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:
#!/usr/bin/env python3
import sys

def rint():
    return map(int, sys.stdin.readline().split())
#lines = stdin.readlines()

n = int(input())

s = list(rint())

set_type = []
type_num = 0

found_candi = 0
candi_index = -1
for i in range(n):
    if s.count(s[i]) == 1:
        type_num += 1
        set_type.append(1)
    elif found_candi == 0 and s.count(s[i]) >=3:
        found_candi = 1
        candi_index = i
        set_type.append(2)
    else:
        set_type.append(0)

ans =[]
type_cnt = 0
if type_num%2 and found_candi == 0:
    print("NO")
else:
    print("YES")
    if type_num %2:
        type_num += 1
    else:
        found_candi = 0
    for i in range(n):
        if found_candi:
            if i == candi_index:
                type_cnt +=1
                if type_cnt <= type_num//2:
                    ans.append('A')
                else:
                    ans.append('B')
                continue
            elif s[i] == s[candi_index]:
                if ans[candi_index] == 'A':
                    ans.append('B')
                else:
                    ans.append('A')
                continue
        if set_type[i] == 0 or found_candi == 0 and set_type[i] == 2:
            ans.append('A')
        elif set_type[i] == 1:
            type_cnt += 1
            if type_cnt <= type_num//2:
                ans.append('A')
            else:
                ans.append('B')
    print("".join(ans))