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 = set(S)
nice = 0
dp = [0 for i in range(102)]
for i in D:
    if(S.count(i)==1):
        nice+=1
    dp[i]=S.count(i)
if(nice%2==0):
    d=0;s=""
    for i in S:
        if(dp[i]==1 and d<nice//2):
            s=s+"A"
            d+=1
        elif(dp[i]==1 and d>=nice//2):
            s=s+"B"
        else:
            s=s+"A"
    print("YES")
    print(s)
elif(nice%2!=0 and len(S)>nice):
    d=0;flag = 0;s=""
    for i in S:
        if(dp[i]==1 and d<nice//2):
            d+=1
            s=s+"A"
        elif(dp[i]==1 and d>=nice//2):
            d+=1
            s=s+"B"
        elif(dp[i]>2 and flag == 0):
            s=s+"A"
            flag = 1
        else:
            s=s+"B"
    if(flag == 0):
        print("NO")
    else:
        print("YES")
        print(s)
elif(nice%2!=0 and len(S)==nice):
    print("NO")