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:
# -*- coding: utf-8 -*-
"""
Created on Thu Sep 27 14:15:04 2018

@author: czx
"""

def init():
    n = int(input())
    Str = input()
    a = list(map(int,str.split(Str)))
    return n,a

def main():
    n,a = init()
    cnt = [0 for x in range(105)]
    tot1 = 0
    tot2 = 0
    tot3 = 0
    for i in range(n):
        cnt[a[i]] += 1
        if cnt[a[i]] == 1:
            tot1 += 1
        if cnt[a[i]] == 2:
            tot1 -= 1
            tot2 += 1
        if cnt[a[i]] == 3:
            tot2 -= 1
            tot3 += 1
    if (tot1%2 != 0 and tot3 == 0):
        print("NO")
        return
    
    if (tot1%2 == 0):
        print("YES")
        for i in range(n):
            if (cnt[a[i]] != 1):
                print('A', end ='')
            else:
                if (tot1%2 == 0):
                    print('A', end = '')
                else:
                    print('B', end = '')
                tot1 -= 1
    else:
        flag = 0
        print("YES")
        for i in range(n):
            if (cnt[a[i]] > 2):
                if (flag == 0):
                    print('A', end = '')
                    flag = 1
                else:
                    print('B', end = '')
            if (cnt[a[i]] == 2):
                print('A', end = '')
            if (cnt[a[i]] == 1):
                if (tot1 % 2 == 1):
                    print('B', end = '')
                else:
                    print('A', end = '')
                tot1 -= 1

if __name__ == '__main__':
    main()