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:
from collections import Counter
n=int(input())
a=[int(x) for x in input().split()]
c=0
l=[]
d={}
d=Counter(a)

for i in d:
    if d[i]==1:
        c=c+1
        l.append(a.index(i)) 
        
if c%2!=0:
    f=0
    for i in d:
        if d[i]>2:
            y=a.index(i)
            f=1
            break
    if f==0:
        print("NO")
    else:
        print("YES")
        r=['0']*n
        x=int((len(l)/2))
        for i in range(x):
            r[l[i]]='A'
        r[y]='A'
        for i in range(len(r)):
            if r[i]=='0':
                r[i]='B'
        print(''.join(r))
        
    
elif c==0:
    print("YES")
    s=""
    while len(s)<n:
        s=s+"A"
    print(s)    
else:
    print("YES")
    r=['0']*n
    x=int(len(l)/2)
    for i in range(x):
        r[l[i]]='A'
    for i in range(len(r)):
        if r[i]=='0':
            r[i]='B'
    print(''.join(r))