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(i) for i in input().split()]
cnt = 0
cnt1 = 0
q = list()
for i in a:
    if i not in q:
        q.append(i)
        if a.count(i) == 1:
            cnt += 1
        elif a.count(i) > 2:
            cnt1 += 1
if cnt % 2 == 1 and cnt1 == 0:
    print('NO')
else:
    nums = list()
    g = list()
    ans = ''
    f = True
    q = False
    for i in a:
        if a.count(i) == 1:
            if f:
                ans += 'A'
                f = False
            else:
                ans += 'B'
                f = True
        elif a.count(i) == 2:
            ans += 'A'
        else:
            if cnt % 2 == 1:
                if not q:
                    ans += 'B'
                    q = True
                else:
                    ans += 'A'
            else:
                ans += 'A'
    print('YES')
    print(ans)