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=int(input())
l=list(map(int,input().split()))
from collections import Counter,defaultdict
c=Counter(l)
l1=[]
for i in c:
    if c[i]==1:
        l1.append(i)
a=0
d=defaultdict(int)
for i in l1:
    if a==0:
        d[i]="A"
        a=1
    else:
        d[i]="B"
        a=0      
if len(l1)%2==0:
    ans=''
    for i in l:
        if c[i]>1:
            d[i]="A"
    for i in l:
        ans+=d[i]
    print("YES")
    print(ans)
else:
    s=''
    ans=''
    for i in l:
        if c[i]>2:
            s=i
            break
    if s!='':
        x=0
        for i in l:
            if c[i]>1:
                if i==s and x==0:
                    ans+="B"
                    x+=1
                else:
                    ans+="A"
            else:
                ans+=d[i]
        print("YES")
        print(ans)
    else:
        print("NO")