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 PYTHON):

Solution:
n = int(raw_input())
nums = list(map(int,raw_input().split()))
cnt = [0 for x in range(101)]
for i in nums:
    cnt[i] += 1
ext = 0
for i in range(101):
    if cnt[i]>2:
        ext += 1
ans = ["" for x in range(n)]
cnt1 = 0
cnt2 = 0
for i in range(n):
    if cnt[nums[i]]==1:
        if cnt1>cnt2:
            ans[i] = 'B'
            cnt2 += 1
        else:
            ans[i] = 'A'
            cnt1 += 1
if cnt1 != cnt2 and not ext:
    print "NO"
else:
    print "YES"
    if cnt1==cnt2:
        for i in range(n):
            if cnt[nums[i]]!=1:
                ans[i] = 'A'
        print "".join(ans)
    else:
        for i in range(101):
            if cnt[i]>2:
                for j in range(n):
                    if nums[j]==i:
                        ans[j] = 'B'
                        break
                break
        for i in range(n):
            if ans[i]=="":
                ans[i] = 'A'
        print "".join(ans)