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 {

    public static void main(String[] args) throws IOException {
//        br = new BufferedReader(new FileReader(new File("input.txt")));
//        out = new PrintWriter(new File("output.txt"));
        int nasral = 1;
        for (int JOPA = 0; JOPA < nasral; JOPA++) {
            int n = nextInt();
            int[] a = new int[n];
            int min = 0;
            int ind_l = 0;
            int ind_r = n - 1;
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            ArrayList<Character> ans = new ArrayList<>();
            while (ind_l <= ind_r) {
                if (a[ind_l] == a[ind_r]) {
                    int cntl = 0;
                    int cntr = 0;
                    int minr = min;
                    int indrr = ind_r;
                    while (indrr >= ind_l) {
                        if (a[indrr] > minr) {
                            minr = a[indrr];
                            indrr--;
                            cntr++;
                        } else break;
                    }
                    int minl = min;
                    int indll = ind_l;
                    while (indll <= ind_r) {
                        if (a[indll] > minl) {
                            minl = a[indll];
                            indll++;
                            cntl++;
                        }else break;
                    }
                    if(cntl >= cntr){
                        for (int i = 0; i < cntl; i++) {
                            ans.add('L');
                        }
                    }else {
                        for (int i = 0; i < cntr; i++) {
                            ans.add('R');
                        }
                    }
                    break;
                } else if (a[ind_l] < a[ind_r]) {
                    if (a[ind_l] > min) {
                        min = a[ind_l];
                        ind_l++;
                        ans.add('L');
                    } else if (a[ind_r] > min) {
                        min = a[ind_r];
                        ind_r--;
                        ans.add('R');
                    } else break;
                } else {
                    if (a[ind_r] > min) {
                        min = a[ind_r];
                        ind_r--;
                        ans.add('R');
                    } else if (a[ind_l] > min) {
                        min = a[ind_l];
                        ind_l++;
                        ans.add('L');
                    } else break;
                }
            }
            out.println(ans.size());
            for (Character jopa : ans) out.print(jopa);
        }
        out.close();

    }


    public static StringTokenizer in = new StringTokenizer("");
    public static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    public static PrintWriter out = new PrintWriter(System.out);

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

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

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