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.util.*;
import java.io.*;
import java.math.*;
import java.awt.geom.*;
import static java.lang.Math.*;
public class Main implements Runnable
{
    boolean multiiple = false;

    void solve() throws Exception
    {
        int n = sc.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = sc.nextInt();
        int last = 0;
        StringBuilder ans = new StringBuilder();
        int left = 0, right = n - 1;

        while (a[left] > last || a[right] > last && left <= right)
        {
            if (left == right)
            {
                ans.append('L');
                break;
            }

            if (a[left] == a[right])
            {
                int h = max(bestLeft(a, left), bestRight(a, right));
                if (bestLeft(a, left) > bestRight(a, right))
                    for (int i = 0; i < h; i++)
                        ans.append('L');
                else
                    for (int i = 0; i < h; i++)
                        ans.append('R');

                break;
            }

            if ((a[left] < a[right] && a[left] > last) || (a[right] <= last))
            {
                last = a[left];
                ans.append('L');
                left++;
            }
            else
            {
                last = a[right];
                ans.append('R');
                right--;
            }
        }

        String s = ans.toString();
        System.out.println(s.length());
        System.out.println(s);
    }

    int bestLeft(int[] a, int start)
    {
        int length = 1;
        for (; length + start < a.length; length++)
            if (a[length + start] <= a[length + start - 1])
                return length;
        return -1;
    }

    int bestRight(int[] a, int start)
    {
        int length = 1;
        for (; start - length > 0; length++)
            if (a[start - length] <= a[start - length + 1])
                return length;
        return -1;
    }

    @Override
    public void run()
    {
        try
        {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
            sc = new FastScanner(in);
            if (multiiple)
            {
                int q = sc.nextInt();
                for (int i = 0; i < q; i++)
                    solve();
            }
            else
                solve();
        }
        catch (Throwable uncaught)
        {
            Main.uncaught = uncaught;
        }
        finally
        {
            out.close();
        }
    }

    public static void main(String[] args) throws Throwable {
        Thread thread = new Thread(null, new Main(), "", (1 << 26));
        thread.start();
        thread.join();
        if (Main.uncaught != null) {
            throw Main.uncaught;
        }
    }

    static Throwable uncaught;
    BufferedReader in;
    FastScanner sc;
    PrintWriter out;
}

class FastScanner
{
    BufferedReader in;
    StringTokenizer st;

    public FastScanner(BufferedReader in)
    {
        this.in = in;
    }

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

    public int nextInt() throws Exception {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws Exception {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws Exception {
        return Double.parseDouble(nextToken());
    }

}