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 PYTHON):

Solution:
raw_input()
s = map(int, raw_input().split())
MAX_SIZE = 101
count = [0] * MAX_SIZE
for num in s:
    count[num] += 1
nUnique = 0
a, b = [0] * MAX_SIZE, [0] * MAX_SIZE
turn = 0
for num in xrange(1, MAX_SIZE):
    if count[num] == 1:
        nUnique += 1
        if turn == 0:
            a[num] = 1
        else:
            b[num] = 1
        turn ^= 1
for num in xrange(1, MAX_SIZE):
    if nUnique & 1 == 1 and count[num] > 2:
        nUnique += 1
        b[num] = 1
        a[num] = count[num] - 1
    elif count[num] > 1:
        a[num] = count[num]
if nUnique & 1 == 1:
    print 'NO'
else:
    print 'YES'
    ret = ''
    for num in s:
        if a[num] > 0:
            ret += 'A'
            a[num] -= 1
        else:
            ret += 'B'
            b[num] -= 1
    print ret