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:
from collections import Counter


def foo():
    input()
    l = []
    for a in input().split(' '):
        l.append(a)
    c = Counter(l)
    has3 = False
    ones = 0
    for key in c:
        if c[key] == 1:
            ones += 1
        elif c[key] > 2:
            has3 = True
            
    if ones % 2 == 1 and has3 == False:
        print("NO")
        return
    
    print("YES")
    put3 = ones % 2 == 1
    putted = False
    put = ''
    a = True
    output = ""
    for num in l:
        if c[num] == 1:
            if a:
                output += "A"
            else:
                output += "B"
            a = not a
        elif num == put:
            output += putted
        elif c[num] > 2 and put3:
            if a:
                output += "A"
                putted = "B"
            else:
                output += "B"
                putted = "A"
            a = not a
            put3 = False
            put = num
        else:
            output += "A"
            
    print(output)
        
foo()