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 CPP):

Solution:
#include <bits/stdc++.h>
#pragma GCC optimize("O3")
#pragma comment(linker, "/stack:200000000")
#pragma GCC optimize("unroll-loops")
using namespace std;
const double pi = acos(-1);
bool isVowel(char ch) {
  if (ch == 'a' || ch == 'e' || ch == 'i' || ch == 'o' || ch == 'u') {
    return 1;
  }
  return 0;
}
bool compare(pair<long long, long long> a, pair<long long, long long> b) {
  return a.second < b.second;
}
bool isPrime(long long n) {
  if (n % 2 == 0 && n != 2) {
    return false;
  }
  for (long long i = 3; i * i <= n; i += 2) {
    if (n % i == 0) {
      return false;
    }
  }
  return true;
}
long long power(long long x, long long y, long long p) {
  long long res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
long long modInverse(long long a, long long p) { return power(a, p - 2, p); }
long long modFact(long long n, long long p) {
  if (p <= n) return 0;
  long long res = (p - 1);
  for (long long i = n + 1; i < p; i++) res = (res * modInverse(i, p)) % p;
  return res;
}
long long binary_exp(long long x, long long n, long long mod) {
  if (n == 0) {
    return 1;
  } else if (n == 1) {
    return x % mod;
  } else {
    long long temp = binary_exp(x, n / 2, mod);
    temp = (temp * temp) % mod;
    if (n % 2 == 0) {
      return temp;
    } else {
      return ((x % mod) * temp) % mod;
    }
  }
}
map<long long, list<long long>> m;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int t = 1;
  while (t--) {
    long long n;
    string s = "";
    cin >> n;
    long long arr[n];
    for (long long i = 0; i < n; i++) {
      cin >> arr[i];
    }
    long long x = 0, y = n - 1, m = -1;
    while (x <= y) {
      if (arr[x] > m && arr[y] <= m) {
        m = arr[x];
        s += "L";
        x++;
      } else if (arr[x] <= m && arr[y] > m) {
        m = arr[y];
        s += "R";
        y--;
      } else if (arr[x] > m && arr[y] > m) {
        if (arr[x] < arr[y]) {
          m = arr[x];
          x++;
          s += "L";
        } else if (arr[x] == arr[y]) {
          if (x == y) {
            s += "L";
            break;
          }
          long long a = x, b = y, mx = m;
          string sa = "", sb = "";
          for (long long i = a; i < b; i++) {
            if (arr[i] > mx) {
              sa += "L";
              mx = arr[i];
            } else {
              break;
            }
          }
          mx = m;
          for (long long i = b; i > a; i--) {
            if (arr[i] > mx) {
              sb += "R";
              mx = arr[i];
            } else {
              break;
            }
          }
          if (sa.size() > sb.size()) {
            s += sa;
            break;
          } else {
            s += sb;
            break;
          }
        } else {
          m = arr[y];
          y--;
          s += "R";
        }
      } else {
        break;
      }
    }
    cout << s.length() << endl;
    cout << s << endl;
  }
}