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:
import sys

def main():
    n = int(input())
    s = list(map(int, input().split()))
    cnt = {i: s.count(i) for i in s}

    if list(cnt.values()).count(1) == 0:
        print("YES")
        print("A" * len(s))
        return

    if list(cnt.values()).count(1) & 1:
        c3 = len(cnt) - list(cnt.values()).count(1) - list(cnt.values()).count(2)
        if c3 == 0:
            print("NO")
            return
        else:
            print("YES")
            ok = False
            f = 0
            for i in s:
                if not ok and cnt[i] >= 3:
                    print('B', end='')
                    ok = True 
                elif cnt[i] == 1:
                    print(['A', 'B'][f], end='')
                    f ^= 1
                else:
                    print('A', end='')
            print()
    else:
        print("YES")
        f = 0
        for i in s:
            if cnt[i] == 1:
                print(['A', 'B'][f], end='')
                f ^= 1
            else:
                print('A', end='')
        print()

if __name__ == '__main__':
    main()