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 sys import stdin
from collections import Counter
input = stdin.readline

n = int(input())
a = [int(x) for x in input().split()]
c = Counter(a)

single = []
multiple_value = -1
multiple_count = -1
for value, count in c.items():
    if count == 1:
        single.append(value)
    elif count >= 3 and multiple_value == -1:
        multiple_value = value
        multiple_count = count

if len(single) % 2 == 0:
    group_a = set(single[:len(single) // 2])
    ans = []
    for i in range(n):
        if a[i] in group_a:
            ans.append("A")
        else:
            ans.append("B")
    print("YES")
    print(*ans, sep="")

elif multiple_value != -1:
    group_a = set(single[:len(single) // 2])
    ans = []
    for i in range(n):
        if a[i] == multiple_value:
            if multiple_count == 1:
                ans.append("A")
            else:
                ans.append("B")
            multiple_count -= 1
        elif a[i] in group_a:
            ans.append("A")
        else:
            ans.append("B")
    print("YES")
    print(*ans, sep="")

else:
    print("NO")