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 PYTHON):

Solution:
n = input()
arr = map(int,raw_input().split(" "))
dic = [0]*101

for i in arr:
    dic[i] += 1
good = 0
for i in range(101):
    if dic[i] == 1:
        good += 1

if good%2 == 0:
    print "YES"
    cnt = 0
    ret = []
    for i in arr:
        if dic[i] == 1:
            cnt += 1
            if cnt <= good/2:
                ret.append("A")
            else:
                ret.append("B")
        else:
            ret.append("A")
    print "".join(ret)

else:
    ret = ["A"]*n
    cnt = 0
    flag = True
    for j,i in enumerate(arr):
        if dic[i] == 1:
            cnt += 1
            if cnt > good/2+1:
                ret[j] = "B"
        elif dic[i] == 2:
            continue

        elif flag:

            flag = False
            ret[j] = "B"

    if flag:
        print "NO"
    else:
        print "YES"
        print "".join(ret)