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:
def swap(s,a,m):
    s=s[0:a:1]+m+s[(a+1):len(s):1]
    return(s)
i=int(input())
s=[int(k) for k in input().split()]
import collections
d=collections.Counter()
p=0
z=0
x=0
e=[]
r=-1
for t in s:
    u=[]
    for m in range(0,len(s)):
        if(s[m]==t):
            u.append(m)
    if(len(u)==1):
        e.append(t)
        p+=1
        z=1
    elif(len(u)>=3):
        x=1
        r=t
    d[t]=tuple(u)
y="0"*i 
if(p==0):
    print("YES")
    print("A"*i)
else:
    if(x==0 and p%2!=0):
        print("NO")
    else:
        print("YES")
        if(p%2==0):
            for w in range(0,len(e)):
                if(w%2==0):
                    y=swap(y,d[e[w]][0],"A")
                else:
                    y=swap(y,d[e[w]][0],"B")
            for b in range(0,len(y)):
                if(y[b]=="0"):
                    y=swap(y,b,"A")
            print(y)
        else:
            for w in range(0,len(e)):
                if(w%2==0):
                    y=swap(y,d[e[w]][0],"A")
                else:
                    y=swap(y,d[e[w]][0],"B")
            y=swap(y,d[r][-1],"B")
            for b in range(0,len(y)):
                if(y[b]=="0"):
                    y=swap(y,b,"A")
            print(y)