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 <bits/stdc++.h>

using namespace std;

using ll = long long;
int dx[4] = {1, -1, 0, 0};
int dy[4] = {0, 0, 1, -1};
char ch[4] = {'R', 'L', 'U', 'D'};

int main(){
  ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
  cout.setf(ios::fixed); cout.precision(17);
  int n;
  cin >> n;
  vector<long long> x(n), y(n);
  for(int i = 0; i < n; i++){
    cin >> x[i] >> y[i];
  }
  for(int i = 1; i < n; i++){
    if(((x[0] + y[0]) & 1) != ((x[i] + y[i]) & 1)){
      cout << "-1\n";
      return 0;
    }
  }
  vector<long long> moves;
  for(int i = 30; i >= 0; i--){
    moves.push_back((1<<i));
  }
  if((x[0] + y[0]) % 2 == 0){ // same parity throws an even lenght, so add +1 to 1,2,4,...
    moves.push_back(1);
  }
  cout << moves.size() << "\n";
  for(int i = 0; i < moves.size(); i++){
    cout << moves[i] << " ";
  } cout << "\n";
  for(int i = 0; i < n; i++){
    string seq = "";
    ll xx = 0, yy = 0;
    for(int k = 0; k < moves.size(); k++){
      ll _min = 1e11;
      int at = -1;
      for(int j = 0; j < 4; j++){
        ll dist = abs( moves[k] * dx[j] - x[i]) + abs( moves[k]* dy[j] - y[i]);
        if(dist < _min){
          _min = dist;
          at = j;
        }
      }
      seq += ch[at];
      xx += moves[k] * dx[at];
      yy += moves[k] * dy[at];
      x[i] -= moves[k] * dx[at];  // now the origin is at (moves[at]*dx[at], moves[at]*dy[at])
      y[i] -= moves[k] * dy[at];  // i.e. (-4,0), so x and y must shifft.
    }
    //cout << xx << " " << yy << "\n";
    cout << seq << "\n";
  }
  return 0;
}