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:

def vasya_and_multisets(v):
    m = dict()
    for e in v:
        m[e] = m.get(e, 0) + 1
    
    ones = 0
    has_gt2 = False
    for e in m.values():
        if (e == 1):
            ones += 1
        if (e > 2):
            has_gt2 = True
    odd_ones = ones % 2 == 1
    
    if (odd_ones and not has_gt2):
        print("NO")
    else:
        print("YES")
        A = True
        ans = ''
        for e in v:
            if (m[e] == 2):
                ans += 'A'
            elif (m[e] == 1):
                if A: 
                    ans += 'A' 
                else:
                    ans += 'B'
                A = not A
            else:
                if (odd_ones):
                    ans += 'B'
                    odd_ones = False
                else:
                    ans += 'A'
        print(ans)
            
    

n = int(input())
v = list(map(int,input().split()))
vasya_and_multisets(v)