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. All these integers are distinct, each value from 1 to n appears in the sequence exactly once.

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 [2, 1, 5, 4, 3] the answer is 4 (you take 2 and the sequence becomes [1, 5, 4, 3], then you take the rightmost element 3 and the sequence becomes [1, 5, 4], then you take 4 and the sequence becomes [1, 5] and then you take 5 and the sequence becomes [1], the obtained increasing sequence is [2, 3, 4, 5]).

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 ≤ n), where a_i is the i-th element of a. All these integers are pairwise distinct.

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
2 1 5 4 3


Output


4
LRRR


Input


7
1 3 5 6 7 4 2


Output


7
LRLRLLL


Input


3
1 2 3


Output


3
LLL


Input


4
1 2 4 3


Output


4
LLRL

Note

The first example is described in the problem statement.

Solution (in JAVA):

Solution:
// @jagrit_07.
import java.util.*;
import java.math.*;
import java.io.*;
import java.lang.*;

public class Main {
	public static void main(String[] args) {
        FastReader sc = new FastReader();
        int length=0;
        int last = 0;
        int n = sc.nextInt();
        int a[] = sc.nextIntArray(n);
        int max = 0;
        int i=0;
        int j=n-1;
        StringBuffer bf = new StringBuffer("");
        while(i<=j)
        {
            if(i==j && a[i]>last)
            {
                bf.append("L");
                i++;
                j--;
            }
            else if(a[i]>last && a[j]>last)
            {
                if(a[i]==a[j])
                {
                    //Now here I have choice but only once;
                    //I can take only one turn, either go left, or right;
                    //If I choice a[j];
                    StringBuffer bf1 = new StringBuffer(bf.toString());
                    int j1=j;
                    int last1=last;
                    while(j1>=i && a[j1]>last1)
                    {
                        bf1.append("R");
                        //choice1++;
                        last1=a[j1];
                        j1--;
                    }
                    StringBuffer bf2 = new StringBuffer(bf.toString());
                    //int choice2=0;
                    int last2=last;
                    int i1=i;
                    while(i1<=j && a[i1]>last2)
                    {
                        bf2.append("L");
                        //choice2++;
                        last2=a[i1];
                        i1++;
                    }
                    if(bf1.length()>bf2.length())
                    {
                        System.out.println(bf1.length()+"\n"+bf1.toString());
                        return;
                    }
                    else
                    {
                        System.out.println(bf2.length()+"\n"+bf2.toString());
                        return;
                    }
                }
                if(a[i]<a[j])
                {
                   bf.append("L");
                   last=a[i];
                   i++; 
                }
                else
                {
                    bf.append("R");
                    last=a[j];
                    j--;
                }
            }
            else if(a[i]>last)
            {
                   bf.append("L");
                   last=a[i];
                   i++; 
            }
            else if(a[j]>last)
            {
                bf.append("R");
                    last=a[j];
                    j--;
            }
            else
            {
                break;
            }
        }
        System.out.println(bf.length()+"\n"+bf.toString());
        
    }
    public static void findDivisors(HashSet<Integer> hs, int num)
    {
        for(int i=2;i<=Math.sqrt(num);i++)
        {
            if(num%i==0)
            {
                if(num/i!=i)
                {
                    hs.add(i);
                    hs.add(num/i);
                }
                else
                {
                    hs.add(i);
                }
            }
        }
    }
    static class Pair
    {
        long x;
        long y;

        //int i;
        public Pair(long x, long  y)
        {
            this.x=x;
            this.y=y;
        }
    }
    static class Comp implements Comparator<Pair>
    {
        public int compare(Pair p1, Pair p2)
        {
            if(p1.x>p2.x)
            {
                return 1;
            }
            if(p1.x<p2.x)
            {
                return -1;
            }
            if(p1.y>p2.y)
            {
                return -1; 
            }
            if(p1.y<p2.y)
            {
                return 1;
            }
            return 0;
        }
    }


    public static int bs(int num[], long x)
    {
        int low=0;
        int high=num.length-1;
        int ans=-1;
        while(low<=high)
        {
            int mid = low + (high-low)/2;
            if(num[mid]==x)
            {
                ans = mid;
                //break;
                low = mid+1;
            }
            else if(num[mid]<x)
            {
               // ans=mid;
                ans = mid;
                low=mid+1;
            }
            else
            {
                //ans=mid;
                high=mid-1;
            }
        }
        return ans;
    }
    
    
    
    
    
    
    
    
    
    
    //Comparing two list;
    public static List<Integer> comp(List<Integer> l1, List<Integer> l2)
    {
        if(l1.size()<l2.size()) return l1;
        if(l2.size()<l1.size()) return l2;
        
        for(int i=0;i<l1.size();i++)
        {
            if(l1.get(i)<l2.get(i))
            {
                return l1;
            }
            else if(l2.get(i)<l1.get(i))
            {
                return l2;
            }
        }
        return l2;
    }
   
    
   
    
 
    /* to find (x^y)%p in O(log y) */
    static long power(long x, long y, int p) 
    { 
        // Initialize result 
        long ans = 1;      
         
        // Update x if it is more   
        // than or equal to p 
        x = x % p;  
  
       if (x == 0) return 0; // In case x is divisible by p;    
  
        while (y > 0) 
        { 
            if((y & 1)==1) 
            {
                 ans = ((long)(ans * x))% p;    
            }
            y = y >> 1;  //y/2; 
            x = ((long)(x * x) )% p;  
        } 
        return ans; 
    } 
    
    
    
    
    
    public static void printList(List<Integer> list)
    {
        StringBuffer bf = new StringBuffer("");
        for(int i: list) bf.append(i+" ");
        System.out.println(bf.toString());
    }
    
    
    
    
    
    public static int sum(int a[])
    {
        int sum=0;
        for(int i: a) sum=sum+i;
        return sum;
    }
    
  
    public static int getMax(int a[])
    {
        int m=Integer.MIN_VALUE;
        for(int i: a) m=Math.max(i,m);
        return m;
    }
 
    
    
    
    public static int partition(int arr[], int low, int high) 
    { 
        int pivot = arr[high];  
        int i = (low-1);
        for (int j=low; j<high; j++) 
        { 
            if (arr[j] < pivot) 
            { 
                i++; 
                int temp = arr[i]; 
                arr[i] = arr[j]; 
                arr[j] = temp; 
            } 
        } 
        int temp = arr[i+1]; 
        arr[i+1] = arr[high]; 
        arr[high] = temp; 
  
        return i+1; 
    } 
    public static void sort(int arr[], int low, int high) 
    { 
        if (low < high) 
        { 
            int pi = partition(arr, low, high); 
            sort(arr, low, pi-1); 
            sort(arr, pi+1, high); 
        } 
    } 
    
    
    
    
    
    
    static long gcd(long a,long b)
    {
        if(b==0) return a;
        return gcd(b,a%b);
    }
    
    
    static void sort(int[] a) {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}
    static void sort(long[] a) {
		ArrayList<Long> l=new ArrayList<>();
		for (long i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}
    
	static class FastReader {
		BufferedReader br;
		StringTokenizer st;
 
		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
 
		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (final 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());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (final IOException e) {
				e.printStackTrace();
			}
			return str;
		}

		int[] nextIntArray(final int n) {
			final int a[] = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = Integer.parseInt(next());
			}
			return a;
		}

	}	
}
//private ArrayList<String[]> action = new ArrayList<String[]>();


//Templates for Comparator and Classes - @jagrit_07
/*
Arrays.sort(newEmployees, new Comparator<Employee>() {
    @Override
    public int compare(Employee emp1, Employee emp2) {
        return emp1.getName().compareTo(emp2.getName());
    }
});
class Pair
	{
		
		long i; //index;
		long l; //left;
		long c; //cost;
		public Pair(long x,long y,long z)
		{
			this.i=x;
			this.l=y;
			this.c=z;
		}
		public String toString()
		{
			return this.i+" "+this.l+" "+this.c;
		}
	}
class Comp implements Comparator<Pair>
	{
		public int compare(Pair p1, Pair p2)
		{
			if(p1.c!=p2.c)
			{
				return (int)(p1.c-p2.c); //sort acc to cost;
			}
			else{
				return (int)(p1.i-p2.i); //sort acc to index;
			}
			
		}
	}
*/

/*
System.out.println( 
      String.format("%.5f", b)); 
  HashMap - Put template - d.put(a1,d.getOrDefault(a1,0)+1);
  for (Map.Entry<String, Integer> entry : map.entrySet()) {
        System.out.println(entry.getKey() + ":" + entry.getValue());
    }
  Deque<String> deque 
            = new LinkedList<String>();  
            
  List<Integer> c[] = new ArrayList[3];          
*/