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:
n=int(input())
s=[int(el) for el in input().split()]

x=[] #уникальные числа
y=[] #кол-во повторений
z=[] #места чисел



for i in range(n):
    if s[i] in x:
        y[x.index(s[i])]+=1
        z[x.index(s[i])].append(i)
    else:
        x.append(s[i])
        y.append(1)
        z.append([])
        z[len(z)-1].append(i)



k=y.count(1)
l=n-k-y.count(2)*2
if l<=0 and k>=1 and k%2==1:
    print ('NO')
    raise SystemExit


s1=0
s2=0
out='A'*n
for i in range(n):
    if y[x.index(s[i])]==2:
        for j in z[x.index(s[i])]:
            out=out[:j]+'A'+out[j+1:]

    if y[x.index(s[i])]==1:
        if s1>s2:
            out=out[:i]+'B'+out[i+1:]
            s2+=1
        else:
            out=out[:i]+'A'+out[i+1:]
            s1+=1

    if y[x.index(s[i])]>=3:
        continue
    y[x.index(s[i])] = 0

if y.count(0)==len(y):
    print('YES')
    print(out)
    raise SystemExit

if s1==s2:
    for i in range(n):
        k=x.index(s[i])
        if y[k]!=0:
            for j in z[k]:
                out=out[:j]+'A'+out[j+1:]

else: #s1>s2
    pos=0
    for i in range(n):
        k=x.index(s[i])
        if y[k]!=0 and pos==0:
            for j in z[k]:
                out=out[:j]+'A'+out[j+1:]
            j=z[k][0]
            out=out[:j]+'B'+out[j+1:]
            pos=1
            y[k]=0
        elif y[k]!=0 and pos==1:
            for j in z[k]:
                out=out[:j]+'A'+out[j+1:]
            y[k]=0

print('YES')
print(out)