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>
#include <unordered_set>
using namespace std;
#define ll long long
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define repeat(i,s,n) for(int (i)=s; (i)<(n); (i)++)
#define revrep(i,n) for(int (i)=(n)-1;i>=0; i--)

ll man_dist(ll x1, ll y1, ll x2, ll y2) {
  return abs(x1-x2)+abs(y1-y2);
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout<<setprecision(std::numeric_limits<float>::max_digits10);
  int n;
  cin>>n;
  vector<ll> x(n);
  vector<ll> y(n);
  vector<ll> p(n);
  rep(i,n)cin>>x[i]>>y[i];
  rep(i,n) p[i]=(abs(x[i])+abs(y[i]))%2;
  rep(i,n) {
    if(p[i]!=p[0]) {
      cout << "-1" << endl;
      return 0;
    }
  }
  vector<ll> ds;
  ll t = 1;
  rep(i,39) {
    ds.push_back(t);
    t*=2;
  }
  if(p[0]==0) ds.push_back(1);
  sort(ds.begin(),ds.end());
  reverse(ds.begin(),ds.end());
  cout << ds.size() << endl;
  for(auto& d : ds) {
    cout << d << " ";
  }
  cout << endl;
  rep(i,n) {
    stringstream ss;
    ll cx=0;
    ll cy=0;
    for(auto& d : ds) {
      vector<tuple<ll,char, ll, ll>> t;
      t.push_back(make_tuple(man_dist(x[i],y[i],cx+d,cy),'R',cx+d,cy));
      t.push_back(make_tuple(man_dist(x[i],y[i],cx-d,cy),'L',cx-d,cy));
      t.push_back(make_tuple(man_dist(x[i],y[i],cx,cy+d), 'U',cx,cy+d));
      t.push_back(make_tuple(man_dist(x[i],y[i],cx,cy-d), 'D',cx,cy-d));
      sort(t.begin(),t.end());
      ll md;
      char direction;
      ll nx,ny;
      tie(md,direction,nx,ny)=t[0];
      ss<<direction;
      cx=nx;
      cy=ny;
    }
    cout << ss.str() << endl;
  }
  return 0;
}