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:
a=int(input())
ans=[0 for i in range(101)]
z=list(map(int,input().split()))
for i in range(len(z)):
    ans[z[i]]+=1

if(ans.count(1)%2==1):
    s=''
    if(len(z)-ans.count(1)-2*ans.count(2)==0):
        print('NO')
    else:
        print('YES')
        flag=0
        tra=0
        for i in range(len(ans)):
            if(ans[i]>=3):
                break;
        tra=i
        count=ans[tra]
        c1=0
        
        for i in range(len(z)):
            if(ans[z[i]]==1):
                if(flag==0):
                    s+='A'
                    flag=1
                else:
                    s+='B'
                    flag=0
            else:
            
                if(z[i]==tra):
                    if(c1==count-1):
                        s+='B'
                    else:
                        s+='A'
                    c1+=1
                else:
                    s+='A'
                
        print(s)
        
else:
    print('YES')
    flag=0
    s=''
    for i in range(len(z)):
        if(ans[z[i]]>1):
            s+='A'
        else:
            if(flag==0):
                s+='A'
                flag=1
            else:
                s+='B'
                flag=0
    print(s)