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:
import math
import sys
from bisect import bisect_right, bisect_left, insort_right
from collections import Counter, defaultdict
from heapq import heappop, heappush
from itertools import accumulate
from sys import stdout

R = lambda: map(int, input().split())
n = int(input())
acc = [0] * 105
arr = list(R())
for i in arr:
    acc[i] += 1
a, b, ac, bc = [0] * 105, [0] * 105, 0, 0
for i, x in enumerate(acc):
    if x == 1:
        if ac > bc:
            b[i] += 1
            bc += 1
        else:
            a[i] += 1
            ac += 1
for i, x in enumerate(acc):
    if x > 1:
        if ac > bc:
            b[i] += 1
            a[i] += x - 1
            bc += 1
            ac += 1 if x == 2 else 0
        elif ac < bc:
            a[i] += 1
            b[i] += x - 1
            ac += 1
            bc += 1 if x == 2 else 0
        else:
            a[i] += x
if ac != bc:
    print('NO')
else:
    print('YES')
    for x in arr:
        if a[x]:
            print('A', end='')
            a[x] -= 1
        else:
            print('B', end='')
            b[x] -= 1