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:

# T = int(input().strip())
# mod = 1000000007
# for t in range(T):
n = int(input().strip())
a = [int(x) for x in input().strip().split(" ")]
d = {}
cng = 0
for i in range(n):
	if a[i] in d:
		d[a[i]] += 1
		if d[a[i]]>2:
			cng = i
	else:
		d[a[i]] = 1
cnt1 = 0
cnt2 = 0
for i in d:
	if d[i]==1:
		cnt1+=1
	elif d[i]>2:
		cnt2+=1
if cnt1%2==0:
	dd = {}
	for i in d:
		if d[i]==1:
			if cnt1%2==0:
				dd[i]="A"
			else:
				dd[i]="B"
			cnt1-=1
		else:
			dd[i]="A"
	print("YES")
	for i in range(n):
		print(dd[a[i]],end="")
elif cnt2>0:
	dd = {}
	d[a[cng]] -= 1
	a[cng] = 101
	d[101] = 1
	cnt1+=1
	#print(a,d)
	for i in d:
		if d[i]==1:
			if cnt1%2==0:
				dd[i]="A"
			else:
				dd[i]="B"
			cnt1-=1
		else:
			dd[i]="A"
	print("YES")
	for i in range(n):
		print(dd[a[i]],end="")
else:
	print("NO")