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: Time Limit Exceeded)

#include <bits/stdc++.h>
#define DEBUG if(0)
#define lli long long int
#define ldouble long double
using namespace std;

const int maxN = 1e5; int n, a, b, c;
char s[maxN][3];
int kind[maxN];

map<pair<int, int>, int> memo[maxN], path[maxN];
bool solve(int i = 0, int aa = a, int bb = b, int cc = c)
{
  if (aa < 0 || bb < 0 || cc < 0) return false;
  if (i == n) return true;
  aa = min(aa, n - i), bb = min(bb, n - i), cc = min(cc, n - i);
  if (aa == n - i && bb == n - i && cc == n - i) return true;
  pair<int, int> u = kind[i] == 0 ? make_pair(aa, bb) : kind[i] == 1 ? make_pair(aa, cc) : make_pair(bb, cc);
  if (memo[i].count(u))
    return memo[i][u];

  bool ans = false;
  if (kind[i] == 0)
  {
    bool aaa = solve(i + 1, aa + 1, bb - 1, cc), bbb = solve(i + 1, aa - 1, bb + 1, cc);
    path[i][u] = aaa >= bbb ? 0 : 1;
    ans = max(aaa, bbb);
  }
  else if (kind[i] == 1)
  {
    bool aaa = solve(i + 1, aa + 1, bb, cc - 1), ccc = solve(i + 1, aa - 1, bb, cc + 1);
    path[i][u] = aaa >= ccc ? 0 : 2;
    ans = max(aaa, ccc);
  }
  else
  {
    bool bbb = solve(i + 1, aa, bb + 1, cc - 1), ccc = solve(i + 1, aa, bb - 1, cc + 1);
    path[i][u] = bbb >= ccc ? 1 : 2;
    ans = max(bbb, ccc);
  }
  return memo[i][u] = ans;
}

int main()
{
  while (scanf("%d %d %d %d", &n, &a, &b, &c) != EOF)
  {
    a = min(a, maxN), b = min(b, maxN), c = min(c, maxN);
    for (int i = 0; i < n; i++)
    {
      scanf(" %s", s[i]);
      kind[i] = !strcmp(s[i], "AB") ? 0 : !strcmp(s[i], "AC") ? 1 : 2;
      memo[i].clear(), path[i].clear();
    }

    bool ans = solve();
    if (!ans) printf("No\n");
    else
    {
      printf("Yes\n");
      for (int i = 0, aa = a, bb = b, cc = c; i < n; i++)
      {
        aa = min(aa, n - i), bb = min(bb, n - i), cc = min(cc, n - i);
        pair<int, int> u = kind[i] == 0 ? make_pair(aa, bb) : kind[i] == 1 ? make_pair(aa, cc) : make_pair(bb, cc);
        if (kind[i] == 0)
        {
          if (path[i][u] == 0)
            aa++, bb--, printf("A\n");
          else
            aa--, bb++, printf("B\n");
        }
        else if (kind[i] == 1)
        {
          if (path[i][u] == 0)
            aa++, cc--, printf("A\n");
          else
            aa--, cc++, printf("C\n");
        }
        else
        {
          if (path[i][u] == 1)
            bb++, cc--, printf("B\n");
          else
            bb--, cc++, printf("C\n");
        }
      }
    }
  }
  return 0;
}