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()))
d={}
m=10000000000
count1=0
p=0
t=0
for i in a:
    d[i]=d.get(i,0)+1
    if d[i]<m:
        m=d[i]
        
if m>=2:
    print('YES')
    print('A'*n)
    
else:
    s='A'*n
    for i in range(n):
        if d[a[i]]==1 and count1%2==0:
            s=s[:i]+'B'+s[i+1:]
            count1+=1
        elif d[a[i]]==1:
            count1+=1
    if count1%2==0:
        print('YES')
        print(s)
    else:
        for i in range(n):
            if d[a[i]]>2:
                k=a[i]
                s=s[:i]+'A'+s[i+1:]
                t=1
                break
        if t==1:
            for p in range(i+1,n):
                if a[p]==k:
                    s=s[:p]+'B'+s[p+1:]
            print('YES')
            print(s)
        if t==0:
            print('NO')