Problem: Vasya has a multiset s consisting of n integer numbers. Vasya calls some number x nice if it appears in the multiset exactly once. For example, multiset \{1, 1, 2, 3, 3, 3, 4\} contains nice numbers 2 and 4.

Vasya wants to split multiset s into two multisets a and b (one of which may be empty) in such a way that the quantity of nice numbers in multiset a would be the same as the quantity of nice numbers in multiset b (the quantity of numbers to appear exactly once in multiset a and the quantity of numbers to appear exactly once in multiset b).

Input

The first line contains a single integer n~(2 ≤ n ≤ 100).

The second line contains n integers s_1, s_2, ... s_n~(1 ≤ s_i ≤ 100) — the multiset s.

Output

If there exists no split of s to satisfy the given requirements, then print "NO" in the first line.

Otherwise print "YES" in the first line.

The second line should contain a string, consisting of n characters. i-th character should be equal to 'A' if the i-th element of multiset s goes to multiset a and 'B' if if the i-th element of multiset s goes to multiset b. Elements are numbered from 1 to n in the order they are given in the input.

If there exist multiple solutions, then print any of them.

Examples

Input

4
3 5 7 1


Output

YES
BABA


Input

3
3 5 1


Output

NO

Solution (in PYTHON3):

Solution:
n=int(input())
l=list(map(int,input().strip().split()))
l1=[0 for i in range(101)]
for i in l:
	l1[i]=l1[i]+1
ans=""
l2=[]
v=0
for i in range(1,101):
	if l1[i]==1:
		l2.append(i)
	if l1[i]>=3:
		v=i
if (v!=0):
	if (len(l2)%2==1):
		l2.insert(0,v)
if (len(l2)%2==1):
	print ("NO")
	exit(0)
d1={}
for i in range(1,101):
	d1[i]="A"
d="A"
for i in l:
	if i in l2:
		ans=ans+d
		if (l1[i]>=3):
			if (d=="A"):
				d1[i]="B"
			else:
				d1[i]="A"
		l2.remove(i)
		if (d=="A"):
			d="B"
		else:
			d="A"
	else:
		ans=ans+d1[i]
print ("YES")
print (ans)