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:
from collections import Counter
n=int(input())
s=list(map(int,input().split()))
sm=Counter(s)
su=set()

for i in sm.keys():
	if sm[i]==1:
		su.add(i)
j=-1
i=0
while i<n and j==-1:
	if sm[s[i]]>=3:j=i
	i+=1

if len(su)%2==1:
	if j==-1:print("NO")
	else:
		print('YES')
		cnt=0
		ch=""
		i=0
		while i<n:
			if (s[i] in su and cnt<len(su)//2) or i==j :
				ch+="A"
				if i!=j:cnt+=1
			else:
				ch+="B"
			i+=1
		print(ch)

else:
	print('YES')
	cnt=0
	ch=""
	i=0
	while i<n:
		if s[i] in su and cnt<len(su)//2:
			ch+="A"
			cnt+=1
		else:
			ch+="B"
		i+=1
	print(ch)