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 PYTHON3):

Solution:
n = input()
data = input()

# n = 15
# data = "37504 79054 80071 95721 135743 164345 189260 190810 191657 196168 200000 200000 190810 190018 185437"
# n = 11
# data = "1 2 3 7 8 10 11 12 17 18 1 1"
data = data.split(' ')
def Left_or_Right_Move(data_temp,direct):
	#data_temp 	: list of number
	#direct		: left of right ('L' or 'R') 
	str_temp = direct
	i_ = 0
	j_ = len(data_temp)-1
	if(direct == 'L'): 	#move left to right
		while(i_ + 1 < j_) :
			if int(data_temp[i_]) < int(data_temp[i_+1]):
				str_temp += 'L'
				i_+=1
			else:
				return str_temp

	else:				#move right to left
		while(j_-1>0) :
			if int(data_temp[j_]) < int(data_temp[j_-1]):
				str_temp += 'R'
				j_-=1
			else:
				return str_temp
	return str_temp

def find_increase_string():
	i = 0
	j = int(n)-1
	sub_sequence = []
	str_ = ""

	if int(data[0]) > int(data[-1]) :
		temp = int(data[-1])
		idx = -1
	elif int(data[0]) < int(data[-1]) :
		temp = int(data[0])
		idx = 0
	else:
		l_ = Left_or_Right_Move(data[i:j+1],'L')
		r_ = Left_or_Right_Move(data[i:j+1],'R')
		if len(l_)> len(r_):
			str_ += l_
		else:
			str_ += r_
		print(len(str_))
		print(str_)
		return

	sub_sequence.append(temp)
	if(idx == 0):
		str_+='L'
		i += 1
	else:
		str_+='R'
		j -= 1

	while(i <= j):
		d0 = int(data[i]) 
		d1 = int(data[j])
		if d0 > d1:
			if d1 > sub_sequence[-1]:
				sub_sequence.append(d1)
				str_+='R'
				j -= 1
			elif d0 > sub_sequence[-1] :
				sub_sequence.append(d0)
				str_+='L'
				i += 1
			else : 
				break
		elif d0 < d1: # data[0] <= data[-1]
			if d0 > sub_sequence[-1]:
				sub_sequence.append(d0)
				str_+='L'
				i += 1
			elif d1 > sub_sequence[-1]:
				sub_sequence.append(d1)
				str_+='R'
				j -= 1
			else:	break
		else:
			if(d0 > sub_sequence[-1]):
				l_ = Left_or_Right_Move(data[i:j+1],'L')
				r_ = Left_or_Right_Move(data[i:j+1],'R')
				if len(l_)> len(r_):
					str_ += l_
				else:
					str_ += r_
			break
	print(len(str_))
	print(str_)

#l_ = Left_or_Right_Move([1],'R')
#print(l_)
find_increase_string()