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;

#define INF (1 << 29)
#define MAX_N 1000

int x[MAX_N];
int y[MAX_N];
int p;
int v[40];

int main()
{
	int n;

	cin >> n;
	for( int i = 0; i < n; i++ ) {
		cin >> x[i] >> y[i];
		int pp = abs(x[i] + y[i]) % 2;
		if( i == 0 ) {
			p = pp;
		}
		if( pp != p ) {
			cout << -1 << endl;
			return 0;
		}
	}

	int m = 31;
	for( int i = 0; i < m; i++ ){
		v[i] = 1 << (m - i - 1);
	}
	if( p == 0 ) {
		v[m] = 1;
		m++;
	}
	

	cout << m << endl;
	for( int i = 0; i < m; i++ ) {
		cout << v[i];
		if( i < m - 1 ) {
			cout << " ";
		}
	}
	cout << endl;

	for( int i = 0; i < n; i++ ) {
		int xx = x[i];
		int yy = y[i];
		for( int j = 0; j < m; j++ ) {
			if( abs(xx) >= abs(yy) ) {
				if( xx >= 0 ) {
					cout << "R";
					xx -= v[j];
				}
				else {
					cout << "L";
					xx += v[j];
				}
			}
			else {
				if( yy >= 0 ) {
					cout << "U";
					yy -= v[j];
				}
				else {
					cout << "D";
					yy += v[j];
				}
			}
		}
		cout << endl;
	}

	return 0;
}