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;
long N,M,X[1000],Y[1000],f[2],xdir,ydir,xsum,ysum;
vector<long>d;
int main(){
  cin>>N;
  for(long i=0;i<N;i++){
    cin>>X[i]>>Y[i];
    f[(X[i]+Y[i])%2]=1;
  }
  if(f[0]==f[1]){
    cout<<-1<<endl;
    return 0;
  }
  for(long i=30;i>=0;i--)d.push_back(1L<<i);
  if(f[0])d.push_back(1);
  M=d.size();
  cout<<M<<endl;
  for(long i=0;i<M-1;i++)cout<<d[i]<<" ";
  cout<<d[M-1]<<endl;
  for(long i=0;i<N;i++){
    xsum=ysum=0;
    for(long j=0;j<M;j++){
      if(xsum<=X[i]+Y[i])xdir=1,xsum+=d[j];
      else xdir=-1,xsum-=d[j];
      if(ysum<=X[i]-Y[i])ydir=1,ysum+=d[j];
      else ydir=-1,ysum-=d[j];
      if((xdir==1)&&(ydir==1))cout<<"R";
      else if((xdir==1)&&(ydir==-1))cout<<"U";
      else if((xdir==-1)&&(ydir==-1))cout<<"L";
      else cout<<"D";
    }
    cout<<endl;
  }
}