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())
a = list(map(int, input().split()))
rec = [0] * 1000
one = 0
for i in range(n):
    rec[a[i]] += 1

for i in range(1000):
    if rec[i] == 1:
        one += 1

if one % 2 != 0 and max(rec) <= 2:
    print("NO")
elif one % 2 != 0:
    print("YES")
    t = ""
    k = 0
    flag = True
    for i in range(n):
        if rec[a[i]] == 1 and k < one // 2:
            t += "A"
            k += 1
        elif rec[a[i]] == 1:
            t += "B"
        elif rec[a[i]] >= 3 and flag:
            t += "A"
            flag = False
        else:
            t += "B"

    print(t)
else:
    print("YES")
    t = ""
    k = 0
    for i in range(n):
        if rec[a[i]] == 1 and k < one // 2:
            t += "A"
            k += 1
        elif rec[a[i]] == 1:
            t += "B"
        else:
            t += "A"

    print(t)