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:
a=int(input())
l=list(map(int,input().split()))
g=0
b=0
m=[0 for i in range(max(l)+1)]
for i in l:
    m[i]+=1
for i in m:
    if i==1:
        g+=1
    elif i>2:
        b+=1
if g%2!=0 and b==0:
    print("NO")
else:
    print("YES")
    if g%2==0:
        c=g/2
        for i in range(len(l)):
            if m[l[i]]==1 and c>0:
                c-=1
                print("A",end="")
            else:
                print("B",end="")
    else:
        c=g//2
        f=True
        for i in range(len(l)):
            if m[l[i]]==1 and c>0:
                c-=1
                print("A",end="")
            elif m[l[i]]>=3 and f:
                f=not f
                print("A",end="")
            else:
                print("B",end="")