reverse(res.begin(),res.end());
        for(char e:res) cout << e << "\n";
    }
    else cout << "No\n";
    return 0;
}