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:
# Author: S Mahesh Raju
# Username: maheshraju2020
# Date: 27/04/2020

from sys import stdin,stdout
from math import gcd, ceil, sqrt
ii1 = lambda: int(stdin.readline().strip())
is1 = lambda: stdin.readline().strip()
iia = lambda: list(map(int, stdin.readline().strip().split()))
isa = lambda: stdin.readline().strip().two()
mod = 1000000007

n = ii1()
arr = iia()
d = {}
for i in arr:
    d.setdefault(i, [0])[0] += 1

one, other = set(), set()
for i in d:
    if d[i][0] == 1:
        one.add(i)
    elif d[i][0] > 2:
        other.add(i)

if len(one) % 2 and not len(other):
    print("NO")
else:
    if len(one) % 2:
        num = other.pop()
    flip = flag = False
    res = ""
    for i in arr:
        if i in one:
            if flip:
                flip = False
                res += 'B'
            else:
                flip = True
                res += 'A'
        elif len(one) % 2 and i == num:
            if not flag:
                res += 'B'
                flag = True
            else:
                res += 'A'
        else:
            res += 'A'
    print("YES")
    print(res)