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:
n = int(input())
s = list(map(int, input().split()))
d = {}
mt = False
mti = -1
for i in range(len(s)):
    if s[i] not in d:
        d[s[i]] = 1
    else:
        d[s[i]] += 1
        if d[s[i]] > 2:
            mt = True
            mti = i
good = []
for i in d.keys():
    if d[i] == 1:
        good.append(i)
if len(good) % 2 == 0:
    print("YES")
    good1 = good[:len(good) // 2]
    for i in s:
        if i in good1:
            print('A', end='')
        else:
            print('B', end='')
else:
    if mt:
        print("YES")
        good1 = good[:len(good) // 2]
        u = False
        for i in s:
            if (i in good1) or ((not u) and (i == s[mti])):
                print('A', end='')
                if i == s[mti]:
                    u = True
            else:
                print('B', end='')    
    else:
        print("NO")