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>
#define rep(i, n) for(int i=0; i<(n); i++)
using namespace std;

int main(){
  int n; cin >> n;
  int x[n], y[n];
  cin >> x[0] >> y[0];
  int mod = abs(x[0]+y[0])%2;
  bool flag = false;
  for(int i=1; i<n; i++){
    cin >> x[i] >> y[i];
    if(abs(x[i]+y[i])%2 != mod){
      flag = true;
      break;
    }
  }
  if(flag) cout << -1 << endl;
  else{
    cout << 32-mod << endl;
    rep(i, 31) cout << (int)pow(2, i) << " ";
    if(mod == 0) cout << 1;
    cout << "" << endl;
    bool u[31], v[31];
    rep(i, n){
      if(mod == 0) y[i]--;
      rep(j, 31) u[j] = v[j] = false;
      rep(j, 31){
        if((((x[i]+y[i]-1)/2+(int)pow(2, 30))>>j)&1) u[j] = true;
        if((((x[i]-y[i]-1)/2+(int)pow(2, 30))>>j)&1) v[j] = true;
      }
      rep(j, 31){
        if(u[j] && v[j]) cout << "R";
        if(u[j] && !v[j]) cout << "U";
        if(!u[j] && v[j]) cout << "D";
        if(!u[j] && !v[j]) cout << "L";
      }
      if(mod == 0) cout << "U";
      cout << "" << endl;
    }
  }
}