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=[int(i) for i in input().split()]
from collections import Counter 
c=Counter(l)
k=sum(c[i]==1 for i in c) 
if k==0:
    print('YES')
    print('A'*n)
    exit()
elif k and  k%2==0:
    print('YES')
    cn=0 
    f=0 
    k=k//2 
    for i in range(n): 
        if c[l[i]]==1 and f==0: 
            print('A',end='')
            cn+=1 
        elif c[l[i]]==1 and f==1:
            print('B',end='')
        else:
            print('A',end='')
        if cn==k:
            f= 1 
else:
    if sum(c[i]>1 for i in c)==0:
        print('NO')
        exit()
    else:
        #m=max(c.values())
        li=list(c.values())
        m=max(li)
        if m==2 :
            print('NO')
            exit()
        print('YES')
        k=k//2+k%2 
        f=0 
        cn=0 
        karma=0 
        for i in range(n):
            if c[l[i]]==1:
                if f==0:
                    print('A',end='')
                    cn+=1 
                    if cn==k:
                        f=1 
                else: 
                    print('B',end='')
            else:
                if c[l[i]]==m:
                    if karma==0:
                        print('B',end='')
                        karma=1 
                    else:
                        print('A',end='')
                else:
                    print('A',end='')