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 <cstdio>

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

int main()
{
	int N, X[1000], Y[1000];
	int i, j, odd, m = 1;
	long long u, v, tmp, length = 0;

	std::scanf("%d", &N);
	for (i = 0; i < N; i++) {
		std::scanf("%d %d", X + i, Y + i);
		tmp = abs(X[i]) + abs(Y[i]);
		if (tmp > length)
			length = tmp;
	}

	odd = (abs(X[0]) + abs(Y[0])) & 1;
	for (i = 1; i < N; i++)
		if (((abs(X[i]) + abs(Y[i])) ^ odd) & 1) {
			std::printf("-1\n");
			return 0;
		}

	tmp = 1, length -= !odd;
	while (tmp < length) {
		tmp *= 2;
		m++;
	}
	length = tmp;

	std::printf("%d\n", m + !odd);
	for (i = 0; i < m; i++) {
		std::printf("%lld ", tmp);
		tmp >>= 1;
	}
	if (!odd)
		std::printf("1");
	std::putchar('\n');

	for (i = 0; i < N; i++) {
		X[i] -= !odd;
		u = X[i] + Y[i], v = X[i] - Y[i], tmp = length;
		for (j = 0; j < m; j++) {
			if (u > 0) {
				if (v > 0) {
					std::putchar('R');
					u -= tmp, v -= tmp;
				}
				else {
					std::putchar('U');
					u -= tmp, v += tmp;
				}
			}
			else {
				if (v > 0) {
					std::putchar('D');
					u += tmp, v -= tmp;
				}
				else {
					std::putchar('L');
					u += tmp, v += tmp;
				}
			}
			tmp /= 2;
		}
		if (!odd)
			std::putchar('R');
		std::putchar('\n');
	}

	return 0;
}