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 = int(input())
a = list(map(int, input().split()))
res = []
end = True
right = n - 1
left = 0
prev = 0
allowLeft = True
allowRight = True
while end:
    d_r = a[right] - prev
    if d_r <= 0 or not allowRight:
        d_r = 300000
    d_l = a[left] - prev
    if d_l <= 0 or not allowLeft:
        d_l = 300000
    if d_l < d_r and allowLeft:
        prev = a[left]
        res.append('L')
        left += 1
    elif d_r < d_l and allowRight:
        prev = a[right]
        res.append('R')
        right -= 1
    elif d_r == d_l:
        if d_r == 300000:
            end = False
        elif left == right:
            prev = a[right]
            res.append('R')
            right -= 1
        elif left != right:
            left_edge = True
            left_2 = left
            prev_2 = prev
            while a[left_2] > prev_2:
                prev_2 = a[left_2]
                left_2 += 1
            right_2 = right
            prev_2 = prev
            while a[right_2] > prev_2:
                prev_2 = a[right_2]
                right_2 -= 1
            if right - right_2 > left_2 - left:
                allowLeft = False
            else:
                allowRight = False
    if left > right:
        end = False
print(len(res))
for i in res:
    print(i, end='')