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 as mt 
import sys,string
input=sys.stdin.readline
import random
from collections import deque,defaultdict
L=lambda : list(map(int,input().split()))
Ls=lambda : list(input().split())
M=lambda : map(int,input().split())
I=lambda :int(input())
n=I()
x=L()
d=defaultdict(int)
v=defaultdict(int)
ans=['0']*n
c=0
y=[]
w=0
l=[]
for i in x:
    l.append((i,w))
    w+=1
    d[i]+=1
    if(d[i]>=3 and v[i]==0):
        v[i]=1
        y.append(i)
l.sort(key=lambda x:x[0])
p=0
a=[]
b=[]
for i in l:
    if(v[i[0]]==0 and p==0):
        ans[i[1]]="A"
        p=1
    elif(v[i[0]]==0 and p==1):
        ans[i[1]]="B"
        p=0
if(p==0):
    for i in range(n):
        if(ans[i]=='0'):
            ans[i]="A"
    print("YES")
    for i in ans:
        print(i,end="")
        
else:
    q=1
    for i in range(n):
        if(ans[i]=='0' and y[0]==x[i] and q==1):
            ans[i]="B"
            q=0
        elif(ans[i]=='0'):
            ans[i]="A"
    if(q):
        print("NO")
    else:
        print("YES")
        for i in ans:
            print(i,end="")
v.clear()
d.clear()