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:
import collections
def main():
    a = int(input())
    b = list(map(int,input().split()))
    Temp = collections.Counter(b)
    num1, num2, num3 = 0, 0, 0
    for c in Temp.values():
        if c == 1: num1 += 1
        elif c == 2: num2 += 1
        else: num3 += 1
    if num1 % 2 == 1 and num3 ==0:
        print('NO')
        exit()
    print('YES')
    A, B, C = 0, 0, 0
    if num1 % 2 == 0:
        C += 1
    Str = []
    for d in b:
        if Temp[d] ==1:
            if A == B:
                Str.append('A')
                A += 1
            else:
                Str.append('B')
                B += 1
        elif Temp[d] >=3 and C ==0:
            Str.append('B')
            C += 1
        else:
            Str.append('A')
    print(''.join(Str))
if __name__ =='__main__':
    main()