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:
// review
#include <iostream>
#include <vector>

using namespace std;
typedef long long ll;
const int MAXN = 1010;
const ll INF = 1e14;

int n;
ll x[MAXN], y[MAXN];
char mode[4] = {'L', 'R', 'U', 'D'};
int du[4] = {-1, 1, 1, -1};
int dv[4] = {-1, 1, -1, 1};

void solve() {
  int parity = (x[0] + y[0]) & 1;
  for (int i=0;i<n;i++) {
    if (parity != ((x[i] + y[i]) & 1)) {
      cout << -1 << endl;
      return;
    }
  }

  vector<ll> arms;
  for (int i=38;i>=0;i--) {
    arms.push_back(1LL << i);
  }
  if (parity == 0) {
    arms.push_back(1LL);
  }

  cout << arms.size() << endl;
  for (int i=0;i<arms.size();i++) {
    cout << arms[i] << " ";
  }
  cout << endl;

  for (int i=0;i<n;i++) {
    ll u = x[i] + y[i];
    ll v = x[i] - y[i];
    for (int j=0;j<arms.size();j++) {
      ll minDist = INF;
      int direction;
      for (int k=0;k<4;k++) {
        ll nu = u - du[k] * arms[j];
        ll nv = v - dv[k] * arms[j];
        if (minDist > abs(nu) + abs(nv)) {
          minDist = abs(nu) + abs(nv);
          direction = k;
        }
      }
      u = u - du[direction] * arms[j];
      v = v - dv[direction] * arms[j];
      cout << mode[direction];
    }
    cout << endl;
  }
}

int main() {
  cin >> n;
  for (int i=0;i<n;i++) {
    cin >> x[i] >> y[i];
  }
  solve();
}