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())
a=list(map(int,input().split()))
cnt=[0]*101
ans=[]
x=0;z=-1
for i in a:
    cnt[i]+=1;
for i in range(101):
    if cnt[i]==1:
        x+=1
    elif cnt[i]>2:
        z=i
#print(x)
if x%2==0:
    y=1
    for i in range(n):
        if cnt[a[i]]==1:
            if y<=x/2:
                ans.append('A')
                y+=1
            else :ans.append('B')
        else: ans.append('A')
else:
    if z==-1: exit(print("NO"))
    else:
        y=1;mxcnt=0
        for i in range(n):
            if cnt[a[i]]==1:
                if y<=x//2:
                    ans.append('A')
                    y+=1
                else:ans.append('B')
            elif a[i]==z:
                if mxcnt==0:
                    ans.append('A')
                    mxcnt+=1
                else:ans.append('B')
            else:ans.append('B')
print("YES")
print(*ans,sep='')