Problem: Snuke is introducing a robot arm with the following properties to his factory:

* The robot arm consists of m sections and m+1 joints. The sections are numbered 1, 2, ..., m, and the joints are numbered 0, 1, ..., m. Section i connects Joint i-1 and Joint i. The length of Section i is d_i.
* For each section, its mode can be specified individually. There are four modes: `L`, `R`, `D` and `U`. The mode of a section decides the direction of that section. If we consider the factory as a coordinate plane, the position of Joint i will be determined as follows (we denote its coordinates as (x_i, y_i)):
* (x_0, y_0) = (0, 0).
* If the mode of Section i is `L`, (x_{i}, y_{i}) = (x_{i-1} - d_{i}, y_{i-1}).
* If the mode of Section i is `R`, (x_{i}, y_{i}) = (x_{i-1} + d_{i}, y_{i-1}).
* If the mode of Section i is `D`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} - d_{i}).
* If the mode of Section i is `U`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} + d_{i}).



Snuke would like to introduce a robot arm so that the position of Joint m can be matched with all of the N points (X_1, Y_1), (X_2, Y_2), ..., (X_N, Y_N) by properly specifying the modes of the sections. Is this possible? If so, find such a robot arm and how to bring Joint m to each point (X_j, Y_j).

Constraints

* All values in input are integers.
* 1 \leq N \leq 1000
* -10^9 \leq X_i \leq 10^9
* -10^9 \leq Y_i \leq 10^9

Input

Input is given from Standard Input in the following format:


N
X_1 Y_1
X_2 Y_2
:
X_N Y_N


Output

If the condition can be satisfied, follow the following format. If the condition cannot be satisfied, print `-1`.


m
d_1 d_2 ... d_m
w_1
w_2
:
w_N


m and d_i are the configurations of the robot arm. Refer to the problem statement for what each of them means. Here, 1 \leq m \leq 40 and 1 \leq d_i \leq 10^{12} must hold. Also, m and d_i must all be integers.

w_j is a string of length m that represents the way to bring Joint m of the robot arm to point (X_j, Y_j). The i-th character of w_j should be one of the letters `L`, `R`, `D` and `U`, representing the mode of Section i.

Examples

Input

3
-1 0
0 3
2 -1


Output

2
1 2
RL
UU
DR


Input

5
0 0
1 0
2 0
3 0
4 0


Output

-1


Input

2
1 1
1 1


Output

2
1 1
RU
UR


Input

3
-7 -3
7 3
-3 -7


Output

5
3 1 4 1 5
LRDUL
RDULR
DULRD

Solution (in CPP):

Solution:
#include <cmath>
#include <iostream>
#include <vector>
#include <tuple>

using lli=long long;
int main(){
  int N;
  std::cin >> N;

  std::vector<std::tuple<lli, lli>> pos_arr(N);
  for(int i = 0; i < N; i++) std::cin >> std::get<0>(pos_arr[i]) >> std::get<1>(pos_arr[i]);

  int par = (std::abs(std::get<0>(pos_arr[0]))+std::abs(std::get<1>(pos_arr[0])))%2;
  for(int i = 1; i < N; i++){
    if(par != (std::abs(std::get<0>(pos_arr[i]))+std::abs(std::get<1>(pos_arr[i])))%2){
      std::cout << "-1" << std::endl;
      return 0;
    }
  }

  if(par==0) std::cout << "40\n1 ";
  else std::cout << "39\n";
  std::vector<lli> d_arr(39);
  for(int i = 0; i < 39; i++){
    d_arr[i] = 1ll << (38-i);
    std::cout << d_arr[i] << (i==39-1?"\n":" ");
  }


  for(int i = 0; i < N; i++){
    lli x,y;
    std::tie(x,y) = pos_arr[i];
    lli cx=0, cy=0;
    if(par==0){
      cx++;
      std::cout << "R";
    }
    for(int j = 0; j < 39; j++){
      lli dx=x-cx, dy=y-cy;
      if(std::abs(dx)>std::abs(dy)){
        if(dx<0){
          cx -= d_arr[j];
          std::cout << "L";
        }else{
          cx += d_arr[j];
          std::cout << "R";
        }
      }else{
        if(dy<0){
          cy -= d_arr[j];
          std::cout << "D";
        }else{
          cy += d_arr[j];
          std::cout << "U";
        }
      }
    }
    std::cout << "\n";
  }

  return 0;
}