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 LL long long
using namespace std;
const int maxn = 1010;
int n;
LL x[maxn],y[maxn],u[maxn],v[maxn],bs[35];

LL power_int(int a, int b) {
  LL x = 1;
  while (b > 0) {x *= a;b--;}
  return x;
}

void work() {
  cin >> n;
  for (int i = 0; i < n; i++) cin >> x[i] >> y[i];

  LL parity = (x[0] + y[0]) % 2;

  for (int i = 0; i < n; i++) if ((x[i] + y[i] - parity) % 2 != 0) {cout<<"-1"<<endl;return;}

    if (parity == 0) {
      cout << 32 << endl;
      for (int i = 30; i > -1; i--) {
        cout << power_int(2, i) << " ";
      }
      cout << 1 << endl;
      for (int i = 0; i < n; i++) {
        x[i]++;
      }
    }
    else {
      cout << 31 << endl;
      for (int i = 30; i > -1; i--) {
        cout << power_int(2, i) << " ";
      }
      cout << endl;
    }

    for (int i = 0; i < n; i++) u[i] = x[i] + y[i], v[i] = x[i] - y[i];

    for (int i = 0; i < n; i++) {
        for (int j = 30; j > -1; j--) {
            if (u[i] > 0 && v[i] > 0) {cout << 'R'; u[i] -= power_int(2, j); v[i] -= power_int(2, j); }
            else if (u[i] > 0 && v[i] < 0) { cout << 'U'; u[i] -= power_int(2, j); v[i] += power_int(2, j); }
            else if (u[i] < 0 && v[i] > 0) { cout << 'D'; u[i] += power_int(2, j); v[i] -= power_int(2, j); }
            else { cout << 'L'; u[i] += power_int(2, j); v[i] += power_int(2, j);}
        }
        if (parity == 0) cout << 'L';
        cout << endl;
    }
}
int main(){
    work();
    return 0;
}