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())
l = list(map(int,input().split()))
c = ["c"]*n
d = {}
for i in l:
    if i in d:
        d[i] = d[i]+1

    else:
        d[i] = 1

t1 = 0
c1 = 0
tl = []
cl = []
for i in d:
    if d[i] == 1:
        t1 += 1
        tl.append(i)

    if d[i] > 2:
        c1 += 1
        cl.append(i)

if t1%2 == 1 and c1 == 0:
    print("NO")

else:
    if t1%2 == 0:
        cnt = 0
        s = set()
        for i in tl:
            x = l.index(i)
            if cnt < t1//2:
                c[x] = "A"

            else:
                c[x] = "B"

            cnt = cnt+1
            s.add(x)

        for i in range(len(c)):
            if i not in s:
                c[i] = "B"

        print("YES")
        print("".join(c))

    else:
        cnt = 0
        s = set()
        for i in tl:
            x = l.index(i)
            if cnt < t1 // 2:
                c[x] = "A"

            else:
                c[x] = "B"

            cnt = cnt + 1
            s.add(x)

        e = cl[0]
        x = l.index(e)
        c[x] = "A"
        s.add(x)
        for i in range(len(c)):
            if i not in s:
                c[i] = "B"

        print("YES")
        print("".join(c))