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())
multiset = list(map(int,input().split()))

A = 0
B = 0
rep = [0 for i in range(100)]
ans = ""
altern = 1

for i in multiset:
    rep[i-1] += 1
suma = sum(1 for i in multiset if rep[i-1]==1 )
triple = any(i>=3 for i in rep)

if suma%2==0 or (triple and suma%2!=0):
    print("YES")
    if suma%2==0:
        for i in multiset:
            if rep[i-1]==1 and altern==1:
                ans += "A"
                altern *= -1
            elif rep[i-1]==1 and altern==-1:
                ans +="B"
                altern *= -1
            else:
                ans += "A"
        print(ans)
    else:
        for i in multiset:
            if rep[i-1]==1 and altern == 1:
                ans +="A"
                altern*=-1
            elif rep[i-1]==1 and altern == -1:
                ans += "B"
                altern *= -1
            elif rep[i-1]>2 and triple:
                ans += "B"
                triple = False
            else:
                ans += "A" 
        print(ans)    
else:
    print("NO")