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:
from collections import defaultdict,deque
import sys,heapq,bisect,math,itertools,string,queue,datetime
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
def inpl(): return list(map(int, input().split()))
def inpls(): return list(input().split())

N = int(input())
aa = inpl()
cnt = [0]*110
nums = [0]*110
nums[0] = N

for a in aa:
    nums[cnt[a]] -= 1
    cnt[a] += 1
    nums[cnt[a]] += 1

if nums[1]%2 == 1:
    if sum(nums[3:]) == 0:
        print('NO')
    else:
        print('YES')
        ans = []
        abflag = True
        First = True
        for a in aa:
            if cnt[a] == 1:
                if abflag:
                    ans.append('A')
                else:
                    ans.append('B')
                abflag = not abflag
            elif cnt[a] == 2:
                ans.append('A')
            else:
                if First:
                    ans.append('B')
                    First = False
                else:
                    ans.append('A')
        print(''.join(ans))
elif nums[1]%2 == 0:
    print('YES')
    ans = []
    abflag = True
    First = True
    for a in aa:
        if cnt[a] == 1:
            if abflag:
                ans.append('A')
            else:
                ans.append('B')
            abflag = not abflag
        else:
            ans.append('A')
    print(''.join(ans))