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 <bits/stdc++.h>
using namespace std;

const int mn = 1010;

int x[mn], y[mn];
int d[50];
char ch[50];
int main()
{
	int n;	scanf("%d", &n);
	for (int i = 1; i <= n; i++)
		scanf("%d %d", &x[i], &y[i]);

	int cnt1 = 0, cnt2 = 0;
	for (int i = 1; i <= n; i++)
	{
		if ((abs(x[i]) + abs(y[i])) % 2 == 1)	cnt1++;
		else	cnt2++;
	}
	if (cnt1 && cnt2)
	{
		printf("-1\n");
		return 0;
	}

    int num = 0;
    if (cnt2)	d[++num] = 1;
    for (int i = 0; i <= 30; i++)
		d[++num] = (1 << i);

	printf("%d\n", num);
	for (int i = 1; i <= num; i++)
		printf("%d ", d[i]);
	printf("\n");

    for (int i = 1; i <= n; i++)
	{
		int cnt = 0;
		for (int j = num; j >= 1; j--)
		{
            if (abs(x[i]) > abs(y[i]))
			{
				if (x[i] > 0)
				{
					ch[++cnt] = 'L';
					x[i] -= d[j];
				}
				else if (x[i] <= 0)
				{
					ch[++cnt] = 'R';
					x[i] += d[j];
				}
			}
			else if (abs(x[i]) <= abs(y[i]))
			{
				if (y[i] > 0)
				{
					ch[++cnt] = 'D';
					y[i] -= d[j];
				}
				else if (y[i] <= 0)
				{
					ch[++cnt] = 'U';
					y[i] += d[j];
				}
			}
			//cout << x[i] << ' ' << y[i] << endl;
		}

		for (int i = cnt; i >= 1; i--)
		{
			if (ch[i] == 'L')	printf("R");
			if (ch[i] == 'R')	printf("L");
			if (ch[i] == 'U')	printf("D");
			if (ch[i] == 'D')	printf("U");
		}
		printf("\n");
	}


	return 0;
}