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 <iostream>
#include <vector>
#include <cstdlib>

using namespace std;

typedef long long LL;

#define ARRAY_LENGTH(array) (sizeof(array) / sizeof(array[0]))
#define ALL(a)  (a).begin(),(a).end()
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n)  FOR(i,0,n)

#define dump(x)  cerr << #x << " = " << (x) << endl;



int main() {
  int N;
  cin >> N;
  vector<int> X(N), Y(N);
  int odd;
  REP(i, N) {
    cin >> X[i] >> Y[i];
  }

  int max_d = abs(X[0]) + abs(Y[0]);
  odd = abs(X[0]) + abs(Y[0]) & 1;
  FOR(i, 1, N) {
    if (((abs(X[i]) + abs(Y[i])) & 1) ^ odd) {
      cout << -1 << endl;
      return 0;
    }
    if (max_d < (abs(X[i]) + abs(Y[i]))) max_d = abs(X[i]) + abs(Y[i]);
  }

  int sum = 1, m = 1;
  
  for(m=1; m<31; ++m) {
    if (sum > max_d) break;
    sum *= 2;
  }
  sum = sum*2-1;
  cout << m + !odd << endl;
  int temp = 1;
  REP(i, m) {
    cout << temp << ' ';
    temp *= 2;
  }
  if (!odd) cout << 1;
  cout << endl;

  REP(i, N) {
    if (!odd) {
      X[i] -= 1;
    }
    int U = X[i] + Y[i], V = X[i] - Y[i];
    int U1 = (sum-U)/2, V1 = (sum-V)/2;
    REP(j, m) {
      int LD = U1 & 1;
      int LU = V1 & 1;
      
      if (LD & LU) cout << 'L';
      else if (LD & (~LU)) cout << 'D';
      else if ((~LD) & LU) cout << 'U';
      else cout << 'R';

      U1 >>= 1;
      V1 >>= 1;
    }
    if (!odd) cout << 'R';
    cout << endl;
  }

  return 0;
}