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;

int main() {

  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  vector<int> x(n);
  vector<int> y(n);
  for (int i=0;i<n;i++) cin >> x[i] >> y[i];
  bool odd = true;
  bool even = true;
  for (int i=0;i<n;i++) {
    if ((abs(x[i])+abs(y[i]))%2 == 0) {
      odd = false;
    }
    else {
      even = false;
    }
  } 
  if (!odd && !even) {
    cout << -1 << endl;
  } 
  else {
    vector<long long> arms(33,1);
    vector<long long> sums(33,0);
    if (odd) {
      for (int i=31;i>=0;i--) {
        arms[i] = arms[i+1]*2;
        sums[i] = sums[i+1]+arms[i+1];
      }
    }
    if (even) {
      sums[31] = 1;
      for (int i=30;i>=0;i--) {
        arms[i] = arms[i+1]*2;
        sums[i] = sums[i+1]+arms[i+1];
      } 
    } 
    cout << 33 << endl;
    for (int i=0;i<33;i++) {
      if (i != 0) cout << ' ';
      cout << arms[i];
    }
    cout << endl;
    vector<int> dx={0,1,0,-1};
    vector<int> dy={1,0,-1,0};
    vector<char> dir={'D','L','U','R'};
    for (int i=0;i<n;i++) {
      long long nx = x[i];
      long long ny = y[i];
      for (int j=0;j<33;j++) {
        for (int k=0;k<4;k++) {
          long long tox = nx+arms[j]*dx[k];
          long long toy = ny+arms[j]*dy[k];
          if(abs(tox)+abs(toy) <= sums[j]) {
            cout << dir[k];
            nx = tox;
            ny = toy;
            break;
          }
        }
      }
      cout << endl;
    }
  }
  
}