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# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;

namespace ConsoleApp
{
    class Program
    {
        static void Main(string[] args)
        {
            var input = Console.ReadLine().Split().Select(long.Parse).ToArray();
            var N = input[0];

            var minA = new PathInfo() { Path = new List<char>(), A = input[1], B = input[2], C = input[3] };
            var minB = new PathInfo() { Path = new List<char>(), A = input[1], B = input[2], C = input[3] };
            var minC = new PathInfo() { Path = new List<char>(), A = input[1], B = input[2], C = input[3] };

            for (int i = 0; i < N; i++)
            {
                if (!SetPath(ref minA, ref minB, ref minC, Console.ReadLine()))
                {
                    Console.WriteLine("No");
                    return;
                }
            }

            Console.WriteLine("Yes");
            minA.Path.ForEach(c => Console.WriteLine(c));
        }

        static bool SetPath(ref PathInfo minA, ref PathInfo minB, ref PathInfo minC, string s)
        {
            if ((s == "AB" && minC.A == 0 && minC.B == 0)
                || (s == "AC" && minB.A == 0 && minB.C == 0)
                || (s == "BC" && minA.B == 0 && minA.C == 0))
            {
                return false;
            }

            SetPath(ref minA, ref minB, ref minC, s[0], s[1]);
            return true;
        }

        static void SetPath(ref PathInfo minA, ref PathInfo minB, ref PathInfo minC, char c1, char c2)
        {
            var paths = new List<PathInfo> {
                minA.Set(c1, c2),
                minA.Set(c2, c1),
                minB.Set(c1, c2),
                minB.Set(c2, c1),
                minC.Set(c1, c2),
                minC.Set(c2, c1)
            }.Where(s => s != null);

            minA = paths.First(s => s.A == paths.Min(t => t.A));
            minB = paths.First(s => s.B == paths.Min(t => t.B));
            minC = paths.First(s => s.C == paths.Min(t => t.C));
        }

        class PathInfo
        {
            public List<char> Path { get; set; }
            public long A { get; set; }
            public long B { get; set; }
            public long C { get; set; }

            private PathInfo Copy()
            {
                return new PathInfo() { Path = new List<char>(Path), A = A, B = B, C = C };
            }

            public PathInfo Set(char plus, char minus)
            {
                var ret = Copy();
                ret.Path.Add(plus);
                ret.SetABC(plus, true);
                ret.SetABC(minus, false);


                return ret.A >= 0 && ret.B >= 0 && ret.C >= 0 ? ret : null;
            }

            private void SetABC(char c, bool plus)
            {
                var x = plus ? 1 : -1;

                switch (c)
                {
                    case 'A':
                        A += x;
                        return;
                    case 'B':
                        B += x;
                        return;
                    case 'C':
                        C += x;
                        return;
                }
            }
        }
    }
}