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:
from __future__ import division, print_function
 
import os
import sys
from io import BytesIO, IOBase
from collections import deque
 
if sys.version_info[0] < 3:
    from __builtin__ import xrange as range
    from future_builtins import ascii, filter, hex, map, oct, zip
else:
    _str = str
    str = lambda x=b"": x if type(x) is bytes else _str(x).encode()
 
 
def main():
    n = int(readline())
    a = deque(readlist())
 
    res, seq = [], [0]
    while a:
        if len(a) == 1 and a[0] > seq[-1]:
            seq.append(a.pop())
            res.append('R')
        elif a[0] < a[-1] and a[0] > seq[-1]:
            seq.append(a.popleft())
            res.append('L')
        elif a[-1] < a[0] and a[-1] > seq[-1]:
            seq.append(a.pop())
            res.append('R')
        elif a[0] == a[-1] and a[0] > seq[-1]:
            case_1, case_2 = 1, 1
            start = a[0]
            i = 1
            while i < len(a) and a[i] > start:
                start = a[i]
                i += 1
                case_1 += 1
            start = a[-1]
            i = len(a) - 2
            while i >= 0 and a[i] > start:
                start = a[i]
                i -= 1
                case_2 += 1
            res += ['L'] * case_1 if case_1 > case_2 else ['R'] * case_2
            break
        elif a[0] > seq[-1]:
            seq.append(a.popleft())
            res.append('L')
        elif a[-1] > seq[-1]:
            seq.append(a.pop())
            res.append('R')
        else:
            break
 
    print(len(res))
    print(''.join(res))
 
 
# region template
 
BUFSIZE = 8192
 
 
class FastIO(IOBase):
    newlines = 0
 
    def __init__(self, file):
        self._buffer = BytesIO()
        self._fd = file.fileno()
        self._writable = "x" in file.mode or "r" not in file.mode
        self.write = self._buffer.write if self._writable else None
 
    def read(self):
        if self._buffer.tell():
            return self._buffer.read()
        return os.read(self._fd, os.fstat(self._fd).st_size)
 
    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self._buffer.tell()
            self._buffer.seek(0, 2), self._buffer.write(b), self._buffer.seek(ptr)
        self.newlines -= 1
        return self._buffer.readline()
 
    def flush(self):
        if self._writable:
            os.write(self._fd, self._buffer.getvalue())
            self._buffer.truncate(0), self._buffer.seek(0)
 
 
class ostream:
    def __lshift__(self, a):
        if a is endl:
            sys.stdout.write(b"\n")
            sys.stdout.flush()
        else:
            sys.stdout.write(str(a))
        return self
 
 
def print(*args, **kwargs):
    sep, file = kwargs.pop("sep", b" "), kwargs.pop("file", sys.stdout)
    at_start = True
    for x in args:
        if not at_start:
            file.write(sep)
        file.write(str(x))
        at_start = False
    file.write(kwargs.pop("end", b"\n"))
    if kwargs.pop("flush", False):
        file.flush()
 
 
sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
cout, endl = ostream(), object()
 
readline = sys.stdin.readline
readlist = lambda var=int: [var(n) for n in readline().split()]
input = lambda: readline().rstrip(b"\r\n")
 
# endregion
 
if __name__ == "__main__":
    main()