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 <algorithm>
#include <cmath>
#include <cstdint>
#include <iostream>
#include <vector>

using namespace std;

int main() {
  int N;
  cin >> N;
  vector<int64_t> us(N);
  vector<int64_t> vs(N);

  int64_t x, y;
  cin >> x >> y;
  int mod = abs(x + y) % 2;
  us[0] = x + y, vs[0] = x - y;
  for (int n = 1; n < N; ++n) {
    cin >> x >> y;
    if (mod != abs(x + y) % 2) {
      cout << -1 << endl;
      return 0;
    }
    us[n] = x + y, vs[n] = x - y;
  }
  int m = 31 + (mod^1);
  cout << m << endl;
  vector<int64_t> ds(m);
  for (int i = 0, size = ds.size(); i < size; ++i) {
    ds[i] = 1ll << max(30 - i, 0);
    if (i) cout << " ";
    cout << ds[i];
  }
  cout << endl;
  for (int n = 0; n < N; ++n) {
    string dir = "";
    int64_t u = us[n], v = vs[n]; 
    for (int64_t d : ds) {
      if (u >= 0) {
        if (v >= 0) {
          dir += "R";
          u -= d, v -= d;
        } else {
          dir += "U";
          u -= d, v += d;
        }
      } else {
        if (v >= 0) {
          dir += "D";
          u += d, v -= d;
        } else {
          dir += "L";
          u += d, v += d;
        }
      }
    }
    cout << dir << endl;
  }
  return 0;
}