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())
arr = list(map(int, input().split()))
num = [0 for i in range(101)]
for i in arr:
    num[i] += 1
od = set()
dv = set()
mn = set()
o = 0
d = 0
m = 0
for i in range(101):
    if(num[i] == 1):
        o += 1
        od.add(i)
    elif(num[i] == 2):
        dv.add(i)
        d += 1
    elif(num[i] > 2):
        mn.add(i)
        m += 1
if(o % 2 == 1 and m == 0):
    print("NO")
else:
    print("YES")
    dob = o % 2
    s = ''
    h = 'A'
    for i in arr:
        if(i in od):
            s += h
            if(h == 'A'):
                h = 'B'
            else:
                h = 'A'
        elif(dob > 0 and i in mn):
            s += 'B'
            dob -= 1
        else:
            s += 'A'
    print(s)