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 JAVA):

Solution:
import java.awt.*;
import java.io.*;
import java.util.*;

public class AA implements Runnable {


    public void run() {
        InputReader sc = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int i=0,j=0,k=0;
        int t=0;
        //t=sc.nextInt();
        while (t-->0)
        {

        }
        int n=sc.nextInt();
        int count=0;
        int arr[]=new int[n];
        ArrayList<Integer> sorted=new ArrayList<>();
        HashSet<Integer> seta=new HashSet<>();
        boolean isgreatedthan2=false;
        int greaaterthan2=0;
        boolean ina=true;
        for (i=0;i<n;i++)
        {
            arr[i]=sc.nextInt();
            sorted.add(arr[i]);
        }
        Collections.sort(sorted);
        i=0;
        while (i<n)
        {
            int temp=sorted.get(i);
            int cnt=0;
            while (i<n&&sorted.get(i)==temp)
            {
                cnt++;
                i++;
            }
            if (cnt==1)
            {
                count++;
                if (ina)
                {
                    seta.add(temp);
                    ina=false;
                }
                else
                    ina=true;
            }
            if (cnt>1)
            {
                seta.add(temp);
            }
            if (!isgreatedthan2&&cnt>2)
            {
                isgreatedthan2=true;
                greaaterthan2=temp;
            }
        }
        if (count%2==0)
        {
            out.println("YES");
            for (i=0;i<n;i++)
            {
                if (seta.contains(arr[i]))
                    out.print("A");
                else
                    out.print("B");
            }
        }
        else if (isgreatedthan2)
        {
            out.println("YES");
            boolean done=false;
            for (i=0;i<n;i++)
            {
                if (!done&&greaaterthan2==arr[i])
                {
                    out.print("B");
                    done=true;
                    continue;
                }
                if (seta.contains(arr[i]))
                    out.print("A");
                else
                    out.print("B");
            }
        }
        else
            out.println("NO");




//=======================================================================================================================================

        out.flush();
        out.close();
    }


//=======================================================================================================================================

    static boolean isValid(Pair x,int n,int m)
    {
        return x.a>=0 && x.a<n && x.b>=0 && x.b<m;
    }
    static int dx[]={0,0,1,-1};
    static int dy[]={1,-1,0,0};
    static class Pair
    {
        int a,b;
        Pair(int aa,int bb)
        {
            a=aa;
            b=bb;
        }
        public String toString()
        {
            return a+" "+b;
        }
    }
    int sa(int a[],InputReader sc)
    {
        int x=0;
        for(int i=0;i<a.length;i++)
        {
            x+=a[i]=sc.nextInt();
        }
        return x;
    }

    static class PairSort implements Comparator<Pair>
    {
        public int compare(Pair a,Pair b)
        {
            return b.b-a.b;
        }
    }


    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars==-1)
                throw new InputMismatchException();

            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                }
                catch (IOException e) {
                    throw new InputMismatchException();
                }

                if(numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt() {
            int c = read();

            while(isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-') {
                sgn = -1;
                c = read();
            }

            int res = 0;
            do {
                if(c<'0'||c>'9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));

            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    public static void main(String args[]) throws Exception {
        new Thread(null, new AA(),"Main",1<<27).start();
    }
}