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:
from collections import Counter
n = input()
a = map(int,raw_input().split())
c  = Counter(a)
count = 0
elem = 0
maxi = 0
for i in c:
    if(c[i] == 1):
        count+=1
    else:
        if(c[i] > maxi):
            elem = i
            maxi = c[i]
if(count == n and (count%2 == 1)):
    print "NO"
elif(count%2 == 0):
    print "YES"
    m = {}
    for i in c:
        if(c[i] == 1):
            if(count%2 == 0):
                m[i] = 'A'
            else:
                m[i] = 'B'
            count-=1
        else:
            m[i] = 'A'
    s = ""
    for i in a:
        s += m[i]
    print s
elif(maxi==2):
    print "NO"
else:
    print "YES"
    m = {}
    for i in c:
        if(i == elem):
            pass
        elif(c[i] == 1):
            if(count%2 == 0):
                m[i] = 'A'
            else:
                m[i] = 'B'
            count-=1
        else:
            m[i] = 'A'
    s = ""
    flag = 0
    for i in a:
        if(i == elem):
            if(flag == 0):
                s += 'A'
                flag = 1
            else:
                s += 'B'
        else:
            s += m[i]
    print s