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.util.Scanner;
import java.util.stream.IntStream;

/**
 * 解説どおりに作成したソースコード
 * 
 * https://atcoder.jp/contests/abc111/submissions/3312161 にも参考
 */
public class Main {

	/** モード一覧 */
	private static final char[] MODES = { 'L', 'D', 'U', 'R' };

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			int n = scanner.nextInt();
			int[] u = new int[n], v = new int[n];
			IntStream.range(0, n).forEach(i -> {
				int x = scanner.nextInt(), y = scanner.nextInt();
				u[i] = x + y;
				v[i] = x - y;
			});
			int r = u[0] & 1;
			for (int i = 1; i < n; i++) {
				if (r != (u[i] & 1)) {
					System.out.println("-1");
					return;
				}
			}
			r = 1 - r;
			int m = 31;
			System.out.println(m + r);
			StringBuilder answer = new StringBuilder();
			if (r > 0) {
				answer.append("1").append(" ");
			}
			IntStream.range(0, m).forEach(i -> answer.append(1 << i).append(" "));
			// 最後のスペースを削除
			answer.deleteCharAt(answer.length() - 1);
			System.out.println(answer.toString());

			long base = (1L << m) - 1 - r;
			for (int i = 0; i < n; i++) {
				StringBuilder sb = new StringBuilder();
				if (r > 0) {
					sb.append('R');
				}
				long uBase = (u[i] + base) >> 1, vBase = (v[i] + base) >> 1;
				for (int j = 0; j < m; j++) {
					int u1 = (int) (uBase & 1L) << 1;
					int v1 = (int) (vBase & 1L);
					sb.append(MODES[u1 + v1]);
					uBase >>= 1;
					vBase >>= 1;
				}
				System.out.println(sb.toString());
			}
		}
	}
}