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())
arr = [int(x) for x in input().split()]

cnt = [0 for i in range(102)]
for x in arr:
    cnt[x] += 1

dp = [[[-1 for i in range(102)] for j in range(102)] for k in range(102)]
jawab = [-1 for i in range(102)]

# -1 = Gaada
# 0 = ambil A = semua
# 1 = ambil buat A = 1
# 2 = ambil buat B = 1
# 3 = ambil buat A = 1 dan B = 1
# 4 = ambil buat B = semua

def kucing(pos, nA, nB):
    global dp
    
    if (dp[pos][nA][nB] == -1):
        if (pos > 100):
            return (nA == nB)
        
        if (cnt[pos] == 0):
            dp[pos][nA][nB] = kucing(pos+1, nA, nB)
            return dp[pos][nA][nB]
        if (cnt[pos] == 1 or cnt[pos] > 2):
            if (cnt[pos] > 2 and kucing(pos+1, nA, nB)):
                jawab[pos] = 0
                dp[pos][nA][nB] = True
                return True
            elif (kucing(pos+1, nA+1, nB)):
                jawab[pos] = 1
                dp[pos][nA][nB] = True
                return True
            elif (kucing(pos+1, nA, nB+1)):
                jawab[pos] = 2
                dp[pos][nA][nB] = True
                return True
            else:
                dp[pos][nA][nB] = False
                return False
        else:
            if (kucing(pos+1, nA, nB)):
                jawab[pos] = 0
                dp[pos][nA][nB] = True
                return True
            elif (kucing(pos+1, nA+1, nB+1)):
                jawab[pos] = 3
                dp[pos][nA][nB] = True
                return True
            else:
                dp[pos][nA][nB] = False
                return False
    else:
        return dp[pos][nA][nB]

if kucing(0, 0, 0):
    print("YES")
    for i in range(N):
        if (jawab[arr[i]] == 0):
            print("A", end = "")
        elif (jawab[arr[i]] == 4):
            print("B", end = "")
        elif (jawab[arr[i]] == 1):
            print("A", end = "")
            jawab[arr[i]] = 4
        elif (jawab[arr[i]] == 2):
            print("B", end = "")
            jawab[arr[i]] = 0
        elif (jawab[arr[i]] == 3):
            print("B", end = "")
            jawab[arr[i]] = 1
else:
    print("NO")