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())
a = [int(x) for x in input().split()]
d = {}
for x in a:
	if x in d:
		d[x] += 1
	else:
		d[x] = 1
kol = 0
kol1 = 0
for key in d:
	if d[key] == 1:
		kol += 1
	if d[key] > 2:
		kol1 += 1
if kol % 2 == 1 and kol1 == 0:
	print("NO")
	exit(0)
print("YES")
if kol % 2 == 0:
	ind = 0
	ind1 = 0
	for i in range(n):
		if d[a[i]] == 1:
			if ind == ind1:
				print('A',end = '')
				ind += 1
			else:
				print('B',end = '')
				ind1 += 1
		else:
			print('A', end = '')
else:
	ind = 0
	ind1 = 0
	f = True
	res = -1
	pic = ""
	for i in range(n):
		if d[a[i]] == 1:
			if ind == ind1:
				print('A', end = '')
				ind += 1
			else:
				print('B', end = '')
				ind1 += 1
		elif d[a[i]] > 2 and f:
			f = False
			res = a[i]
			if ind == ind1:
				print('A', end = '')
				ind += 1
				pic = 'B'
			else:
				print('B', end = '')
				ind1 += 1
				pic = 'A'
		else:
			if a[i] == res:
				print(pic, end = '')
			else:
				print('A', end = '')