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:
s=input()
s=input()
s1=s.split()
l=[int(i) for i in s1]

d={}

for i in l:

    if i not in d:

        d[i]=1
    else:
        d[i]=d[i]+1

cnt=0
for i in d:

    if d[i]==1:
        cnt=cnt+1

if cnt%2==1:
    flag=0
    for i in d:

        if d[i]>=3:
            flag=1
            break
            
    if flag==0:
        
        print('NO')

    else:

        s=''
        state=0
        flag=0
        for i in l:

            if d[i]>=3 and flag==0:

                s=s+'B'
                flag=1
            elif d[i]>1:

                s=s+'A'
                
            else:

                if state==0:
                    s=s+'A'
                else:
                    s=s+'B'
                state=1-state
        print('YES')
        print(s)

        

else:

    print('YES')
    s=''
    state=0
    for i in l:

        if d[i]!=1:

            s=s+'A'
        else:

            if state==1:
                s=s+'A'
            else:
                s=s+'B'
            state=1-state
    print(s)