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:
from collections import defaultdict
n=int(input())
a=list(map(int,input().split()))
d={};b=defaultdict(list);c=0;ms=['A','B'];w=['']*n;k=l=A=B=0;x=-1
for i in range(n):
    if a[i] in d:
        d[a[i]]+=1
    else:
        d[a[i]]=1
    b[a[i]].append(i)
for i in d.keys():
    if d[i]==1:
        c+=1
    elif d[i]>2:
        x=i
#print (d)
if c%2==0:
    print ('YES')
    for i in d.keys():
        if d[i]>1:
            for j in b[i]:
                w[j]=ms[k%2]
            k+=1
            #print (w)
        else:
            w[b[i][0]]=ms[l%2]
            l+=1
    print (''.join(w))
elif x>=0:
    print ('YES')
    for i in d.keys():
        if d[i]>1:
            if i==x:
                pass
            else:
                for j in b[i]:
                    w[j]=ms[k%2]
            k+=1
        else:
            w[b[i][0]]=ms[l%2]
            if ms[l%2]=='A':
                A+=1
            else:
                B+=1
            l+=1
    #print (b[x])
    for i in range(len(b[x])-1):
        if A>B:
            w[b[x][i]]=ms[0]
        else:
            w[b[x][i]]=ms[1]
    if A>B:
        w[b[x][-1]]=ms[1]
    else:
        w[b[x][-1]]=ms[0]
    print (''.join(w))
else:
    print ('NO')