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>
using namespace std;

typedef long long ll;

int main(){
	int N;
	cin >> N;
	ll X[N], Y[N];
	for(int i=0; i<N; i++){
		cin >> X[i] >> Y[i];
		if(i>0 && (abs((X[i]+Y[i])%2) != abs((X[i-1]+Y[i-1])%2))){
			cout << -1 << endl;
			return 0;
		}
	}
	if((X[0]+Y[0])%2 == 0){
		cout << 32 << endl;
		ll d[32];
		d[0] = 1;
		d[1] = 1;
		for(int i=2; i<32; i++){
			d[i] = d[i-1]*2;
		}
		for(int i=31; i>=0; i--){
			cout << d[i] << " ";
		}
		cout << endl;
		for(int i=0; i<N; i++){
			X[i] = X[i] + 1;
			Y[i] = Y[i];
			for(int j=31; j>0; j--){
				if((abs(X[i]-d[j])+abs(Y[i])) <= d[j]-1){
					X[i] = X[i] - d[j];
					cout << "R";
				}else if((abs(X[i]+d[j])+abs(Y[i])) <= d[j]-1){
					X[i] = X[i] + d[j];
					cout << "L";
				}else if((abs(X[i])+abs(Y[i]-d[j])) <= d[j]-1){
					Y[i] = Y[i] - d[j];
					cout << "U";
				}else{
					Y[i] = Y[i] + d[j];
					cout << "D";
				}
			}
			cout << "L" << endl;
		}
	}else{
		cout << 31 << endl;
		ll dd[31];
		dd[0] = 1;
		for(int i=1; i<31; i++){
			dd[i] = dd[i-1]*2;
		}
		for(int i=30; i>=0; i--){
			cout << dd[i] << " ";
		}
		cout << endl;
		for(int i=0; i<N; i++){
			for(int j=30; j>=0; j--){
				if((abs(X[i]-dd[j])+abs(Y[i])) <= dd[j]-1){
					X[i] = X[i] - dd[j];
					cout << "R";
				}else if((abs(X[i]+dd[j])+abs(Y[i])) <= dd[j]-1){
					X[i] = X[i] + dd[j];
					cout << "L";
				}else if((abs(X[i])+abs(Y[i]-dd[j])) <= dd[j]-1){
					Y[i] = Y[i] - dd[j];
					cout << "U";
				}else{
					Y[i] = Y[i] + dd[j];
					cout << "D";
				}
			}
			cout << endl;
		}
	}
	return 0;
}