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()))

cnt=[0]*105
for i in range(n):
    cnt[s[i]]+=1

cnt_nice = 0
for i in range(105):
    if cnt[i] == 1:
        cnt_nice+=1

if cnt_nice % 2 == 0:
    print("YES")
    tmp = cnt_nice/2
    res=""
    for i in range(n):
        if (cnt[s[i]]!=1) or (tmp>0 and cnt[s[i]]==1):
            res+='A'
            if cnt[s[i]]==1:
                tmp-=1
        else:
            res+='B'
    print(res)
        
            
else:
    flag = False
    key_num = 0

    for i in range(n):
        if (cnt[s[i]]!=1 and cnt[s[i]] > 2):
            flag = True
            key_num = s[i]
            break
    # print("keynum: ",key_num)
    if flag:
        print("YES")
        tmp = cnt_nice/2
        res=""
        flag_key=False
        for i in range(n):
            # print("si",s[i],type(s[i]),key_num)
            
            if flag_key and s[i] == key_num:
                res+='A'
            elif flag_key==False and s[i] == key_num:
                res+='B'
                flag_key = True
            elif (cnt[s[i]]!=1) or (tmp>0 and cnt[s[i]]==1):
                res+='A'
                if cnt[s[i]]==1:
                    tmp-=1

            else:
                res+='B'
        print(res)
    else:
        print("NO")