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:
// Problem : D - Robot Arms
// Contest : AtCoder Regular Contest 103
// URL : https://atcoder.jp/contests/arc103/tasks/arc103_b
// Memory Limit : 1024 MB
// Time Limit : 2000 ms
// Powered by CP Editor (https://github.com/cpeditor/cpeditor)

#include <iostream>
#include <algorithm>
#include <vector>
using namespace std;
struct node
{
 int x,y;
}p[1005];
const char s[]="LRDU";
char res[55];
vector<int> d;
int main()
{
 int n,op;
 cin>>n;
 for(int i=1;i<=n;i++)
 {
  cin>>p[i].x>>p[i].y;
  if(i==1)op=(p[i].x+p[i].y)&1;
  else if(op!=((p[i].x+p[i].y)&1))
  {
   cout<<-1<<endl;
   return 0;
  }
 }
 cout<<32-op<<endl;
 cout<<1<<' ';
 d.push_back(0),d.push_back(1);
 for(int i=op;i<=30;i++)
 {
  d.push_back(1<<i);
  cout<<(1<<i)<<' ';
 }
 cout<<endl;
 for(int i=1;i<=n;i++)
 {
  long long x=0,y=0,tx=p[i].x,ty=p[i].y;
  for(int j=32-op;j;j--)
  {
   if(abs(tx-x)>abs(ty-y))
   {
    if(tx-x>0)res[j]='R',x=x+d[j];
    else res[j]='L',x=x-d[j];
   }
   else
   {
    if(ty-y>0)res[j]='U',y=y+d[j];
    else res[j]='D',y=y-d[j];
   }
  }
  cout<<(res+1)<<endl; 
 }
 return 0;
}