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>
#define N 1003

int n,m;
int arm[50];
int x[N],y[N];
bool odd[2];

inline int Abs(int x) {
	if(x>-x) return x;return -x;
}
//1:Up 2:Down 3:Left 4:Right
void Print(int x,int y) {
	for(int i=1;i<=m;i++) {
		if(Abs(x)<Abs(y)) {
			if(y>0)
				printf("U"),y-=arm[i];
			else printf("D"),y+=arm[i];
		} else {
			if(x>0)
				printf("R"),x-=arm[i];
			else printf("L"),x+=arm[i];
		}
	}
}
int main() {
	scanf("%d",&n);
	for(int i=1;i<=n;i++) {
		scanf("%d %d",&x[i],&y[i]);
		odd[Abs(x[i]+y[i])%2]=true;
	}
	if(odd[0]&&odd[1]) {
		printf("-1");
		return 0;
	}
	/******************/
	m=32;arm[31]=arm[32]=1;
	if(odd[1]) m--;
	for(int i=30;i>=1;i--)
		arm[i]=2*arm[i+1];
	printf("%d\n",m);
	for(int i=1;i<m;i++)
		printf("%d ",arm[i]);
	printf("%d\n",arm[m]);
	/******************/
	for(int i=1;i<=n;i++)
		Print(x[i],y[i]),puts("");
	return 0;
}