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())
a = [int(s) for s in input().split()]

goodElems = 0
Scope = [0]*101
Bscope = [False]*101
for i in range(n):
    Scope[a[i]] += 1

for elem in Scope:
    if elem == 1:
        goodElems +=1


if goodElems == 0:
    print("YES")
    for i in range(n):
        print("A", end="")

elif goodElems % 2 == 0:
    print("YES")
    goodElems = goodElems // 2
    for i in range(n):
        if Scope[a[i]] == 1 and goodElems > 0:
            print("B", end="")
            goodElems -= 1
        else:
            print("A", end="")
else:
    s = ["A"]*n
    goodElemsAll = (goodElems+1)//2
    goodElemsA = 0
    goodElemsB = 0
    for i in range(len(a)):
        if Scope[a[i]] == 1 and goodElemsA != goodElemsAll:
            Scope[a[i]] -= 1
            s[i] = "A"
            goodElemsA += 1
        elif Scope[a[i]] == 1 and goodElemsB != goodElemsAll:
            Scope[a[i]] -= 1
            s[i] = "B"
            goodElemsB += 1
    for i in range(n):
        if Scope[a[i]] > 2:
            goodElemsB += 1
            s[i] = "B"
            break


    if goodElemsA == goodElemsB:
        print("YES")
        print("".join(s))
    else:
        print("NO")