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 <bits/stdc++.h>
using namespace std;

const int nm = 1e5;
int n, m[3], q[nm][2], x, y;
string s;
char ans[100000];

int main() {
	cin >> n;
	for (int i = 0; i < 3; i++)
		cin >> m[i];
	for (int i = 0; i < n; i++) {
		cin >> s;
		q[i][0] = s[0] - 'A';
		q[i][1] = s[1] - 'A';
	}
	for (int i = 0; i < n; i++) {
		x = q[i][0], y = q[i][1];
		if (!m[x] && !m[y]) {
			cout << "No" << endl;
			return 0;
		} else if (m[x] == 1 && m[y] == 1 && i + 1 < n) {
			if (q[i + 1][0] == y || q[i + 1][1] == y)
				swap(x, y);
		} else if (m[y] < m[x])
			swap(x, y);
		ans[i] = 'A' + x;
		m[x]++;m[y]--;

	}
	cout << "Yes" << endl;
	for (int i = 0; i < n; i++)
		cout << ans[i] << endl;
}