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:
from collections import Counter
N = int(input())
List = [int(x) for x in input().split()]
Dict = Counter(List)
Counts = list(Dict.values())
n = len(Counts)
One = Counts.count(1)
if(One  % 2 == 0): # Completed
    # Go Normal
    flip = 0
    print("YES")
    Ans = ""
    for i in range(N):
        if(Dict[List[i]] == 1):
            Ans += chr(65 + flip)
            flip^=1
        else:
            Ans+="A"
    print(Ans)
else:
    notDecided = -1
    flip = 0
    Ans = ""
    for i in range(N):
        if(Dict[List[i]] == 1):
            Ans += chr(65 + flip)
            flip^=1
        elif(Dict[List[i]] != 2 and notDecided == -1):
            notDecided = Dict[List[i]] 
            Ans += "B"
        elif(Dict[List[i]] % 2 != 0 and Dict[List[i]] == notDecided):
            Ans += "A"
        else:
            Ans += "A"
    if(notDecided == -1):
        print("NO")
    else:
        print("YES")
        print(Ans)