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())
y=list(map(int,input().split()))
y1=[]
d={}
for i in y:
    if i not in d:
        d[i]=1
    else:
        d[i]+=1

d1=sorted(d.items(), key=lambda kv: kv[1])
count=f=0
for i in d1:
    if i[1]==1:
        count+=1
    elif i[1]>=3 and f==0:
        x1=i[0]
        f=1
        
    
if count%2!=0:
    if f==0:
        print("NO")
    else:
        c=count
        for j in y:
            if d[j]==1 and c%2==0:
                y1.append("A")
                c-=1
            elif d[j]==1 and c%2!=0:
                y1.append("B")
                c-=1
            elif j==x1 and f==1:
                y1.append("A")
                f=2
            else:
                y1.append("B")
                
        print("YES")
        for i in y1:
            print(i,end="")
        
else:
    c=count
    for j in y:
        if d[j]==1 and c%2==0:
            y1.append("A")
            c-=1
        elif d[j]==1 and c%2!=0:
            y1.append("B")
            c-=1
        else:
            y1.append("A")
    
    print("YES")
    for i in y1:
        print(i,end="")