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:
import sys
n=int(input())
l=list(map(int,raw_input().split()))
dup=list(set([x for x in l if l.count(x) > 1]))
uni=list(set(dup) ^ set(l))
if uni==[]:
    print"YES"
    print"A"*n
    sys.exit()
d={}
c3=0
for i in xrange(len(l)):
    key=l[i]
    if key in d:
        d[key]+=1
        if d[key]>2:
            c3+=1
    else:
        d[key]=1
s=""
luni=len(uni)
if luni%2==0:
    c=1
    for i in xrange(len(l)):
        key=l[i]
        if d[key]==1:
            if c<=(luni/2):
                s+="A"
            else:
                s+="B"
            c+=1
        else:
            s+="A"
    print "YES"
    print s
else:
    c=1
    if c3==0:
        print"NO"
        sys.exit()
    else:
        co=0
        for i in xrange(len(l)):
            key=l[i]
            if d[key]==1:
                if c<=((luni//2)+1):
                    s+="A"
                else:
                    s+="B"
                c+=1
            elif d[key]>2:
                if co==0:
                    s+="B"
                else:
                    s+="A"
                co+=1
            else:
                s+="A"

    print"YES"
    print s