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;
char dir(int a, int b){
	if(a == 0 && b == 0) return 'U'; 
	else if(a == 0 && b == 1) return 'R'; 
	else if(a == 1 && b == 0) return 'L'; 
	else if(a == 1 && b == 1) return 'D'; 
}
int main() {
	int N; 
	cin >> N; 
	long long int X[1010] = {}, Y[1010] = {}, Z[1010] = {}; 
	for(int i = 0; i < N; i++){
		cin >> X[i] >> Y[i]; 
		Z[i] = (abs(X[i]) + abs(Y[i])) % 2; 
	}
	bool possible = true; 
	for(int i = 0; i < N; i++){
		if(Z[i] != Z[0]){
		possible = false;
		break; 
        	}
	}
	if(!possible){
		cout << -1 << endl; 
	}
	else if(Z[0] == 1){
		cout << 31 << endl; 
		for(int i = 0; i <= 30; i++){
			cout << (1 << i) << " "; 
		}
		cout << endl; 
		for(int i = 0; i < N; i++){
          		long long int a = (2147483647 - Y[i] - X[i])/2; 
			long long int b = (2147483647 - Y[i] + X[i])/2; 
			for(int j = 0; j < 31; j++){
				cout << dir((int) a % 2, (int) b % 2); 
				a = (a >> 1), b = (b >> 1);
			}
		cout << endl; 
		}
	}
	else if(Z[0] == 0){
		cout << 32 << endl; 
		cout << 1 << " "; 
		for(int i = 0; i <= 30; i++){
			cout << (1 << i) << " "; 
		}
		cout << endl; 
		for(int i = 0; i < N; i++){
			cout << 'L'; 
          		long long int a = (2147483647 - Y[i] - X[i] - 1)/2; 
			long long int b = (2147483647 - Y[i] + X[i] + 1)/2; 
			for(int j = 0; j < 31; j++){
				cout << dir((int) a % 2, (int) b % 2); 
				a = (a >> 1), b = (b >> 1);
			}
		cout << endl; 
		}
	}
}