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:
#include <cstdio>
const int MAXN = 1e5+5;
const int MAXS = 5;
char  out[MAXN];
char    S[MAXN][MAXS];
int C[3];
int N;

bool check(int i, char c) {
  return (S[i][0] == c) || (S[i][1] == c);
}

bool solve() {
  int sum = C[0] + C[1] + C[2];
  if (sum == 0) {
    return false;
  }
  for (int i = 0; i < N; ++i) {
    int u = S[i][0] - 'A';
    int v = S[i][1] - 'A';
    if (!C[u] && !C[v]) {
      return false;
    }
    bool U = C[u];
    if (C[u] && C[v]) {
      int nxt = i+1;
      if ((nxt < N) && !check(nxt, S[i][1])) U = false;
    }
    if (U) {
      out[i] = S[i][1];
      --C[u];
      ++C[v];
    } else {
      out[i] = S[i][0];
      ++C[u];
      --C[v];
    }
  }
  return true;
}

int main() {
  scanf("%d", &N);
  for (int i = 0; i < 3; ++i) {
    scanf("%d", &C[i]);
  }
  for (int i = 0; i < N; ++i) {
    scanf(" %s", S[i]);
  }
  if (solve()) {
    puts("Yes");
    for (int i = 0; i < N; ++i) {
      putchar(out[i]);
      puts("");
    }
  } else {
    puts("No");
  }
  return 0;
}