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:

// Problem : F - Three Variables Game
// Contest : AtCoder - AtCoder Beginner Contest 166
// URL : https://atcoder.jp/contests/abc166/tasks/abc166_f
// Memory Limit : 1024 MB
// Time Limit : 2000 ms
// Powered by CP Editor (https://github.com/cpeditor/cpeditor)

#include <bits/stdc++.h>

int n, a[100], d[100005];
char c[100005][4];

inline void doit(int &x, int &y, bool choice) {
  if (choice) --x, ++y; else ++x, --y;
}

void dfs(int x) {
  if (x > n) { puts("Yes"); for (int i = 1; i <= n; ++i) putchar(c[i][d[i]]), putchar('\n'); exit(0); }
  if (a[c[x][0]] != a[c[x][1]]) { d[x] = a[c[x][1]] < a[c[x][0]]; doit(a[c[x][0]], a[c[x][1]], d[x]); dfs(x + 1); }
  else if (a[c[x][0]] != 0) {
    d[x] = 0, ++a[c[x][0]], --a[c[x][1]];
    dfs(x + 1);
    d[x] = 1, --a[c[x][0]], --a[c[x][0]], ++a[c[x][1]], ++a[c[x][1]];
    dfs(x + 1);
    ++a[c[x][0]], --a[c[x][1]];
  }
}

int main() {
  scanf("%d%d%d%d", &n, &a['A'], &a['B'], &a['C']);
  for (int i = 1; i <= n; ++i) scanf("%s", c[i]);
  dfs(1);
  puts("No");
  return 0;
}