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:
# list input
def linp(): return list(map(int, input().split()))


# map input
def minp(): return map(int, input().split())


# int input
def iinp(): return int(input())


# no of testcase
def test(): return int(input())


# normal input
def inp(): return input()

def fun(l, curr, res):
    while l:
        if l[0]> curr and l[-1]>curr:
            if l[0] < l[-1]:
                curr = l.pop(0)
                res+= 'L'
            elif l[-1] > l[0]:
                curr = l.pop()
                res += 'R'
            else:
                pass
        elif l[0]> curr:
            curr = l.pop(0)
            res += 'L'
        elif l[-1] > curr:
            curr = l.pop()
            res += 'R'
        else:
            break
    return res



def solve():
    # write your solution for one testcase
    n = iinp()
    l = linp()
    curr = -1
    res = ''
    while l:
        if l[0]> curr and l[-1]>curr:
            if l[0] < l[-1]:
                curr = l.pop(0)
                res+= 'L'
                n-=1
            elif l[0] > l[-1]:
                curr = l.pop()
                res += 'R'
                n-=1
            else:
                flag = 'L'
                i, j = 0, n-1

                counti, countj = 0, 0
                while i < n-1 and j >0:
                    flag1 = True
                    if l[i+1] > l[i]:
                        counti += 1
                        i+=1
                        flag1 =False
                    if l[j-1] > l[j]:
                        countj += 1
                        j-=1
                        flag1 = False
                    if counti>countj:
                        flag = 'L'
                        break
                    elif countj>counti:
                        flag = 'R'
                        break
                    if flag1:
                        break
                # print(flag)
                if flag == 'L':
                    curr = l.pop(0)
                    res += 'L'
                else:
                    curr = l.pop()
                    res += 'R'

        elif l[0]> curr:
            curr = l.pop(0)
            res += 'L'
            n-=1
        elif l[-1] > curr:
            curr = l.pop()
            res += 'R'
            n-=1
        else:
            break
    print(str(len(res)) + '\n' + res)





def main():
    # for _ in range(test()):
        solve()


if __name__ == '__main__':
    main()