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())
c = [0] * 101
a = [int(i) for i in input().split()]
for i in range(n):
    c[a[i]] += 1
if n == c.count(1) + c.count(2) * 2:
    if c.count(1) % 2 == 1:
        print("NO")
    else:
        print("YES")
        k = c.count(1) // 2
        for i in range(n):
            if c[a[i]] == 1:
                if k:
                    k -= 1
                    print("A", end = "")
                else:
                    print("B", end = "")
            else:
                print("A", end = "")
else:
    print("YES")
    if c.count(1) % 2 == 0:
        k = c.count(1) // 2
        for i in range(n):
            if c[a[i]] == 1:
                if k:
                    k -= 1
                    print("A", end = "")
                else:
                    print("B", end = "")
            else:
                print("A", end = "")
    else:
        d = 0
        k = c.count(1) // 2
        for i in range(n):
            if c[a[i]] == 1:
                if k:
                    k -= 1
                    print("A", end = "")
                else:
                    print("B", end = "")
            elif not d and c[a[i]] > 2:
                print("A", end = "")
                d = 1
            else:
                print("B", end = "")