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;
#define REP(i,N) for(i=0;i<N;i++)
typedef long long ll;
typedef pair<ll, ll> P;
typedef struct{
  int first;
  int second;
  int third;
}T;

//昇順
bool comp_Se(T& l, T& r){
  return l.second < r.second;
}

int N;
vector<P> v;

int main(void){
  bool sat=true;
  cin >> N;
  int i,j,mode;
  vector<ll> d;
  v.resize(N);
  ll x,y,max=0,length=0,L;
  REP(i,N){
    cin >> x >> y;
    if(!i) mode = abs(x+y)%2;
    else if(abs(x+y)%2 != mode) sat = false;
    if(max < abs(x) + abs(y)) max = abs(x) + abs(y);
    v[i].first = x;
    v[i].second = y;
  }
  if(!sat){
    cout << -1 << endl;
    return 0;
  }
  if(!mode){
    d.push_back(1);
    length++;
  }
  while(max>length){
    if(d.size() + mode==1)d.push_back(1);
    else d.push_back(2*d[d.size()-1]);
    length += d[d.size()-1];
  }
  sort(d.begin(),d.end(),greater<ll>());

  cout << d.size() << endl;
  REP(i,d.size()) cout << d[i] << " ";
  cout << endl;
  REP(i,N){
    x = v[i].first;
    y = v[i].second;
    L = length;
    REP(j,d.size()){
      if(abs(x+d[j])+abs(y)<=L-d[j]){
        cout << "L";
        x += d[j];
        L -= d[j];
      }else if(abs(x-d[j])+abs(y)<=L-d[j]){
        cout << "R";
        x -= d[j];
        L -= d[j];
      }else if(abs(x)+abs(y+d[j])<=L-d[j]){
        cout << "D";
        y += d[j];
        L -= d[j];
      }else if(abs(x)+abs(y-d[j])<=L-d[j]){
        cout << "U";
        y -= d[j];
        L -= d[j];
      }else{
      }
    }
    cout << endl;
  }


  return 0;
}