Problem: The only difference between problems C1 and C2 is that all values in input of problem C1 are distinct (this condition may be false for problem C2).

You are given a sequence a consisting of n integers.

You are making a sequence of moves. During each move you must take either the leftmost element of the sequence or the rightmost element of the sequence, write it down and remove it from the sequence. Your task is to write down a strictly increasing sequence, and among all such sequences you should take the longest (the length of the sequence is the number of elements in it).

For example, for the sequence [1, 2, 4, 3, 2] the answer is 4 (you take 1 and the sequence becomes [2, 4, 3, 2], then you take the rightmost element 2 and the sequence becomes [2, 4, 3], then you take 3 and the sequence becomes [2, 4] and then you take 4 and the sequence becomes [2], the obtained increasing sequence is [1, 2, 3, 4]).

Input

The first line of the input contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of elements in a.

The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 2 ⋅ 10^5), where a_i is the i-th element of a.

Output

In the first line of the output print k — the maximum number of elements in a strictly increasing sequence you can obtain.

In the second line print a string s of length k, where the j-th character of this string s_j should be 'L' if you take the leftmost element during the j-th move and 'R' otherwise. If there are multiple answers, you can print any.

Examples

Input


5
1 2 4 3 2


Output


4
LRRR


Input


7
1 3 5 6 5 4 2


Output


6
LRLRRR


Input


3
2 2 2


Output


1
R


Input


4
1 2 4 3


Output


4
LLRR

Note

The first example is described in the problem statement.

Solution (in JAVA):

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

public class Main {
    static  OutputWriter out;
    public static void main(String[] args) throws Exception
    {
        Scanner in = new Scanner(System.in);
        out = new OutputWriter(System.out);
        int n = in.nextInt();
        int[]a = new int[n];
        for (int i =0;i<n;i++)
            a[i]=in.nextInt();
        int p0=0;
        int p1=n-1;
        List<Character>l = new ArrayList<>();
        PriorityQueue<Integer> p = new PriorityQueue<>();
        while (p0<=p1)
        {
            if (p.isEmpty()||(a[p0]>-p.peek()&&a[p1]>-p.peek())) {
                if (a[p0] < a[p1]) {
                    l.add('L');
                    p.add(-a[p0]);
                    p0++;
                }
                else if (a[p1]<a[p0]){
                    l.add('R');
                    p.add(-a[p1]);
                    p1--;
                }
                else
                {
                    int  p2=p0+1;
                    int p3 = p1-1;
                    int max0=a[p0];
                    int max1 = a[p1];
                    while (p2<=p1&&p3>=p0)
                    {
                        if (a[p2]<=max0&&a[p3]>max1)
                        {
                            while (p1>=p0)
                            {
                                if (p.isEmpty()||a[p1]>-p.peek())
                                {
                                    l.add('R');
                                    p.add(-a[p1]);
                                    p1--;
                                }
                                else
                                    break;

                            }
                            p0=n;
                            p1=-1;
                            break;
                        }
                        else if (a[p2]>max0&&a[p3]<=max1)
                        {
                            while (p0<=p1)
                            {
                                if (p.isEmpty()||a[p0]>-p.peek())
                                {
                                    l.add('L');
                                    p.add(-a[p0]);
                                    p0++;
                                }
                                else
                                    break;
                            }
                            p0=n;
                            p1=-1;
                            break;
                        }
                        max0=a[p2];
                        max1=a[p3];
                        p2++;
                        p3--;
                    }
                    if (p0!=-1)
                    {

                        while (p0<=p1)
                        {
                            if (p.isEmpty()||a[p1]>-p.peek())
                            {
                                l.add('R');
                                p.add(-a[p1]);
                                p1--;
                            }
                            else
                                break;
                        }
                        p0=n;
                        p1=-1;
                        break;
                    }

                }
            }
            else
            {
                if (a[p0]>-p.peek())
                {
                    l.add('L');
                    p.add(-a[p0]);
                    p0++;
                }
                else if (a[p1]>-p.peek())
                {
                    l.add('R');
                    p.add(-a[p1]);
                    p1--;
                }
                else
                    break;
            }
        }
        out.printLine(l.size());
        for (char item:l
                ) {
            out.print(item);
        }
        out.flush();
    }

}

class Graph {


    int n;
    ArrayList<Integer>[] adjList;

    public Graph(int n) {
        this.n = n;
        adjList = new ArrayList[n];
        for (int i = 0; i < n; i++)
            adjList[i] = new ArrayList<>();
    }

}
class pair  implements Comparable
{

    int key;
    int value;

    public pair(Object key, Object value) {

        this.key = (int)key;
        this.value=(int)value;

    }

    @Override
    public int compareTo(Object o) {
        pair temp =(pair)o;
        return  key-temp.key;
    }
}
class Scanner {

    StringTokenizer st;
    BufferedReader br;

    public Scanner(InputStream s) {
        br = new BufferedReader(new InputStreamReader(s));
    }

    public Scanner (FileReader f) {
        br = new BufferedReader(f);
    }

    public String next() throws IOException {
        while (st == null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

    public int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    public long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    public String nextLine() throws IOException {
        return br.readLine();
    }

    public double nextDouble() throws IOException {
        String x = next();
        StringBuilder sb = new StringBuilder("0");
        double res = 0, f = 1;
        boolean dec = false, neg = false;
        int start = 0;
        if (x.charAt(0) == '-') {
            neg = true;
            start++;
        }
        for (int i = start; i < x.length(); i++)
            if (x.charAt(i) == '.') {
                res = Long.parseLong(sb.toString());
                sb = new StringBuilder("0");
                dec = true;
            } else {
                sb.append(x.charAt(i));
                if (dec)
                    f *= 10;
            }
        res += Long.parseLong(sb.toString()) / f;
        return res * (neg ? -1 : 1);
    }

    public boolean ready() throws IOException {
        return br.ready();
    }

    public boolean nextEmpty() throws IOException {
        String s = nextLine();
        st = new StringTokenizer(s);
        return s.isEmpty();
    }
}
class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }

    public void print(Object... objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0)
                writer.print(' ');
            writer.print(objects[i]);
        }
    }


    public void printLine(Object... objects) {
        print(objects);
        writer.println();
    }

    public void close() {
        writer.close();
    }

    public void flush() {
        writer.flush();
    }

}