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(){
  int n;
  cin >> n;
  typedef pair<int,int> P;
  vector<P> coordinate = {};
  int x,y;
  int tmp;
  int maximum = 0;
  bool flag = false;
  for (int i = 0; i<n; i++){
    cin >> x >> y;
    maximum = max(maximum,abs(x)+abs(y));
    if (i==0) {
      tmp = (abs(x) + abs(y))%2;
      if (tmp%2==0) flag = true;
    }
    //if (x+y)%2 dose not match with tmp, we cannot meat the condition
    else if (tmp != (abs(x) + abs(y))%2){
      cout << -1 << endl;
      exit(0);
    }
    if (flag) x--;
    coordinate.push_back({x,y});
  }
  //出力
  //case:tmp%2==0 you should add 1 to some direction
  int ranges = 1;
  while (1){
    if (maximum < pow(2,ranges)) break;
    else ranges++;
  }
  //m:the number of arms
  if (flag) cout << ranges+1 << endl;
  else cout << ranges << endl;
  //d:the length of arms
  if (flag) cout << 1 << " ";
  for (int i = ranges-1; i>=0; i--){
    cout << (int)pow(2,i);
    if (i!=0) cout << " ";
    else cout << endl;
  }
  //w:the mode of each arms
  vector<int> dx={1,-1,0,0};
  vector<int> dy={0,0,1,-1};
  vector<char> dz={'R','L','U','D'};
  for (int i=0; i<n; i++){
    x=coordinate[i].first;
    y=coordinate[i].second;
    if (flag){
      cout << 'R';
    }
    for (int j=ranges-1; j>=0; j--){
    for (int k=0; k<4; k++){
      if (abs(x-dx[k]*pow(2,j))+abs(y-dy[k]*pow(2,j))<pow(2,j)){
        cout << dz[k];
        x-=pow(2,j)*dx[k];
        y-=pow(2,j)*dy[k];
        break;
      }
    }
    }
    cout << endl;
  }
}