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;

int n;
long long x[1010], y[1010], v[1010], w[1010];
vector<long long> d;
int M = 31;

int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);
	cin >> n;
	int c = 0;
	for(int i=0; i<n; ++i){
		cin >> x[i] >> y[i];
		v[i] = x[i] + y[i];
		w[i] = x[i] - y[i];
		c += ((v[i] % 2) + 2) % 2;
	}
	if(c != 0 && c != n){
		cout << -1 << "\n";
		return 0;
	}
	if(c == 0){
		d.push_back(1);
	}
	for(int i=0; i<M; ++i)
		d.push_back((long long)1 << i);
	cout << d.size() << "\n";
	for(int i=0; i<d.size(); ++i)
		cout << d[i] << " \n"[i+1==d.size()];
	for(int i=0; i<n; ++i){
		if(c == 0){
			cout << 'R';
			--v[i]; --w[i];
		}
		long long a = -((long long)1<<M)+1;
		for(int j=0; j<M; ++j){
			// v\w + -
			//  +  R U
			//  -  D L
			int t = 0;
			if((((v[i] - a) / 2) >> j) % 2 == 1) t += 2;
			if((((w[i] - a) / 2) >> j) % 2 == 1) t += 1;
			cout << "LDUR"[t];
		}
		cout << "\n";
	}
}