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())
b=list(map(int,input().split()))
d=dict()
for j in range(n):
    if b[j] in d.keys():
        d[b[j]]+=1
    else:
        d[b[j]]=1
p=0
q=-1
for j in range(n):
    if d[b[j]]==1:
        p+=1
    elif d[b[j]]>2:
        q=j
r=0
c=["A"]*(n)
if p%2==0:
    for j in range(n):
        if d[b[j]]==1:
            if r%2==0:
                c[j]="A"
            else:
                c[j]="B"
            r+=1
        else:
            c[j]="A"
    print("YES")
    print("".join(c))
elif p%2!=0:
    if q==-1:
        print("NO")
    else:
        for j in range(n):
            if d[b[j]] == 1:
                if r % 2 == 0:
                    c[j] = "A"
                else:
                    c[j] = "B"
                r += 1
            else:
                c[j] = "A"
        c[q]="B"
        print("YES")
        print("".join(c))