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 JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.util.InputMismatchException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;
 
/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }
 
    static class TaskD {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            long[] x = new long[n];
            long[] y = new long[n];
            for (int i = 0; i < n; i++) {
                x[i] = in.nextLong();
                y[i] = in.nextLong();
            }
 
            boolean isAllOdd = true;
            boolean isAllEven = true;
            for (int i = 0; i < n; i++) {
                if ((x[i] + y[i]) % 2 == 0) isAllOdd = false;
                else isAllEven = false;
            }
 
            if (!(isAllOdd ^ isAllEven)) {
                out.println(-1);
                return;
            }
 
            if (isAllEven) {
                for (int i = 0; i < n; i++) {
                    x[i] -= 1;
                }
            }
 
            for (int i = 0; i < n; i++) {
                long tmpX = x[i];
                long tmpY = y[i];
                x[i] = tmpX - tmpY;
                y[i] = tmpX + tmpY;
            }
 
            if (isAllEven) {
                out.println(38);
                out.print("1 ");
            } else {
                out.println(37);
            }
            for (int i = 0; i < 37; i++) {
                if (i > 0) out.print(" ");
                out.print(1L << 36 - i);
            }
            out.println();
 
            for (int i = 0; i < n; i++) {
                if (isAllEven) out.print("R");
 
                for (int j = 36; j >= 0; j--) {
                    if (x[i] > 0) {
                        if (y[i] > 0) {
                            out.print("R");
                            y[i] -= 1L << j;
                        } else {
                            out.print("D");
                            y[i] += 1L << j;
                        }
                        x[i] -= 1L << j;
                    } else {
                        if (y[i] > 0) {
                            out.print("U");
                            y[i] -= 1L << j;
                        } else {
                            out.print("L");
                            y[i] += 1L << j;
                        }
                        x[i] += 1L << j;
                    }
                }
 
                out.println();
            }
        }
 
    }
 
    static class InputReader {
        private BufferedReader br;
        private StringTokenizer st;
 
        public InputReader(InputStream inputStream) {
            br = new BufferedReader(new InputStreamReader(inputStream));
            st = new StringTokenizer("");
        }
 
        public String nextString() {
            while (!st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine(), " ");
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
            }
            return st.nextToken();
        }
 
        public int nextInt() {
            return Integer.parseInt(nextString());
        }
 
        public long nextLong() {
            return Long.parseLong(nextString());
        }
 
    }
}