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())
Set = list(map(int, input().split()))
#print(sorted(Set))
Stat = [0] * 101
A = 0
B = 0
a, b, c = 0, 0, 0
ans = ""
ch = False

for el in Set:
    Stat[el] += 1


for i in range(1, 101):
    if Stat[i] == 1:
        a += 1
    elif Stat[i] > 2:
        c += 1
#print(a, "aaaa", c, "cccc")
elem = -1
if a % 2 == 0:
    print("YES")
    count = 1
    for el in Set:
        if Stat[el] == 1:
            if count <= a // 2:
                ans += 'A'
                count += 1
            else:
                ans += 'B'
        else:
            ans += 'B'
    print(ans)

else:
    if c > 0:
        count = 1
        print("YES")
        #print(a // 2 + 1)
        for el in Set:
            #print(el, end=' ')
            if Stat[el] == 1:
                if count <= a // 2 + 1:
                    ans += 'A'
                    count += 1
                    #print(1)
                else:
                    ans += 'B'
                    #print(2)
            elif Stat[el] > 2 and elem < 0:
                ans += 'B'
                elem = el
                #print(3)
            elif el == elem:
                ans += 'A'
                #print(4)
            else:
                #print(5)
                ans += 'B'
        print(ans)
    else:
        print("NO")