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:
#define NDEBUG

#include <bits/stdc++.h>

using namespace std;
using pii = pair<int, int>;

#ifdef NDEBUG
#  define debug(...)
#else
#  include "debug.hh"
#endif

const int N = 1000;
int n, x[N], y[N];

void move(int i, int len) {
  if (abs(x[i]) > abs(y[i])) {
    if (x[i] > 0) {
      cout << 'R';
      x[i] -= len;
    } else {
      cout << 'L';
      x[i] += len;
    }
  } else {
    if (y[i] > 0) {
      cout << 'U';
      y[i] -= len;
    } else {
      cout << 'D';
      y[i] += len;
    }
  }
}

int main() {
  ios_base::sync_with_stdio(false), cin.tie(0), cout << fixed;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> x[i] >> y[i];
  bool odd = (abs(x[0]) + abs(y[0])) % 2;
  for (int i = 1; i < n; i++) {
    if ((abs(x[i]) + abs(y[i])) % 2 != odd) {
      cout << "-1\n";
      return 0;
    }
  }
  int m = 31 + !odd;
  cout << m << '\n';
  if (!odd) cout << "1 ";
  for (int k = 30; k >= 0; k--) cout << (1<<k) << (k == 0 ? '\n' : ' ');
  for (int i = 0; i < n; i++) {
    if (!odd) move(i, 1);
    for (int k = 30; k >= 0; k--) move(i, 1<<k);
    assert(x[i] == 0);
    assert(y[i] == 0);
    cout << '\n';
  }
  return 0;
}