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:
from math import ceil,gcd,sqrt
def ii():return int(input())
def mi():return map(int,input().split())
def li():return list(mi())
def si():return input()

n=ii()
m={}
a=li()
for i in range(n):
    if a[i] not in m:
        m[a[i]]=[]
        m[a[i]].append(i)
    else:
        m[a[i]].append(i)
a.clear()
x=[]
c=-1
for i in m.keys():
    if(len(m[i])==1):
        x.append(m[i][0])
    else:
        if(len(m[i])>2):
            c=m[i][0]
        for j in range(len(m[i])):
            a.append(m[i][j])
ans=['0']*n
if(len(x)%2==0 or c!=-1):
    print('YES')
    for i in a:
        ans[i]='A'
    if(len(x)%2):
        for i in range(0,len(x)-1,2):
            ans[x[i]]='A'
            ans[x[i+1]]='B'
        ans[x[len(x)-1]]='A'
        ans[c]='B'
    else:
        for i in range(0,len(x),2):
            ans[x[i]]='A'
            ans[x[i+1]]='B'
    print("".join(ans))
else:
    print('NO')