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 = [0]*200
l = list(map(int,input().split()))
for i in l:
    s[i]+=1
cnt,cnt1,cnt2=0,0,0

for i in range(len(s)):
    if(s[i]==1):
        cnt1+=1
    elif(s[i]>2):
        cnt+=1
if(cnt1%2):
    if(cnt==0):
        print('NO')
    else:
        print('YES')
        f = 1
        f1 = 1
        for i in l:
            if(f and s[i]==1):
                print('A',end='')
                f = 0
            elif((not f) and s[i]==1):
                print('B',end='')
                f = 1
            elif(f1 and s[i]>2):
                print('B',end='')
                f1 = 0
            else:
                print('A',end='')
else:
    print('YES')
    f = 1
    for i in l:
        if(f and s[i]==1):
            print('A',end='')
            f = 0
        elif((not f) and s[i]==1):
            print('B',end='')
            f = 1
        else:
            print('A',end='')