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())
lis = [int(x) for x in input().split()]
result = [-1 for _ in range(n)]
count = {}
for j,i in enumerate(lis):
    #print(j,i)
    if i not in count:
        count[i] = []
    count[i].append(j)
turn = 1
isEven = True
for key in count.keys():
    li = (count[key])
    le = len(li)
    if le == 1:
        result[li[0]] = turn
        turn = 1 if turn==0 else 0
        isEven = False if isEven else True
    elif le == 2:
        for i in li:
            result[i] = 1
for key in count.keys():
    li = (count[key])
    le = len(li)
    if le>2:
        if isEven:
            for i in li:
                result[i]=1
        else:
            result[li[0]] = turn
            turn = 1 if turn==0 else 0
            isEven = True
            for i in li[1:]:
                result[i] = turn
if isEven:
    print("YES")
    for i in result:
        if i==0:
            print("A",end="")
        else:
            print("B",end="")
else:
    print("NO")           
                
            
            
            
            
#print(count)