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;
typedef long long ll;
#define rep(i, N) for (int i = 0; i < (int)N; i++)

typedef pair<int, int> sig;

int main () {
  map<sig, char> dir;
  dir[sig(+1, +1)] = 'R';
  dir[sig(+1, -1)] = 'U';
  dir[sig(-1, +1)] = 'D';
  dir[sig(-1, -1)] = 'L';

  int N;
  cin >> N;
  vector<int> U(N), V(N);

  rep(i,N) {
    int X, Y;
    cin >> X >> Y;
    U[i] = X + Y;
    V[i] = X - Y;
  }

  int p = U[0] & 1;
  rep(i,N) {
    if((U[i] & 1) != p) {
      cout << "-1" << endl;
      return 0;
    }
  }


  int m = 31;
  cout << m + (!p) << endl;
  if(!p) cout << "1 ";
  for(int i = m - 1; i >= 0; i--) {
    cout << (1<<i);
    if(i != 0) cout << " ";
  }
  cout << endl;

  rep(i,N) {
    int u = 0, v = 0;
    if(!p) {
      cout << 'R';
      u++; v++;
    }

    for(int j = m - 1; j >= 0; j--) {
      int d = (1<<j);

      sig s = sig((U[i]-u)/abs(U[i] - u), (V[i] - v)/abs(V[i] - v));
      u += d*s.first;
      v += d*s.second;
      cout << dir[s];
    }
    cout << endl;
  }

  return 0;
}