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>
#include<cstring>
#include<algorithm>
#include<cmath>
#define MN 1005
using namespace std;
int n,cnt;
struct node{int x,y;}a[MN];
void solve(int x,int y){
	for(int i=30;i>=0;i--){
		if(abs(x)>=(1<<i)){
			if(x<=0)x+=(1<<i),putchar('L');
			else x-=(1<<i),putchar('R');
		}else if(abs(y)>=(1<<i)){
			if(y<=0)y+=(1<<i),putchar('D');
			else y-=(1<<i),putchar('U');
		}else if(abs(x)>abs(y)){
			if(x<=0)x+=(1<<i),putchar('L');
			else x-=(1<<i),putchar('R');
		}else {
			if(y<=0)y+=(1<<i),putchar('D');
			else y-=(1<<i),putchar('U');
		}
	}//puts("");
	if(x!=0||y!=0){
		if(x!=0){
			if(x<0)putchar('R');
			else putchar('L');
		}else {
			if(y<0)putchar('D');
			else putchar('U');
		}
	}
}
int main(){
//	freopen("test.out","w",stdout);
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%d%d",&a[i].x,&a[i].y);int ty=(a[1].x+a[1].y)&1;
	for(int i=2;i<=n;i++)if(((a[i].x+a[i].y)&1)!=ty)return 0*puts("-1");
	cnt=32-ty;printf("%d\n",cnt);int tt=0;
	for(int i=30;i>=0;i--)printf("%d ",(1<<i));if(!ty)puts("1");else puts("");
	for(int i=1;i<=n;i++){
		solve(a[i].x,a[i].y);puts("");
	//	if(!ty)puts("D");else puts("");
	}
}