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())
s1=0
s2=0
s=['A']*101
dic={}
lis=list(map(int,input().split()))
length=len(lis)
count=0
flag=0
backup=-1
for i in lis:
    dic[i]=dic.get(i,0)+1 
for i in dic:
    if dic[i]==1:
        count+=1
    if dic[i]>2:
        flag=1 
        backup=i
if count%2==1:
    if flag==0:
        print("NO")
        exit()
lis2=[]
if count%2==0:
    backup=-1
for i in dic:
    if dic[i]==1:
        lis2.append(i)
if backup!=-1:
    lis2.append(backup)
 
for i in lis2:
    if s1==0 or s1==s2:
        s[i]='A'
        s1+=1 
        continue
    if s2+1==s1:
        s[i]='B'
        s2+=1 
        continue
print("YES")
flag2=0

for i in lis:
    if i==backup and flag2==0:
        print(s[i],end="")
        flag2=1
        if s[i]=='A':
           
            s[i]='B'
        else:
            s[i]='A'
        continue
    print(s[i],end="")