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 = input()
a = list(map(int,input().split()))
d = {i:0 for i in range(1,101)}
for i in a:d[i]+=1
g = []
g2 = []
mg = []
for i in range(1,101):
    if d[i] ==1:
        g.append(i)
    elif d[i] ==2:
        g2.append(i)
    elif d[i]>2:
        mg.append(i)
if len(g)%2:
    if len(mg):
        print('YES')
        flag1 = True
        flag2 = False
        for i in a:
            if i in g:

                if flag1:
                    print('A', end='')
                    flag1 = False
                else:
                    print('B', end='')
                    flag1 = True

            elif i in mg:
                if flag2:
                    print('A', end='')
                else:
                    print('B',end='')
                    flag2 = True

            else:
                print('A',end = '')

    else:
        print('NO')

else:
    print('YES')
    flag = False
    for i in a:
        if i in g:
            if flag:
                print('A',end='')
                flag = False
            else:
                print('B',end='')
                flag = True
        else:
            print('A',end='')