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>

#define MAX_N 1000
typedef long long int ll;

int main() {
  int n;
  ll u[MAX_N], v[MAX_N];

  std::cin >> n;
  for(int i = 0; i < n; ++i) {
    ll x, y;
    std::cin >> x >> y;
    u[i] = x + y;
    v[i] = x - y;
  }

  bool flg;
  int mod;
  for(int i = 0; i < n; ++i) {
    if(i == 0) mod = std::abs(u[i]) % 2;
    flg = mod == std::abs(u[i]) % 2;
    if(!flg) break;
  }
  if(!flg) {
    std::cout << -1 << std::endl;
    return 0;
  }

  std::vector<ll> arms;
  int m = 31;
  for(int i = m - 1; i >= 0; --i) {
    arms.push_back(1LL << i);
  }
  if(mod == 0) {
    arms.push_back(1LL);
    ++m;
  }


  std::cout << m << std::endl;
  for(int i = 0; i < m; ++i) {
    std::cout << arms[i] << " ";
  }
  std::cout << std::endl;

  for(int i = 0; i < n; ++i) {
    std::string ans = "";
    for(int j = 0; j < m; ++j) {
      if(u[i] >= 0 && v[i] >= 0) {
        u[i] -= arms[j];
        v[i] -= arms[j];
        ans.push_back('R');
      } else if(u[i] >= 0 && v[i] < 0) {
        u[i] -= arms[j];
        v[i] += arms[j];
        ans.push_back('U');
      } else if(u[i] < 0 && v[i] >= 0) {
        u[i] += arms[j];
        v[i] -= arms[j];
        ans.push_back('D');
      } else if(u[i] < 0 && v[i] < 0) {
        u[i] += arms[j];
        v[i] += arms[j];
        ans.push_back('L');
      }
    }
    //std::cout << "(" << u[i] << ", " << v[i] << ")" << std::endl;
    std::cout << ans << std::endl;
  }
}