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:
#   ==========     //\\       //||     ||====//||
#       ||        //  \\        ||     ||   // ||
#       ||       //====\\       ||     ||  //  ||
#       ||      //      \\      ||     || //   ||
#   ========== //        \\  ========  ||//====|| 
#  code

def solve():
    from collections import Counter as C
    n = int(input())
    s = list(map(int, input().split()))

    c = C(s)
    a = s[:]
    s = list(set(s))

    once = []
    fl = 0
    for i in s:
        if c[i] == 1:
            once.append(i)
        if c[i] > 2:
            fl = i
    
    if len(once) % 2 == 0:
        d = {}
        for i in once[:len(once) // 2]:
            d[i] = 'A'
        for i in once[len(once) // 2:]:
            d[i] = 'B'
        
        st = ""
        for i in a:
            st += d.get(i, 'A')
        
        print('YES')
        print(st)
    else:
        if fl == 0:
            print('NO')
        else:
            d = {}
            for i in once[:len(once) // 2]:
                d[i] = 'A'
            for i in once[len(once) // 2:]:
                d[i] = 'B'

            st = ""
            for i in a:
                if fl == i:
                    st += 'A'
                    fl = 0
                else:
                    st += d.get(i, 'B')
            
            print('YES')
            print(st)


def main():
    t = 1
    # t = int(input())
    for _ in range(t):
        solve()

if __name__ == "__main__":
    main()