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 maxn 1003
#define INF 100000000000000000ll
using namespace std;
long long x[maxn],y[maxn],p[36];
int n,cnt,dx[4]={1,0,-1,0},dy[4]={0,1,0,-1};
char s[4]={'R','U','L','D'};
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%lld%lld",x+i,y+i);
	for(int i=2;i<=n;i++)if(((x[i-1]+y[i-1]+INF)&1)^((x[i]+y[i]+INF)&1)){puts("-1");return 0;}
	cnt=((x[1]+y[1]+INF)&1?34:35);
	for(int i=33;i>=0;i--)p[34-i]=(1ll<<i);
	if(cnt==35)p[cnt]=1;
	printf("%d\n",cnt);
	for(int i=1;i<=cnt;i++)printf("%lld ",p[i]);puts("");
	for(int j=1;j<=n;j++){
		long long X=0,Y=0,mi,tmp;
		int mii;
		for(int step=1;step<=cnt;step++){
			mi=INF;
			for(int i=0;i<4;i++){
				tmp=abs(X+p[step]*dx[i]-x[j])+abs(Y+p[step]*dy[i]-y[j]);
				if(tmp<mi)mi=tmp,mii=i;
			}
			X+=p[step]*dx[mii],Y+=p[step]*dy[mii];
			putchar(s[mii]);
		}
		puts("");
	}
	return 0;
}