## Algorithm

C2. Increasing Subsequence (hard version)
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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][1,2,4,3,2] the answer is 44 (you take 11 and the sequence becomes [2,4,3,2][2,4,3,2], then you take the rightmost element 22 and the sequence becomes [2,4,3][2,4,3], then you take 33 and the sequence becomes [2,4][2,4] and then you take 44 and the sequence becomes [2][2], the obtained increasing sequence is [1,2,3,4][1,2,3,4]).

Input

The first line of the input contains one integer n (1n21051≤�≤2⋅105) — the number of elements in a.

The second line of the input contains n integers a1,a2,,an�1,�2,…,�� (1ai21051≤��≤2⋅105), where ai�� 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 sj�� 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
Copy
5
1 2 4 3 2

output
Copy
4
LRRR

input
Copy
7
1 3 5 6 5 4 2

output
Copy
6
LRLRRR

input
Copy
3
2 2 2

output
Copy
1
R

input
Copy
4
1 2 4 3

output
Copy
4
LLRR

Note

The first example is described in the problem statement.

## Code Examples

### #1 Code Example with C++ Programming

Code - C++ Programming

#include <bits/stdc++.h>

using namespace std;

int const N = 2e5 + 10;
int n, a[N];

int main() {
scanf("%d", &n);
for(int i = 0; i < n; ++i)
scanf("%d", a + i);

int l = 0, r = n - 1, lst = -1;
string res = "";

while(l <= r && a[l] != a[r]) {
if(a[l] < a[r] && a[l] > lst) {
lst = a[l++];
res += 'L';
} else if(a[r] < a[l] && a[r] > lst) {
lst = a[r--];
res += 'R';
} else if(a[l] > lst) {
lst = a[l++];
res += 'L';
} else if(a[r] > lst) {
lst = a[r--];
res += 'R';
} else
break;
}

if(l == r && a[l] > lst)
res += 'L', ++l;
else if(l < r && a[l] == a[r] && a[l] > lst) {
int lst1 = lst;
string res1 = res;
int lst2 = lst;
string res2 = res;

for(int i = l; i <= r; ++i)
if(a[i] > lst1) {
lst1 = a[i];
res1 += 'L';
} else
break;

for(int i = r; i >= l; --i) {
if(a[i] > lst2) {
lst2 = a[i];
res2 += 'R';
} else
break;
}

if(res1.length() > res2.length())
res = res1;
else
res = res2;
}

printf("%d\n", int(res.length()));
puts(res.c_str());

return 0;
}
Copy The Code &

Input

cmd
5
1 2 4 3 2

Output

cmd
4
LRRR