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
from sys import stdin,stdout
n=int(stdin.readline())
l=map(int,stdin.readline().split(" "))
d=Counter(l)
key=d.keys()
val=d.values()
cnt=val.count(1)

if cnt%2:
    c=0
    f=0
    for i in key:
        if d[i]>2:
            f=1
            break
    if not f:
        print "NO"
        exit()
    else:
        print "YES"
        f=0
        for i in range(n):
            if d[l[i]]>2 and f==0:
                f=1
                l[i]='B'
            else:
                if d[l[i]]>=2:
                    l[i]='A'
                else:
                    if c%2==0:
                        l[i]='A'
                        c+=1
                    else:
                        l[i]='B'
                        c+=1
    print ''.join(l)
else:
    c=0
    print "YES"
    for i in range(n):
        if d[l[i]]==1:
            if c%2:
                l[i]='A'
            else:
                l[i]='B'
            c+=1
        else:
            l[i]='A'
    print ''.join(l)