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())
y=list(map(int,input().split()))

arr=[0]*(100+1)
y1=y.copy()
y1=sorted(y1)

for i in y1:
    arr[i]+=1

x=count1=0
for i in arr:
    if i==1:
        count1+=1
    elif i>2:
        x+=1
    

if count1%2==0:
    ans=[]
    i=0
    k=0
    while i<n:
        if arr[y[i]]==1:
            if k%2==0:
                ans.append("A")
            else:
                ans.append("B")
            k+=1
        else:
            ans.append("A")
        i+=1
    print("YES")
    for i in ans:
        print(i,end="")
else:
    if x>0:
        last=0
        last1="A"
        ans=[]
        i=0
        k=0
        flag=0
        while i<n:
            if arr[y[i]]==1:
                if k%2==0:
                    ans.append("A")
                else:
                    ans.append("B")
                k+=1
            elif arr[y[i]]>2 and flag==0:
                if k%2==0:
                    ans.append("A")
                else:
                    ans.append("B")
                k+=1
                flag=1
                last=y[i]
                last1=ans[-1]
            else:
                if last==y[i]:
                    if last1=="A":
                        ans.append("B")
                    else:
                        ans.append("A")
                else:
                    ans.append("A")
            i+=1
        print("YES")
        for i in ans:
            print(i,end="")
        
    else:
        print("NO")