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:
n=input()
a=map(int,raw_input().split())
f=[0]*101
for i in a:
    f[i]+=1
x=[]
y=[]
for i in range(101):
    if f[i]==1:
        x.append(i)
    elif f[i]>2:
        y.append(i)
if len(x)%2==0:
    p=x[:len(x)/2]
    q=x[len(x)/2:]
    print "YES"
    s=''
    for i in a:
        if i in p:
            s+='A'
        elif i in q:
            s+='B'
        else:
            s+='A'
    print s
else:
    if len(y)==0:
        print "NO"
    else:
        d=y[0]
        p=x[:len(x)//2+1]
        q=x[len(x)//2+1:]
        t=0
        print "YES"
        s=''
        for i in a:
            if i in p:
                s+='A'
            elif i in q:
                s+='B'
            elif i==d:
                if t==0:
                    s+="B"
                else:
                    s+="A"
                t+=1
            else:
                s+="A"
        print s