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:
cnt=[0 for i in range(101)]
n=int(input())
s=input().split()
l=[int(s[i]) for i in range(n)]
for i in l:
    cnt[i]+=1
small=0
large=0
for i in range(1,101):
    if cnt[i]==1:
        small+=1
    elif cnt[i]>2:
        large+=1
        largenum=i
if small%2==1 and large==0:
    print("NO")
elif small%2==1:
    print("YES")
    counter=0
    flag=True
    for i in l:
        if cnt[i]==1:
            print("AB"[counter%2],end="")
            counter+=1
        elif i==largenum and flag:
            print("B",end="")
            flag=False
        else:
            print("A",end="")
    print("")
else:
    print("YES")
    counter=0
    for i in l:
        if cnt[i]==1:
            print("AB"[counter%2],end="")
            counter+=1
        else:
            print("A",end="")
    print("")