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:
n = int(input())
s = list(map(int,input().split()))
for x in range(0,len(s),+1):
    s[x] = [s[x],x]
s_ile = []
for x in range(0,n,+1):
    s_ile.append([0,0])
s = sorted(s)
tmp_ile = 1
ile_p = 0
s_wyn = [0]*n
i1 = 0
iw = 0
ia = 0
ib = 0
r = False
bb = False
for x in range(0,len(s)-1,+1):
    if s[x][0] == s[x+1][0]:
        tmp_ile += 1
        s_ile[x][1] = s[x][1]
    else:
        s_ile[x][0] = tmp_ile
        s_ile[x][1] = s[x][1]
        tmp_ile = 1
s_ile[-1][0] = tmp_ile
s_ile[-1][1] = s[-1][1]
for x in range(len(s_ile)-1,-1,-1):
    if s_ile[x][0]==0:
        s_ile[x][0]=s_ile[x+1][0]
c1 = 0
for x in range(0,len(s_ile),+1):
    if s_ile[x][0] == 1:
        i1 += 1
    if s_ile[x][0] > 2:
        iw += 1
if i1%2==1 and iw==0:
    print('NO')
    exit(0)
if i1%2 == 1:
    r = True
if r == True:
    for x in range(0,len(s_ile),+1):
        if s_wyn[s_ile[x][1]] == 'A' or s_wyn[s_ile[x][1]] == 'B':
            continue
        if s_ile[x][0] == 1:
            if ia < ib:
                s_wyn[s_ile[x][1]] = 'A'
                ia += 1
            else:
                s_wyn[s_ile[x][1]] = 'B'
                ib += 1
            continue
        if s_ile[x][0]>2 and bb == False:
            bb=True
            s_wyn[s_ile[x][1]] = 'A'
            ia += 1
            for z in range(x + 1, x + s_ile[x][0], +1):
                s_wyn[s_ile[z][1]] = 'B'
            continue
        s_wyn[s_ile[x][1]] = 'A'
else:
    for x in range(0,len(s_ile),+1):
        if s_ile[x][0]==1:
            if ia < int(i1/2):
                s_wyn[s_ile[x][1]] = 'A'
                ia += 1
            else:
                s_wyn[s_ile[x][1]] = 'B'
                ib += 1
        else:
            s_wyn[s_ile[x][1]] = 'A'
for x in range(0,len(s_ile),+1):
    if s_ile[x][0] == 0 or s_ile[x][0] == 2:
        s_wyn[s_ile[x][1]] = 'B'
        continue
print('YES')
print(''.join(s_wyn))