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()))
ct={}
a=[0]*(101)
for i in range(n):
    ct[s[i]]=ct.get(s[i],0)+1
for i in ct:
    a[ct[i]]+=1
if a[1]%2==0:
    c='A'
    print('YES')
    ans=''
    for i in range(n):
        if ct[s[i]]==1:
            ans=ans+c
            c='A' if c=='B' else 'B'
        else:
            ans=ans+'A'
    print(ans)
else:
    f=0
    for i in range(3,101):
        if a[i]>0:
            f=i
            break
    if f:
        p=0
        c='A'
        ans=''
        print('YES')
        for i in range(n):
            if ct[s[i]]==1:
                ans=ans+c
                c='A' if c=='B' else 'B'
            elif ct[s[i]]==f and p==0:
                ans=ans+'B'
                p=1
            else:
                ans=ans+'A'
        print(ans)
    else:
        print('NO')