Problem:
Score : 600 points

Problem Statement

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

Partial Score

In the test cases worth 300 points, -10 \leq X_i \leq 10 and -10 \leq Y_i \leq 10 hold.

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.

Sample Input 1

3
-1 0
0 3
2 -1

Sample Output 1

2
1 2
RL
UU
DR

In the given way to bring Joint m of the robot arm to each (X_j, Y_j), the positions of the joints will be as follows:

To (X_1, Y_1) = (-1, 0): First, the position of Joint 0 is (x_0, y_0) = (0, 0). As the mode of Section 1 is R, the position of Joint 1 is (x_1, y_1) = (1, 0). Then, as the mode of Section 2 is L, the position of Joint 2 is (x_2, y_2) = (-1, 0).

To (X_2, Y_2) = (0, 3): (x_0, y_0) = (0, 0), (x_1, y_1) = (0, 1), (x_2, y_2) = (0, 3).

To (X_3, Y_3) = (2, -1): (x_0, y_0) = (0, 0), (x_1, y_1) = (0, -1), (x_2, y_2) = (2, -1).

Sample Input 2

5
0 0
1 0
2 0
3 0
4 0

Sample Output 2

-1

Sample Input 3

2
1 1
1 1

Sample Output 3

2
1 1
RU
UR

There may be duplicated points among (X_j, Y_j).

Sample Input 4

3
-7 -3
7 3
-3 -7

Sample Output 4

5
3 1 4 1 5
LRDUL
RDULR
DULRD

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#define _CRT_SECURE_NO_WARNINGS
#define _USE_MATH_DEFINES
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <cstdlib>
#include <algorithm>
#include <string>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <unordered_map>
#include <functional>
#include <utility>
#include <tuple>
#include <cctype>
#include <bitset>
#include <complex>
#include <cmath>
#include <array>
using namespace std;
#define INF 0x3f3f3f3f
#define INFLL 0x3f3f3f3f3f3f3f3fLL
#define MOD 1000000007
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define eb emplace_back
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int, int> pint;
typedef pair<ll,ll> pll;
typedef tuple<int,int,int> tint;
typedef vector<int> vint;
typedef vector<ll> vll;
typedef vector<ull> vull;
typedef vector<pint> vpint;
int dx[8]={0,0,-1,1,1,1,-1,-1};
int dy[8]={-1,1,0,0,1,-1,1,-1};
const int SIZE=100050;
//ここまでテンプレ
int main(){
	int N;
	cin>>N;
	vint X,Y;
	for(int i=0;i<N;i++){
		int x,y;
		cin>>x>>y;
		X.pb(x);
		Y.pb(y);
	}
	//x+yが全部同じじゃないなら無理
	bool flag=abs(X[0]+Y[0])%2;
	for(int i=0;i<N;i++){
		if(abs(X[i]+Y[i])%2!=flag){
			cout<<-1<<endl;
			return 0;
		}
	}
	//V=X+Y,W=X-Y
	vint V,W;
	for(int i=0;i<N;i++){
		V.pb(X[i]+Y[i]);
		W.pb(X[i]-Y[i]);
	}
	int arms=31;
	vint A={1};
	if(!flag)
		A.pb(1);
	for(int i=1;i<arms;i++)
		A.pb(A.back()*2);
	reverse(A.begin(),A.end());
	cout<<A.size()<<endl;
	for(int i=0;i<A.size();i++)
		cout<<A[i]<<(i==A.size()-1?'\n':' ');
	for(int i=0;i<N;i++){
		int v=0,w=0;
		for(int j=0;j<A.size();j++){
			if(v<=V[i] && w<=W[i]){
				cout<<'R';
				v+=A[j],w+=A[j];
			}
			else if(v<=V[i] && w>W[i]){
				cout<<'U';
				v+=A[j],w-=A[j];
			}
			else if(v>V[i] && w<=W[i]){
				cout<<'D';
				v-=A[j],w+=A[j];
			}
			else{
				cout<<'L';
				v-=A[j],w-=A[j];
			}
		}
		cout<<endl;
	}
	return 0;
}