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:
/*
[ H A C K   Y O U ! ! ]
*/
import java.io.*;
import java.util.*;


public class test {
    int INF = (int)1e9;
    long MOD = 1000000007;
    
    
    
    void solve(InputReader in, PrintWriter out) throws IOException {
        int n = in.nextInt();
        int[][] a = new int[n][2];
        int[] rs = new int[n];
        for(int i=0; i<n; i++) {
            a[i][0] = in.nextInt();
            a[i][1] = i;
        }
        Arrays.sort(a, new Comparator<int[]>(){
            public int compare(int[] x, int[] y) {
                return x[0] - y[0];
            }
        });
        int i = 0;
        int x = 0;
        while(i<n) {
            int v = a[i][0], c = 0;
            while(i<n && a[i][0]==v) {
                c++;
                i++;
            }
            if(c==1) x++;
        }
        if(x==0) {
            out.println("YES");
            for(i=0; i<n; i++) out.print("A");
            out.println();
            return;
        }
        int f = 1;
        if(x%2==0) {
            i = 0;
            while(i<n) {
                int v = a[i][0], c = 0;
                while(i<n && a[i][0]==v) {
                    c++;
                    i++;
                }
                if(c==1) {
                    rs[a[i-1][1]] = f;
                    f*=-1;
                }
            }
            out.println("YES");
            for(i=0; i<n; i++) {
                if(rs[i]==-1) out.print("B");
                else out.print("A");
            }
            out.println();
        } else {
            boolean bla = false;
            i = 0;
            out: while(i<n) {
                int v = a[i][0], c = 0;
                while(i<n && a[i][0]==v) {
                    c++;
                    i++;
                }
                if(c>2) {
                    a[i-1][0] = 999;
                    bla = true;
                    break out;
                }
            }
            if(!bla) {
                out.println("NO");
                return;
            }
            f = -1;
            i = 0;
            while(i<n) {
                int v = a[i][0], c = 0;
                while(i<n && a[i][0]==v) {
                    c++;
                    i++;
                }
                if(c==1) {
                    rs[a[i-1][1]] = f;
                    f*=-1;
                    int j = i - 1;
                    if(a[j][0]==999) {
                        j--;
                        if(j>=0) {
                            v = a[j][0];
                            while(j>=0 && a[j][0]==v) {
                                rs[a[j][1]] = f;
                                j--;
                            }
                        }
                    }
                }
            }
            out.println("YES");
            for(i=0; i<n; i++) {
                if(rs[i]==-1) out.print("B");
                else out.print("A");
            }
            out.println();
        }
    }
    
    
    public static void main(String[] args) throws IOException {
        if(args.length>0 && args[0].equalsIgnoreCase("d")) {
            DEBUG_FLAG = true;
        }
        InputReader in = new InputReader();
        PrintWriter out = new PrintWriter(System.out);
        int t = 1;//in.nextInt();
        long start = System.nanoTime();
        while(t-->0) {
            new test().solve(in, out);
        }
        long end = System.nanoTime();
        debug("\nTime: " + (end-start)/1e6 + " \n\n");
        out.close();
    }
    
    static boolean DEBUG_FLAG = false;
    static void debug(String s) {
        if(DEBUG_FLAG) System.out.print(s);
    }
    
    public static void show(Object... o) {
        System.out.println(Arrays.deepToString(o));
    }
    
    static class InputReader {
        static BufferedReader br;
        static StringTokenizer st;
    
        public InputReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        
        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        
        int nextInt() {
            return Integer.parseInt(next());
        }
        
        long nextLong() {
            return Long.parseLong(next());
        }
        
        double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}