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())
s=list(map(int,input().split()))
unik=[]
dui=[]
tinbeshi=[]

for i in range(n):
    if s.count(s[i])==1:
        unik.append(s[i])
    elif s.count(s[i])==2:
        dui.append(s[i])
    else:
        tinbeshi.append(s[i])
dui=set(dui)
tin=list(set(tinbeshi))
if len(unik)%2==1 and len(tin)==0:
    print("NO")
else:
    if len(unik)==0:
        print("YES")
        for i in range(n):
            print("A",sep="",end="")
    
    else:
        print("YES")
        if len(unik)%2==0:
            flg=True
            cnt=0
            for i in range(n):
                if s[i] in unik and flg:
                    print("A",sep="",end="")
                    cnt+=1
                    if cnt==len(unik)/2:
                        flg=False
                else:
                    print("B",sep="",end="")
        else:

            index=[]
            for i in range(int((len(unik)+1)/2-1)):
                index.append(s.index(unik[i]))
            index.append(s.index(tin[0]))
            
            for i in range(n):
                if i in index:
                    print("A",sep="",end="")
                else:
                    print("B",sep="",end="")