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:
input()
i = input().split()
for a in range(len(i)): i[a] = int(i[a])

counts = {}
nice = []
not_nice = []
for a in i:
    if a in not_nice:
        counts[a] += 1
    elif a in nice:
        counts[a] += 1
        del nice[nice.index(a)]
        not_nice.append(a)
    else:
        counts[a] = 1
        nice.append(a)
        
if len(nice) % 2 == 0:
    n = 0
    output = ""
    for a in i:
        if n < len(nice) / 2 and a in nice:
            output += "A"
        else:
            output += "B"
        if a in nice:
            n += 1
    print("YES")
    print(output)
else:
    move = None
    for a in counts:
        if counts[a] > 2:
            move = a
            break
    if move is None:
        print("NO")
    else:
        output = ""
        n = 0
        moved = 0
        for a in i:
            if a == move:
                if moved == 0:
                    output += "A"
                    moved += 1
                else:
                    output += "B"
            elif n < len(nice) // 2:
                output += "A"
            else:
                output += "B"
            if a in nice:
                n += 1
        print("YES")
        print(output)