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()))
d=dict()
for i in s:
    if i in d:
        d[i]+=1
    else:
        d.update({i:1})
c=0
for i in d:
    if d[i]==1:
        c+=1
ans=""
if c%2==0:
    t=True
    for i in s:
        if d[i]==1:
            if t:
                ans+=("A")
            else:
                ans+=("B")
            t=not t
        else:
            ans+=("A")
    print("YES")
    print(ans)
else:
    can=False
    for i in d:
        if d[i]>2:
            can=True
            x=i
    if can:
        t=True
        t1=False
        t3=True
        for i in s:
            if d[i]==1 or (i==x and t1==False):
                if i==x and t1==False:
                    t1=True
                    if t:
                        ans+=("A")
                        t3=True
                    else:
                        ans+=("B")
                        t3=False
                    t=not t

                else:
                    if t:
                        ans+=("A")
                    else:
                        ans+=("B")
                    t=not t
            else:
                if i==x:
                    if t3:
                        ans+="B"
                    else:
                        ans+="A"
                else:
                    ans+=("A")
        print("YES")
        print(ans)
    else:
        print("NO")