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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class VasyaAndMultisets {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        int n = Integer.parseInt(st.nextToken());
        int[] a = new int[n];
        int[] count = new int[100 + 1];

        st = new StringTokenizer(br.readLine());

        for (int i = 0; i < n; i++) {
            a[i] = Integer.parseInt(st.nextToken());
            count[a[i]]++;
        }

        int singles = 0, multiIndex = -1;
        for(int i=0; i<101; i++){
            if(count[i] == 1){
                singles++;
                continue;
            }
            if(multiIndex == -1 && count[i] >2){
                multiIndex = i;
            }
        }

        int multi = -1;
        if(singles % 2 == 1){
            if(multiIndex == -1){
                System.out.println("NO");
                return;
            }
            multi = multiIndex;
        }

        System.out.println("YES");
        for(int i=0; i<n; i++){
            if(multi == a[i]){
                System.out.print("A");
                multi = -1;
                continue;
            }

            if(count[a[i]] == 1){
                if(singles % 2 == 0){
                    System.out.print("A");
                } else {
                    System.out.print("B");
                }
                singles--;
            } else {
                System.out.print("B");
            }

        }
        System.out.println();
    }
}




/*
Trying to maximise the number of nice elements

public class VasyaAndMultisets {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        int n = Integer.parseInt(st.nextToken());
        int[] a = new int[n];
        int[] count = new int[100 + 1];

        st = new StringTokenizer(br.readLine());

        int distinct = 0;
        for(int i=0; i<n; i++){
            a[i] = Integer.parseInt(st.nextToken());
            if(count[a[i]] == 0){
                distinct++;
            }
            count[a[i]]++;
        }

        int two = 0;
        if(distinct%2 == 1){
            int multipleIndex = 0;
            for(int i=0; i<101; i++){
                if(count[i] == 2){
                    two++;
                }
                if(count[i] > 2){
                    multipleIndex = i;
                }
            }

            if(two%2 == 1){
                distinct += two;
            } else {
                if(multipleIndex == 0 && count[0] <= 1){
                    System.out.println("NO");
                    return;
                }
                count[multipleIndex] = -1;
                distinct--;
            }
        }

        System.out.println("YES");
        for(int i=0; i<n; i++){
            if(count[a[i]] == 0){
                continue;
            }
            if(count[a[i]] == -1){
                System.out.print("A");
                continue;
            }
            if(count[a[i]] == -2){
                System.out.print("B");
                continue;
            }

            if(distinct%2 == 0){
                System.out.print("A");
                count[a[i]] = -2;
            } else {
                System.out.print("B");
                count[a[i]] = -1;
            }
            distinct--;
        }
        System.out.println();
    }
}
*/