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:
a=int(input())
b=list(map(int,input().split()))
c=[0]*101
for i in b:
    c[i]+=1
k=0
kk=0
for j in range(1,101):
   if c[j]==1:
       k+=1
   if c[j]>2:
       kk+=1
if k%2==0:
    print('YES')
    l=0
    for j in b:
        if c[j]==1:
            if l<k//2:
                print('A',end='')
                l+=1
            else:
                print('B',end='')
        else:
            print('B',end='')
else:
    if kk==0:
        print('NO')
    else:
        print('YES')
        l=0
        p=0
        for j in b:
            if c[j]==1:
                if l<k//2:
                    print('A',end='')
                    l+=1
                else:
                    print('B',end='')
            elif c[j]>2:
                if p==0:
                    print('A',end='')
                    p=1
                else:
                    print('B',end='')
            else:
                print('B',end='')