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 = [int (i) for i in input().split()]
k = [0 for i in range (101)]
flag = False;
for i in s:
    k[i]+=1
    if k[i]>2:
        flag = True;
        
b = k.count(1)//2
a = k.count(1)-b
if a==b:
    print ('YES')
    for i in s:
        if k[i] == 1 and a!=0:
            print('A',end ='');
            a-=1
            k[i]-=1
        elif k[i] == 1:
            print('B',end ='');
            k[i]-=1
        else:
            print('A',end ='');
elif (flag):
        print ('YES')
        for i in s:
            if k[i] == 1 and a!=0:
                print('A',end ='');
                a-=1;
                k[i]-=1
            elif k[i] == 1:
                print('B',end ='');
                k[i]-=1
                
            elif k[i] >2 and flag:
                print ('B', end='');
                flag = False;
            else:
                print('A',end = '');
else:
    print ('NO')