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 PYTHON):

Solution:
import sys, math
from sys import stdin, stdout
rem = 10 ** 9 + 7
sys.setrecursionlimit(10 ** 6+5)
#from resource import *; setrlimit(RLIMIT_STACK, (RLIM_INFINITY, RLIM_INFINITY))
take = lambda: map(int, stdin.readline().split())
from heapq import heappush,heappop,heapify
from collections import deque
from bisect import *




n=input()
arr=take()
cnt=[0 for i in range(105)]
for i in arr:
    cnt[i]+=1
one=0
for i in cnt:
    if i==1:
        one+=1
ans=[0 for i in range(n)]
prev='B'
for i in range(n):
    a=arr[i]
    if cnt[a]>1:
        ans[i]='A'
    else:
        if prev=='B':
            ans[i]='A'
            prev='A'
        else:
            ans[i]='B'
            prev='B'
done=True
if one%2==1:
    done=False
    for i in range(n):
        if cnt[arr[i]]>2:
            ans[i]='B'
            done=True
            break
if done:
    print 'YES'
    print ''.join(ans)
else:
    print 'NO'