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>
#define int long long
using namespace std;
int x[50005],y[50005],mp[50005],tot=31;
int xx[4]={0,0,1,-1};
int yy[4]={1,-1,0,0};
char s[4]={'U','D','R','L'};
void work(int x,int y)
{
	for(int i=1;i<=tot;i++)
	{
		int minn=1e18,mn;
		for(int j=0;j<4;j++)
		{
			int sum=abs(x-xx[j]*mp[i])+abs(y-yy[j]*mp[i]);
			if(sum<minn) minn=sum,mn=j;
		}
		x-=xx[mn]*mp[i],y-=yy[mn]*mp[i];
		printf("%c",s[mn]);
	}
	printf("\n");
}
signed main()
{
	int n;
	scanf("%lld",&n);
	for(int i=1;i<=n;i++) scanf("%lld%lld",x+i,y+i);
	for(int i=1;i<=n;i++) if(((x[i]+y[i])&1!=((x[i-1]+y[i-1])&1))&&i!=1){printf("-1\n");return 0;}
	for(int i=1;i<=31;i++) mp[i]=1<<(31-i);
	if(((x[1]+y[1])&1)==0) mp[++tot]=1;
	printf("%lld\n",tot);
	for(int i=1;i<=tot;i++) printf("%lld ",mp[i]);printf("\n");
	for(int i=1;i<=n;i++) work(x[i],y[i]);
	return 0;
}