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:
from collections import Counter
n = input()
s = raw_input().split()
a = Counter(s)
a1 = []
a2 = []
a3 = []
for k,v in a.items():
    if v==1:
        a1.append(k)
    elif v==2:
        a2.append(k)
    else:
        a3.append(k)
a11 = set(a1[:len(a1)/2])
a12 = set(a1[len(a1)/2:])
r = ''
if len(a1)%2==0:
    for i in s:
        if i in a11:
            r+='A'
        else:
            r+='B'
else:
    if len(a3)==0:
        print 'NO'
        exit(0)
    else:
        a31 = set(a3[:1])
        for i in s:
            if i in a11:
                r+='A'
            elif i in a31:
                r+='A'
                a31.remove(i)
            else:
                r+='B'
print 'YES'
print r