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(x) for x in input().split()]
INDEX = {}
for k in set(a):
    INDEX[k] = []
for i in range(n):
    INDEX[a[i]].append(i)

add = 0
IS = True
pAns = [None] * n
one = 0
ONE1 = {True:[],False:[]}
Over2 = {True:[],False:[]}
for j in INDEX.values():
    t = len(j)
    if t > 2:
        add += 1
        Over2[IS].append(j)
    elif t == 1:
        add += 1
        one += 1
        ONE1[IS].append(j)
    pAns[j[0]] = IS
    IS = not IS if t != 2 else IS
    for l in range(1,t):
        pAns[j[l]] = IS
        

if add % 2 == 0:
    STRING = ""
    for x in pAns:
        if x:
            STRING += 'A'
        else:
            STRING += 'B'
    print("YES")
    print(STRING)
else:
    if one == add:
        print("NO")
    elif Over2[True] != [] :
        pAns[Over2[True][0][0]] = False
        STRING = ""
        for x in pAns:
            if x:
                STRING += 'A'
            else:
                STRING += 'B'
        print("YES")
        print(STRING)
    elif Over2[False] != [] and ONE1[True]:
        pAns[Over2[False][0][0]] = True
        pAns[ONE1[True][0][0]] = False
        STRING = ""
        for x in pAns:
            if x:
                STRING += 'A'
            else:
                STRING += 'B'
        print("YES")
        print(STRING)
    else:
        print("NO")