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:
r = input
n = int(r())
a = [int(x) for x in r().split()]
cnt = [0]*(100+1)
A = []
B = []
res =""
for i in a:
    cnt[i]+=1
for i,j in enumerate(a):
    if(cnt[j]==1):
        A.append(i)
    if(cnt[j]>2):
        B.append(i)
pr = [0]*(n+1)
if(len(A)%2 == 0):
    len2 = len(A)//2
    res="YES\n"
    for i in A[:len2]:
        pr[i] = 1
    for i in A[len2:]:
        pr[i] = 2
    for i in range(n):
        if(pr[i] == 1):
            res+='A'
        else:
            res+='B'
else:
    res="YES\n"
    dupx = -1
    len2 = len(A)//2+1
    for i,j in enumerate(a):
        if(cnt[j]>2):
            dupx = i
            break
    pr = [0]*(n+1)
    if(dupx ==-1):
        res="NO\n"
    else:
        pr[dupx] = 1
        for i in A[:len2]:
            pr[i] = 2
        for i in A[(len2):]:
            pr[i] = 1
        for i in range(n):
            if(pr[i] == 1):
                res+='B'
            else:
                res+='A'
print(res)