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 static java.lang.Math.*;

import java.util.*;

public class Main {
    int dx[] = { 0, 1, 0, -1 };
    int dy[] = { 1, 0, -1, 0 };
    char dr[] = "DLUR".toCharArray();

    private class Point {
        long x, y, len;
        boolean isOdd;

        public Point(int x, int y) {
            this.x = x;
            this.y = y;
            this.len = abs(x) + abs(y);
            this.isOdd = (x + y) % 2 == 0;
        }
    }

    public void main(Scanner sc) {
        int n = sc.nextInt();
        Point p[] = new Point[n];
        BitSet bs = new BitSet();
        long max = 0;

        for (int i = 0; i < n; i++) {
            p[i] = new Point(sc.nextInt(), sc.nextInt());
            if (p[i].isOdd) {
                bs.set(i);
            }
            max = max(max, p[i].len);
        }
        sc.close();

        if (bs.cardinality() > 0 && bs.cardinality() < n) {
            System.out.println(-1);
            return;
        }

        boolean isOdd = bs.cardinality() == n;
        if (isOdd) {
            for (int i = 0; i < n; i++) {
                p[i].x--;
            }
        }

        int m = 0;
        for (; max > 0; m++) {
            max /= 2;
        }
        long l[] = new long[m];
        for (int i = 0; i < m; i++) {
            l[i] = 1L << i;
        }
        System.out.println(m + (isOdd ? 1 : 0));
        System.out.println((isOdd ? "1 " : "") + Arrays.toString(l).replaceAll("[^0-9 ]+", ""));

        for (int i = 0; i < n; i++) {
            char move[] = new char[m];
            long nx = p[i].x;
            long ny = p[i].y;

            for (int j = m - 1; j >= 0; j--) {
                for (int k = 0; k < 4; k++) {
                    if (check(nx + l[j] * dx[k], ny + l[j] * dy[k], l[j])) {
                        nx += l[j] * dx[k];
                        ny += l[j] * dy[k];
                        move[j] = dr[k];
                        break;
                    }
                }
            }

            if (isOdd) {
                System.out.print("R");
            }
            System.out.println(new String(move));
        }
    }

    private boolean check(long x, long y, long range) {
        return abs(x) + abs(y) <= (range - 1);
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        new Main().main(sc);
    }
}