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())
a = list(map(int, input().split()))
m = {}
s = [[],[]]

for i in a:
    if i in m:
        m[i] += 1
    else:
        m[i] = 1

pos = 0
for p in m:
    if m[p] == 1:
        s[pos].append(p)
        pos = 1 - pos




if len(s[0]) == len(s[1]):
    res = ''
    for i in range(n):
        if(a[i] in s[1]):
            res += 'B'
        else:
            res += 'A'
    print("YES")
    print(res)
else:
    res = ''
    idd = -1
    for p in m:
        if(m[p] >= 3):
            idd = p
            break
    if(idd == -1):
        print("NO")
        exit(0)

    flag = False
    for i in range(n):
        if(a[i] in s[1]):
            res += 'B'
        elif(a[i] == idd and flag == False):
            res += 'B'
            flag = True
        else:
            res += 'A'
    print("YES")
    print(res)