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:
# coding: utf-8
import sys
from collections import Counter
sys.setrecursionlimit(int(1e7))

def main():
    while 1:
        try: n = int(input())
        except EOFError: break
        arr = [int(x) for x in input().split()]
        s = Counter(arr)
        a = len([x for x,y in s.items() if y==1])
        c = len([x for x,y in s.items() if y>2])
        if a%2==1 and c==0:
            print('NO')
            continue
        aux = 0
        ans = []
        for x in arr:
            if s[x]==1:
                y = 'AB'[aux] ; aux = 1-aux
            elif s[x]==2:
                y = 'A'
            elif a%2==1 and c>0:
                y = 'B'; c = 0
            else:
                y = 'A'
            ans.append(y)
        print('YES')
        print(''.join(ans))

main()