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())
a=list(map(int,input().split()))
counts=[0]*101
for guy in a:
    counts[guy]+=1
useless=counts.count(0)+counts.count(2)
forced=counts.count(1)
useful=101-useless-forced
if useful==0 and forced%2==1:
    print("NO")
else:
    if forced%2==0:
        each=forced//2
        out=""
        seen=0
        for guy in a:
            if counts[guy]==1 and seen<each:
                out+="A"
                seen+=1
            else:
                out+="B"
    else:
        As=forced//2
        out=""
        seen=0
        good=0
        for guy in a:
            if counts[guy]==1 and seen<As:
                out+="A"
                seen+=1
            elif counts[guy]>2 and good==0:
                out+="A"
                good=1
            else:
                out+="B"
    print("YES")
    print(out)