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:
def main():
    n = int(input())
    a = list(map(int, input().split()))

    s = set()

    elem = -1
    
    for i in range(n):
        if (a.count(a[i]) == 1):
            s.add(a[i])
        elif (a.count(a[i]) >= 3):
            elem = a[i]
    
    if (len(s) == 0):
        print("YES")
        for i in range(n):
            print("A", end='')
    elif (len(s) % 2 == 0):
        print("YES")
        f = True
        for i in range(n):
            if (a[i] in s):
                if (f):
                    print("A", end='')
                    f = False
                else:
                    print("B", end='')
                    f = True
            else:
                print("A", end='')
    else:
        if (elem == -1):
            print("NO")
        else:
            print("YES")
            a1 = []
            a2 = []
            
            for i in range(len(s) // 2):
                a1.append(s.pop())
            a1.append(elem)
            for i in range(len(s)):
                a2.append(s.pop())
                
            c = 0
                
            for i in range(n):
                if (a[i] == elem):
                    if (c == 0):
                        print("A", end='')
                        c += 1
                    else:
                        print("B", end='')
                elif (a[i] in a1):
                    print("A", end='')
                elif (a[i] in a2):
                    print("B", end='')                
                else:
                    print("A", end='')
if __name__ == "__main__":
    main()