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())
s=list(map(int,input().split()))
num1=0
b=['A']*n
cnt={}
fst={}
for i in range(len(s)):
    if(s[i]) in cnt:
        cnt[s[i]]+=1
    else:
        cnt[s[i]]=1
        fst[s[i]]=i
for i in range(len(s)):
    if(cnt[s[i]]==1):
        if(num1%2==1):
            b[i]='B';
        num1+=1

if(num1%2==1):
    res=False
    for i in range(len(s)):
        if(cnt[s[i]]>2):
            b[i]='B'
            res=True
            break
else:
    res=True
if(res):
    print('YES')
    s1=''
    for i in b:
        s1+=i
    print(s1)
else:
    print('NO')