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())
arr = list(map(int, input().split()))
count = [0]*101
unique = 0
multiple = 0
answer = ''
for i in range(n):
    count[arr[i]] += 1
for i in range(1, len(count)):
    if count[i] == 1:
        unique += 1
    elif count[i] > 2:
        multiple += 1
if unique % 2 == 0:
    multi = 0
    for j in range(n):
        if count[arr[j]] == 1:
            if multi == 0:
                answer += 'A'
                multi = 1
            elif multi == 1:
                answer += 'B'
                multi = 0
        elif count[arr[j]] > 1:
            answer += 'A'
else:
    if multiple == 0:
        answer = 'NO'
    else:
        put = False
        multi = 0
        for j in range(n):
            if count[arr[j]] == 1:
                if multi == 0:
                    answer += 'A'
                    multi = 1
                elif multi == 1:
                    answer += 'B'
                    multi = 0
            elif count[arr[j]] == 2:
                answer += 'A'
            elif count[arr[j]] > 2:
                if not put:
                    answer += 'B'
                    put = True
                else:
                    answer += 'A'
if answer == 'NO':
    print(answer)
else:
    print('YES')
    print(answer)