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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Math;
using static ABC166.abc166_f.Cin;
using static ABC166.abc166_f.Util;
using Pair = ABC166.abc166_f.VTuple<long, long>;

/// <summary>
/// ABC166
/// F - Three Variables Game
/// https://atcoder.jp/contests/ABC166/tasks/abc166_f
/// </summary>
namespace ABC166.abc166_f
{
    public class Program
    {
        public static void Main(string[] args)
        {
            int N = ri;
            int A = ri;
            int B = ri;
            int C = ri;

            string[] choice = new string[N];
            for (int i = 0; i < N; i++)
            {
                choice[i] = rs;
            }

            DontAutoFlush();
            char[] result = new char[N];
            HashMap<ValueTuple<int, int, int, int>, bool> memo
                = new HashMap<ValueTuple<int, int, int, int>, bool>();

            Action<int,int,int,int> rec = null;
            rec = (i, a, b, c) =>
            {
                ValueTuple<int, int, int, int> key = (i, a, b, c);
                if (memo.ContainsKey(key) &&
                    memo[key] == false)
                {
                    return;
                }

                if (a < 0 || b < 0 || c < 0)
                {
                    memo[key] = false;
                    return;
                }

                if (i == N)
                {
                    for (int j = 0; j < N; j++)
                    {
                        Console.WriteLine(result[j]);
                    }
                    Flush();
                    Environment.Exit(0);
                }

                if (choice[i] == "AB")
                {
                    result[i] = 'B';
                    rec(i + 1, a - 1, b + 1, c);
                    result[i] = 'A';
                    rec(i + 1, a + 1, b - 1, c);
                }
                else if (choice[i] == "AC")
                {
                    result[i] = 'C';
                    rec(i + 1, a - 1, b, c + 1);
                    result[i] = 'A';
                    rec(i + 1, a + 1, b, c - 1);
                }
                else if (choice[i] == "BC")
                {
                    result[i] = 'C';
                    rec(i + 1, a, b - 1, c + 1);
                    result[i] = 'B';
                    rec(i + 1, a, b + 1, c - 1);
                }
            };

            rec(0, A, B, C);
        }        
    }

    /// <summary>
    /// 競プロライブラリ
    /// https://github.com/ha2ne2/ABC/tree/master/Lib
    /// </summary>
    public struct Mint:System.IComparable<Mint>,System.IEquatable<Mint>{public static readonly long MOD=(long)1e9+7;public long Value;public Mint(long val){Value=val%MOD;if(Value<0)Value+=MOD;}private static Mint Ctor(long val){return new Mint(){Value=val};}public static Mint operator+(Mint a,Mint b){long res=a.Value+b.Value;if(res>MOD)res-=MOD;return Ctor(res);}public static Mint operator-(Mint a,Mint b){long res=a.Value-b.Value;if(res<0)res+=MOD;return Ctor(res);}public static Mint operator*(Mint a,Mint b){long res=a.Value*b.Value;if(res>MOD)res%=MOD;return Ctor(res);}public static Mint operator/(Mint a,Mint b){return a*Inv(b);}public override bool Equals(object obj){return obj is Mint&&Value==((Mint)obj).Value;}public override int GetHashCode(){return Value.GetHashCode();}public override string ToString(){return Value.ToString();}public static implicit operator Mint(long a){return new Mint(a);}public static explicit operator long(Mint a){return a.Value;}public static Mint Pow(Mint a,long n){if(n==0)return new Mint(1);Mint b=Pow(a,n>>1);b*=b;if((n&1)==1)b*=a;return b;}public static Mint Inv(Mint n){long a=n.Value;long b=MOD;long x=1;long u=0;while(b!=0){long k=a/b;long _x=u;u=x-k*u;x=_x;long _a=a;a=b;b=_a-(k*b);}return new Mint(x);}public bool Equals(Mint other){return Value==other.Value;}public int CompareTo(Mint other){return Comparer<long>.Default.Compare(Value,other.Value);}}public class HashMap<K,V>:System.Collections.Generic.Dictionary<K,V>{private V DefaultValue;private static Func<V>CreateInstance=System.Linq.Expressions.Expression.Lambda<Func<V>>(System.Linq.Expressions.Expression.New(typeof(V))).Compile();public HashMap(){}public HashMap(V defaultValue){DefaultValue=defaultValue;}new public V this[K i]{get{V v;if(TryGetValue(i,out v)){return v;}else{return base[i]=DefaultValue!=null?DefaultValue:CreateInstance();}}set{base[i]=value;}}}public struct VTuple<T1,T2>:System.IComparable<VTuple<T1,T2>>,System.IEquatable<VTuple<T1,T2>>{public T1 Item1;public T2 Item2;public T1 First{get{return Item1;}}public T2 Second{get{return Item2;}}public VTuple(T1 item1,T2 item2){Item1=item1;Item2=item2;}public override bool Equals(object obj){return obj is VTuple<T1,T2>&&Equals((VTuple<T1,T2>)obj);}public override int GetHashCode(){int h1=Item1!=null?Item1.GetHashCode():0;int h2=Item2!=null?Item2.GetHashCode():0;return HashHelpers.CombineHashCodes(h1,h2);}public override string ToString(){return"("+Item1?.ToString()+", "+Item2?.ToString()+")";}public bool Equals(VTuple<T1,T2>other){return EqualityComparer<T1>.Default.Equals(Item1,other.Item1)&&EqualityComparer<T2>.Default.Equals(Item2,other.Item2);}public int CompareTo(VTuple<T1,T2>other){int c=Comparer<T1>.Default.Compare(Item1,other.Item1);if(c!=0)return c;return Comparer<T2>.Default.Compare(Item2,other.Item2);}}public struct VTuple3<T1,T2,T3>:System.IComparable<VTuple3<T1,T2,T3>>,System.IEquatable<VTuple3<T1,T2,T3>>{public T1 Item1;public T2 Item2;public T3 Item3;public VTuple3(T1 item1,T2 item2,T3 item3){Item1=item1;Item2=item2;Item3=item3;}public override bool Equals(object obj){return obj is VTuple3<T1,T2,T3>&&Equals((VTuple3<T1,T2,T3>)obj);}public override int GetHashCode(){int h1=Item1!=null?Item1.GetHashCode():0;int h2=Item2!=null?Item2.GetHashCode():0;int h3=Item3!=null?Item3.GetHashCode():0;return HashHelpers.CombineHashCodes(h1,h2,h3);}public override string ToString(){return"("+Item1?.ToString()+", "+Item2?.ToString()+", "+Item3?.ToString()+")";}public bool Equals(VTuple3<T1,T2,T3>other){return EqualityComparer<T1>.Default.Equals(Item1,other.Item1)&&EqualityComparer<T2>.Default.Equals(Item2,other.Item2)&&EqualityComparer<T3>.Default.Equals(Item3,other.Item3);}public int CompareTo(VTuple3<T1,T2,T3>other){int c=Comparer<T1>.Default.Compare(Item1,other.Item1);if(c!=0)return c;c=Comparer<T2>.Default.Compare(Item2,other.Item2);if(c!=0)return c;return Comparer<T3>.Default.Compare(Item3,other.Item3);}}public struct VTuple4<T1,T2,T3,T4>:System.IComparable<VTuple4<T1,T2,T3,T4>>,System.IEquatable<VTuple4<T1,T2,T3,T4>>{public T1 Item1;public T2 Item2;public T3 Item3;public T4 Item4;public VTuple4(T1 item1,T2 item2,T3 item3,T4 item4){Item1=item1;Item2=item2;Item3=item3;Item4=item4;}public override bool Equals(object obj){return obj is VTuple4<T1,T2,T3,T4>&&Equals((VTuple4<T1,T2,T3,T4>)obj);}public override int GetHashCode(){int h1=Item1!=null?Item1.GetHashCode():0;int h2=Item2!=null?Item2.GetHashCode():0;int h3=Item3!=null?Item3.GetHashCode():0;int h4=Item3!=null?Item4.GetHashCode():0;return HashHelpers.CombineHashCodes(h1,h2,h3,h4);}public override string ToString(){return"("+Item1?.ToString()+", "+Item2?.ToString()+", "+Item3?.ToString()+", "+Item4?.ToString()+")";}public bool Equals(VTuple4<T1,T2,T3,T4>other){return EqualityComparer<T1>.Default.Equals(Item1,other.Item1)&&EqualityComparer<T2>.Default.Equals(Item2,other.Item2)&&EqualityComparer<T3>.Default.Equals(Item3,other.Item3)&&EqualityComparer<T4>.Default.Equals(Item4,other.Item4);}public int CompareTo(VTuple4<T1,T2,T3,T4>other){int c=Comparer<T1>.Default.Compare(Item1,other.Item1);if(c!=0)return c;c=Comparer<T2>.Default.Compare(Item2,other.Item2);if(c!=0)return c;c=Comparer<T3>.Default.Compare(Item3,other.Item3);if(c!=0)return c;return Comparer<T4>.Default.Compare(Item4,other.Item4);}}public static class HashHelpers{public static readonly int RandomSeed=new System.Random().Next(int.MinValue,int.MaxValue);public static int Combine(int h1,int h2){uint rol5=((uint)h1<<5)|((uint)h1>>27);return((int)rol5+h1)^h2;}public static int CombineHashCodes(int h1,int h2){return Combine(Combine(RandomSeed,h1),h2);}public static int CombineHashCodes(int h1,int h2,int h3){return Combine(CombineHashCodes(h1,h2),h3);}public static int CombineHashCodes(int h1,int h2,int h3,int h4){return Combine(CombineHashCodes(h1,h2,h3),h4);}}public static class Cin{public static int ri{get{return ReadInt();}}public static int[]ria{get{return ReadIntArray();}}public static long rl{get{return ReadLong();}}public static long[]rla{get{return ReadLongArray();}}public static double rd{get{return ReadDouble();}}public static double[]rda{get{return ReadDoubleArray();}}public static string rs{get{return ReadString();}}public static string[]rsa{get{return ReadStringArray();}}public static int ReadInt(){return int.Parse(Next());}public static long ReadLong(){return long.Parse(Next());}public static double ReadDouble(){return double.Parse(Next());}public static string ReadString(){return Next();}public static int[]ReadIntArray(){Tokens=null;return Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);}public static long[]ReadLongArray(){Tokens=null;return Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);}public static double[]ReadDoubleArray(){Tokens=null;return Array.ConvertAll(Console.ReadLine().Split(' '),double.Parse);}public static string[]ReadStringArray(){Tokens=null;return Console.ReadLine().Split(' ');}public static void ReadCol(out long[]a,long N){a=new long[N];for(int i=0;i<N;i++){a[i]=ReadLong();}}public static void ReadCols(out long[]a,out long[]b,long N){a=new long[N];b=new long[N];for(int i=0;i<N;i++){a[i]=ReadLong();b[i]=ReadLong();}}public static void ReadCols(out long[]a,out long[]b,out long[]c,long N){a=new long[N];b=new long[N];c=new long[N];for(int i=0;i<N;i++){a[i]=ReadLong();b[i]=ReadLong();c[i]=ReadLong();}}public static int[,]ReadIntTable(int h,int w){Tokens=null;int[,]ret=new int[h,w];for(int i=0;i<h;i++){for(int j=0;j<w;j++){ret[i,j]=ReadInt();}}return ret;}public static long[,]ReadLongTable(long h,long w){Tokens=null;long[,]ret=new long[h,w];for(int i=0;i<h;i++){for(int j=0;j<w;j++){ret[i,j]=ReadLong();}}return ret;}public static char[,]ReadCharTable(int h,int w){Tokens=null;char[,]res=new char[h,w];for(int i=0;i<h;i++){string s=ReadString();for(int j=0;j<w;j++){res[i,j]=s[j];}}return res;}private static string[]Tokens;private static int Pointer;private static string Next(){if(Tokens==null||Tokens.Length<=Pointer){Tokens=Console.ReadLine().Split(' ');Pointer=0;}return Tokens[Pointer++];}}public static class Util{public static readonly long INF=(long)1e17;public readonly static long MOD=(long)1e9+7;public readonly static int[]DXY4={0,1,0,-1,0};public readonly static int[]DXY8={1,1,0,1,-1,0,-1,-1,1};public static void DontAutoFlush(){if(Console.IsOutputRedirected)return;var sw=new System.IO.StreamWriter(Console.OpenStandardOutput()){AutoFlush=false};Console.SetOut(sw);}public static void Flush(){Console.Out.Flush();}public static T[]Sort<T>(T[]array){Array.Sort<T>(array);return array;}public static T[]SortDecend<T>(T[]array){Array.Sort<T>(array);Array.Reverse(array);return array;}public static void Swap<T>(ref T a,ref T b){T _a=a;a=b;b=_a;}public static long GCD(long a,long b){while(b!=0){long _a=a;a=b;b=_a%b;}return a;}public static long LCM(long a,long b){if(a==0||b==0)return 0;return a*b/GCD(a,b);}public static void ChMax(ref long a,long b){if(a<b)a=b;}public static void ChMin(ref long a,long b){if(a>b)a=b;}public static void ChMax(ref int a,int b){if(a<b)a=b;}public static void ChMin(ref int a,int b){if(a>b)a=b;}public static void FillArray<T>(T[]array,T value){int max=array.Length;for(int i=0;i<max;i++){array[i]=value;}}public static void FillArray<T>(T[,]array,T value){int max0=array.GetLength(0);int max1=array.GetLength(1);for(int i=0;i<max0;i++){for(int j=0;j<max1;j++){array[i,j]=value;}}}public static void FillArray<T>(T[,,]array,T value){int max0=array.GetLength(0);int max1=array.GetLength(1);int max2=array.GetLength(2);for(int i=0;i<max0;i++){for(int j=0;j<max1;j++){for(int k=0;k<max2;k++){array[i,j,k]=value;}}}}public static long[]Accumulate(long[]array){long[]acc=new long[array.Length+1];for(int i=0;i<array.Length;i++){acc[i+1]=acc[i]+array[i];}return acc;}public static double[]Accumulate(double[]array){double[]acc=new double[array.Length+1];for(int i=0;i<array.Length;i++){acc[i+1]=acc[i]+array[i];}return acc;}}
}