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 = list(map(int, input().split()))
b = dict()
for x in a:
    b[x] = b.get(x, 0) + 1
A = dict()
B = dict()
cnta = 0
cntb = 0
for k, v in b.items():
    if v == 1:
        if cnta > cntb:
            cntb += 1
            B[k] = 1
        else:
            cnta += 1
            A[k] = 1

for k, v in b.items():
    if v == 2:
        A[k] = 2
    elif v > 1:
        if cnta > cntb:
            A[k] = v-1
            B[k] = 1
            cntb+=1
        else:
            A[k] = v
if cnta==cntb:
    print('YES')
    for i in a:
        if A.get(i, 0) > 0:
            A[i] = A.get(i, 0) - 1
            print('A', end='')
        else:
            B[i] = B.get(i, 0) - 1
            print('B', end='')
else:
    print('NO')