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 sys
inf = float("inf")
#mod = 10**9+7

#from collections import deque, Counter, OrderedDict,defaultdict
#from heapq import nsmallest, nlargest, heapify,heappop ,heappush, heapreplace
#from math import ceil,floor,log,sqrt,factorial,pow,pi
#from bisect import bisect_left,bisect_right
#from decimal import *,threading

abc='abcdefghijklmnopqrstuvwxyz'
abd={'a': 0, 'b': 1, 'c': 2, 'd': 3, 'e': 4, 'f': 5, 'g': 6, 'h': 7, 'i': 8, 'j': 9, 'k': 10, 'l': 11, 'm': 12, 'n': 13, 'o': 14, 'p': 15, 'q': 16, 'r': 17, 's': 18, 't': 19, 'u': 20, 'v': 21, 'w': 22, 'x': 23, 'y': 24, 'z': 25}
mod,MOD=1000000007,998244353
vow=['a','e','i','o','u']
dx,dy=[-1,1,0,0],[0,0,1,-1]



def get_array(): return list(map(int, sys.stdin.readline().strip().split()))
def get_ints(): return map(int, sys.stdin.readline().strip().split())
def input(): return sys.stdin.readline().strip()
n=int(input())
Arr=get_array()
mydict=dict()
for i in Arr:
    mydict[i]=mydict.get(i,0)+1
count_1=0;count_2=0;count_3=0;Arr1=[];Arr2=[];Arr3=[]
for i in mydict:
    if mydict[i]==1:
        count_1+=1;Arr1.append(i)
    elif mydict[i]==2:
        count_2+=1;Arr2.append(i)
    elif mydict[i]>=3:
        count_3+=1;Arr3.append(i)
if count_1&1 and count_3==0:
    print("NO")
    exit(0)
if not count_1&1:
    result=[]
    Arr_new=Arr1[:len(Arr1)//2]
    Arr_new2=Arr1[len(Arr1)//2:]
    for i in Arr:
        if i in Arr_new:
            result.append('A')
        else:
            result.append('B')
elif count_1&1 and count_3>0:
    result=[]
    Arr_new=Arr1[:len(Arr1)//2]
    Arr_new2=Arr1[len(Arr1)//2:]
    Arr_new3=Arr3[:1]
    for i in Arr:
        if i in Arr_new:
            result.append('A')
        elif i in Arr_new3:
            result.append('A')
            Arr_new3.remove(i)
        else:
            result.append('B')
print("YES")
print(''.join(result))