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().strip().split()))[:n]

from collections import Counter,defaultdict
store = Counter(arr)
mark = defaultdict(int)

rem = 0;sattire = -1
for a,b in store.items():
    if store[a] == 1:
        rem +=b
    elif store[a] == 2:
        mark[a] = True
    else:
        sattire = a



if rem %2 == 1 and sattire == -1:
    print('NO')
    exit(0)

if rem %2 == 0:
    sattire = -1
print('YES')
flag = 0;ans = [""]*n
for i in range(n):
    if mark[arr[i]] == True:
        if store[arr[i]] %2 == 0:
            ans[i] = 'A'
        else:
            ans[i] = 'B'

        store[arr[i]]-=1
    elif store[arr[i]] == 1:
        if flag == 0:
            ans[i] = 'A'
        else:
            ans[i] = 'B'

        flag = flag^1
    elif arr[i] == sattire:
        ans[i] = 'B'
        sattire = -1
    else:
        ans[i] = 'A'

    print(ans[i],end = "")

print()