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 <iostream>
#include <cstdio>
#define N 1005
using namespace std;

int n, x[N], y[N];

int abs(int p) {return p > 0 ? p : -p;}

int main()
{
	int i, j;
	cin >> n;
	for (i = 0; i < n; i++) scanf("%d %d", &x[i], &y[i]);
	for (i = 1; i < n; i++) {
		if (abs(x[i] + y[i]) % 2 != abs(x[i - 1] + y[i - 1]) % 2) {
			puts("-1");
			return 0;
		}
	}
	if (abs(x[0] + y[0]) % 2) {
		puts("31");
		for (i = 30; i >= 0; i--) printf("%d ", 1 << i);
		puts("");
	} else {
		puts("32");
		for (i = 30; i >= 0; i--) printf("%d ", 1 << i);
		puts("1");
	}
    for (i = 0; i < n; i++) {
		for (j = 30; j >= 0; j--) {
			if (abs(x[i]) > abs(y[i])) {
				if (x[i] > 0) {
					printf("R");
					x[i] -= 1 << j;
				} else {
					printf("L");
					x[i] += 1 << j;
				}
			} else {
				if (y[i] > 0) {
					printf("U");
					y[i] -= 1 << j;
				} else {
					printf("D");
					y[i] += 1 << j;
				}
			}
		}
		if (x[i] == 1) printf("R");
		else if (x[i] == -1) printf("L");
		else if (y[i] == 1) printf("U");
		else if (y[i] == -1) printf("D");
		puts("");
    }
    return 0;
}