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()))

LIST=[0 for i in range(101)]

for s in S:
    LIST[s]+=1

for i in range(len(LIST)):
    if LIST[i]==2:
        LIST[i]=0
    elif LIST[i]>2:
        LIST[i]=3

if sum(LIST)%2==1 and not (3 in LIST):
    print("NO")




else:
    if sum(LIST)%2==1:
        LIST[LIST.index(3)]=0

    for i in range(len(LIST)):
        if LIST[i]>2:
            LIST[i]=1
        



    
    APP=sum(LIST)//2

    ANS=""

    for s in S:
        if APP>0 and LIST[s]==1:
            ANS+="A"
            APP-=1
            LIST[s]="B"
        elif LIST[s]==1:
            ANS+="B"
            LIST[s]="A"
        else:
            if LIST[s]=="A":
                ANS+="A"
            else:
                ANS+="B"
            
    print("YES")
    print(ANS)