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 PYTHON):

Solution:
n=int(raw_input())
arr=map(int,raw_input().split())
mp={}
for i in arr:
	mp[i]=0
for i in arr:
	mp[i]=(mp[i]+1)
nice=[]
no=[]
for i in mp:
	if(mp[i]==1):
		nice.append(i)
	else:
		no.append(i)
if((len(nice)%2)==1):
	m=nice[:(len(nice)-1)/2]
	flag=0
	for i in no:
		if(mp[i]>2):
			flag=i
			break
	if(flag!=0):
		s=""
		op=arr.index(flag)
		for i in range(len(arr)):
			if(i==op):
				s=s+'A'
			elif arr[i] in m:
				s=s+"A"
			else:
				s=s+"B"
		print "YES"
		print s						
	else:
		print "NO"
	exit()
else:	
	m=nice[:len(nice)/2]
	s=""
	for i in arr:
		if i in m:
			s=s+"A"
		else:
			s=s+"B"
	print "YES"
	print s