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 <iostream>
#include <iomanip>
#include <vector>
#include <set>
#include <string>
#include <queue>
#include <algorithm>
#include <map>
#include <cmath>
#include <numeric>
#include <list>
#include <stack>
#include <cstdio>
#include <cstdlib>
#include <cstring>

#define rep(i, n) for (int i = 0; i < n; i++)
#define rep1(i, n) for (int i = 1; i <= n; i++)
#define show(a, n) rep(i,n) {cout<<a[i]<<' ';} cout<<endl;

using namespace std;
typedef vector<int> vi;
typedef pair<int, int> pii;
typedef long long ll;
typedef pair<long long, long long> pll;

const int INF = 1 << 30;
const long long INFL = 1LL << 62;
const int MOD = 1000000007;
const int MAX = 100000;
const int N = 1000;

int main() {
	int n;cin>>n;
	int x[N],y[N];
	rep(i,n) {cin>>x[i]>>y[i];}
	bool odd;
	if(abs(x[0]+y[0])%2==1) odd=true;
	else odd=false;
	rep(i,n) if((abs(x[i]+y[i])%2==1)!=odd) {cout<<-1<<endl;return 0;}
	int d[40],m=31;
	for(int i=0;i<=30;i++) d[i]=1<<(30-i);
	if(!odd) {m++;d[31]=1;}
	string w[N];
	rep(i,n){
		for(int j=0;j<m;j++){
			if(y[i]>=-x[i]&&y[i]<x[i]) {w[i]+='R';x[i]-=d[j];}
			else if(y[i]>=x[i]&&y[i]>-x[i]) {w[i]+='U';y[i]-=d[j];}
			else if(y[i]<=-x[i]&&y[i]>x[i]) {w[i]+='L';x[i]+=d[j];}
			else {w[i]+='D';y[i]+=d[j];}
		}
	}
	cout<<m<<endl;
	rep(i,m-1) cout<<d[i]<<' ';
	cout<<d[m-1]<<endl;
	rep(i,n) cout<<w[i]<<endl;
}