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 Tue Oct  9 20:56:01 2018

@author: Andrei
"""

n = int(input())

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

count = [0 for i in range(200)]

for i in range(n):
    count[s[i]] = count[s[i]] + 1
    
big = 0
total = 0
biggie = 0
for i in range(1,101):
    if count[i] == 1:
        total = total + 1
    if count[i] > 2:
        big = big + 1
        
for i in range(n):
    if count[s[i]]>2:
        biggie = i
            
if total % 2 == 0:
    print("YES")
    alternate = 0
    string = ""
    for i in range(n):
        if count[s[i]] == 1:
            if alternate == 0:
                string = string + "A"
                alternate = 1
            else:
                string = string + "B"
                alternate = 0
        else:
            string = string + "B"
    print(string)
else:
    if big == 0: 
        print("NO")
    else:
        print("YES")
        alternate = 0
        string = ""
        for i in range(n):
            if count[s[i]] == 1:
                if alternate == 0:
                    string = string + "A"
                    alternate = 1
                else:
                        string = string + "B"                        
                        alternate = 0
            else:
                if i==biggie:
                    string = string + "B"
                else:
                    string = string + "A"
        print(string)