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:
# import sys
# sys.stdin = open("F:\\Scripts\\input","r")
# sys.stdout = open("F:\\Scripts\\output","w")


MOD = 10**9 + 7
I = lambda:list(map(int,input().split()))

n, = I()
l = I()
ans = []
char = 'A'
d = {'A' : 0,'B' : 0}
cs = [0]*105
for i in l:
	cs[i] += 1
for i in l:
	if cs[i] == 1:
		d[char] += 1
		ans.append(char)
		char = 'B' if char == 'A' else 'A'
	else:
		ans.append('A')
if d['A'] == d['B']:
	print('YES')
	print(*ans,sep = '')
	exit()
fuc = 0
for i in range(1,101):
	if cs[i] > 2:
		fuc = i
		break
if not fuc:
	print('NO')
	exit()

for i in range(n):
	if l[i] == fuc:
		ans[i] = 'B'
		break
print('YES')
print(*ans,sep = '')