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:
# https://codeforces.com/problemset/problem/1051/C
from collections import Counter

def solution(S):
    dict = Counter(S)
    distinct_nums = []
    extra_idx = []
    idx_nums = []
    for i in range(len(S)):
        if(dict[S[i]] == 1):
            distinct_nums.append(S[i])
            idx_nums.append(i)
    if(len(distinct_nums) % 2 == 1):
        sol = ["A"] * len(S)
        found = False
        for k, v in dict.items():
            if(v > 2):
                extra_idx = [i for i, x in enumerate(S) if x == k]
                idx_nums.append(extra_idx[0])
                idx_nums.sort()
                found = True
                break
        if(not found):
            return False, None
    # 0 = A - 1 = B
    sol = [""] * len(S)
    for i in range(len(S)):
        if(i in idx_nums):
            if(idx_nums.index(i) < (len(idx_nums) / 2)):
                sol[i] = "B"
                if(extra_idx):
                    if(i == extra_idx[0]):
                        for y in range(len(extra_idx)):
                            if(y > 0):
                                sol[extra_idx[y]] = "A"
            else:
                sol[i] = "A"
                if(extra_idx):
                    if(i == extra_idx[0]):
                        for y in range(len(extra_idx)):
                            if(y > 0):
                                sol[extra_idx[y]] = "B"
        else:
            if(i not in extra_idx):
                sol[i] = "A"
    return True, sol

N = int(input())
S = [int(x) for x in input().split()]   
if(N == len(S)):
    solved, solution = solution(S)
    if(not solved):
        print("NO")
    else:
        print("YES")
        print(''.join(str(i) for i in solution))
else: print("NO")